Math Homework Questions & Answers Archive

Partie I Pour tout entier naturel non nul n, on considère la fonction fₙ définie sur I = [0, +∞[ par : fₙ(0) = 0 et (∀ x ∈ ]0, +∞[) ; fₙ(x) = √x(ln x)ⁿ et soit (Cₙ) sa courbe représentative dans un repère orthonormé (O ; i, j) 1-a) Vérifier que : (∀ x ∈ ]0, +∞[) ; √x(ln x)ⁿ = (2n)ⁿ(x^(1 / 2n) ln(x^(1 / 2n)))ⁿ, en déduire que fₙ est continue à droite en 0 b) Calculer lim x → +∞ fₙ(x) c) Vérifier que : (∀ x ∈ ]0, +∞[) ; fₙ(x) / x = (2n)ⁿ(ln(x^(1 / 2n)) / x^(1 / 2n))ⁿ, en déduire lim x → +∞ (fₙ(x) / x) puis interpréter graphiquement le résultat obtenu d) Calculer, suivant la parité de n, lim x → 0⁺ (fₙ(x) / x) puis interpréter graphiquement le résultat obtenu 2-a) Montrer que fₙ est dérivable sur ]0, +∞[ et que : (∀ x ∈ ]0, +∞[) ; fₙ'(x) = 1 / (2√x)(ln x)ⁿ⁻¹(2n + ln x) b) Vérifier que : ∀ n ≥ 2, fₙ'(x) = 0 si et seulement si (x = 1 ou x = e⁻²ⁿ) c) Étudier, suivant la parité de n, le sens de variation de fₙ et donner son tableau de variations d) Montrer que si n est impair et n ≥ 3 alors le point d'abscisse 1 est un point d'inflexion de (Cₙ) Partie II : 1- Soit β ∈ ]1, e[ un réel fixé. On considère la suite numérique (uₙ)ₙ ≥ 1 définie par : (∀ n ∈ ℕ*) ; uₙ = fₙ(β) a) Montrer que : (∀ n ∈ ℕ*) ; 0 < uₙ < √e b) Montrer que la suite (uₙ)ₙ ≥ 1 est décroissante c) Déterminer lim n → +∞ uₙ 2-a) Montrer que pour tout entier n non nul, il existe un unique réel xₙ ∈ ]1, e[ tel que : f(xₙ) = 1

APLICACION - Resolución de los siguientes problemas a) Sean los vectores en R3: a = (3, -2, 5), b = (-1, 4, 2) 1. Calcula a + b 2. Calcula a - b b) Sean los vectores: u = (1, 2, -1), v = (-3, 0, 4) 1. Calcula u ⋅ v 2. Encuentre 2(v)

Simplify if AᵀA + BᵀB - 2AᵀB = 0 (4(m-1)/(nm))BᵀSB + (4(n-1)/(nm))AᵀYA - (4/n)AᵀSB - (4/m)BᵀYA + (4(n-2)/(n(n-1)))AᵀSA + (4(m-2)/(m(m-1)))BᵀYB

Gegeben ist die Funktion f: R → R, f(x) = √x. Bestimmen Sie den Definitionsbereich der Funktion f.

Determine which numbers in the set -7, -6, -5, -4, -3, -2 are solutions of the inequality. x + 8 ≤ 3 The solutions are . (Use a comma to separate answers as needed.)

Four distributions, labeled (a), (b), (c), and (d) are represented below by their histograms. Each distribution is made of 9 measurements. Without performing any calculations, order their respective means μa, μb, μc, and μd. Enter the four subscripts appropriately below.

4. La suma de dos números es 1894. Si dividimos la suma de ellos entre su diferencia obtenemos 11 de cociente y 156 de residuo. Hallar el mayor número. A. 1024 B. 1026 C. 1090 D. 1310 E. 1100

1.1 - A partir de la definición 1 in = 2.54 cm, determine a) cuántos kilómetros hay en 1.00 milla y b) cuántos pies hay en 1.00 km. 1.2 • Según la etiqueta de un frasco de aderezo para ensalada, el volumen del contenido es 0.473 litros (L). Use solo las conversiones 1 L = 1000 cm³ y 1 in = 2.54 cm para expresar dicho volumen en pulgadas cúbicas. 1.3 • ¿Cuántos nanosegundos tarda la luz en viajar 1.00 ft en el vacío? (Este resultado es una cantidad útil de recordar). 1.4 • La densidad del oro es de 19.3 g/cm³. ¿Cuál es su equivalencia en kilogramos por metro cúbico? 1.5 - El motor más potente que había para el automóvil clásico Chevrolet Corvette Sting Ray modelo 1963 desarrollaba 360 caballos de fuerza y tenía un desplazamiento de 327 pulgadas cúbicas. Exprese este desplazamiento en litros (L) usando solo las conversiones 1 L = 1000 cm³ y 1 in = 2.54 cm. 1.6 - Un campo cuadrado que mide 100.0 m por 100.0 m tiene un área de 1.00 hectárea. Un acre tiene un área de 43,600 ft². Si un campo tiene un área de 12.0 acres, ¿cuál es su equivalencia en hectáreas? 1.7 - ¿Cuántos años más tendrá usted dentro de 1.00 mil millones de segundos? (Suponga que un año tiene 365 días). 1.8 - Mientras va conduciendo en un país extranjero, observa un letrero que indica el límite de velocidad en una carretera como 180,000 estadios (furlongs) por quincena. ¿Cuánto es esto en millas por hora? (Un furlong es 1/8 de milla, y una quincena equivale a 14 días. Originalmente, el estadio se refería a la longitud de un surco arado). 1.9 - Cierto automóvil híbrido que consume poco combustible tiene un rendimiento de gasolina de 55.0 mpg (millas por galón). a) Si usted va manejando dicho auto en Europa y quiere comparar su rendimiento con el de otros autos europeos, exprese tal rendimiento en km/L (L = litro). Utilice los factores de conversión del apéndice E. b) Si el depósito de gasolina de este automóvil tiene una capacidad de 45 L, ¿cuántas veces deberá llenar el depósito de gasolina para conducir 1500 km? 1.10 - Las conversiones que siguen son comunes en física, además de muy útiles. a) Use 1 mi = 5280 ft y 1 h = 3600 s para convertir 60 mph a unidades de ft/s. b) La aceleración de un objeto en caída libre es de 32 ft/s². Use 1 ft = 30.48 cm para expresar esta aceleración en unidades de m/s². c) La densidad del agua es de 1.0 g/cm³. Convierta esta densidad a unidades de kg/m³. 1.11 - Neptunio. En el otoño de 2002, un grupo de científicos de Los Alamos National Laboratory determinó que la masa crítica del neptunio 237 es de unos 60 kg. La masa crítica de un material fisionable es la cantidad mínima que debe reunirse para iniciar una reacción en cadena. Este elemento tiene una densidad de 19.5 g/cm³. ¿Cuál será el radio de una esfera de este material que tiene dicha masa crítica? 1.12 - BIO a) La dosis diaria recomendada (RDA, por las siglas de recommended daily allowance) del metal traza magnesio es de 410 mg/día para los hombres. Exprese esta cantidad en μg/día. b) La RDA del aminoácido lisina es de 12 mg por kg de peso corporal. ¿Cuántos gramos diarios debe recibir un adulto de 75 kg de peso? c) Una tableta multivitamínica típica contiene 2.0 mg de vitamina B₂ (riboflavina) y la RDA recomendada es de 0.0030 g/día. ¿Cuántas de estas tabletas debe tomar a diario una persona para obtener la cantidad adecuada de esta vitamina, suponiendo que no tiene ninguna otra fuente de abasto? d) La RDA para el elemento traza selenio es de 0.000070 g/día. Exprese esta dosis en mg/día.

In the figure, ABCDEFGH is a regular octagon and DEIJK is a regular pentagon. Find x.

3 2x^2 / (3x^2 - 4x)

10 1/2 ÷ 9 2/6 =

Given the function f(x) = (3/20)x^5 + 2x^4 + 8x^3, find all intervals on which f is concave down.

Determine the terms and degree of the polynomial. -7x⁴ + 2x³ - 5x² + x + 12 (A) Terms: 7x⁴, 2x³, 5x², x, -12; degree: 10 (B) Terms: -7x⁴, 2x³, -5x², x, 12; degree: 10 (C) Terms: 7x⁴, 2x³, 5x², x, -12; degree: 4 (D) Terms: -7x⁴, 2x³, -5x², x, 12; degree: 4

a) f(x)=k x, si k=0,1,2, 1/2,-1,-2

1) Write an equation to represent the relationship of x and y. A) y = -2x B) y = 2x C) y = -2x + 1 D) y = 2x + 1

Evaluate the following expressions by two methods. (i) Use Theorem 5.1. (ii) Use a calculator. a. ∑ from k=1 to 45 of k b. ∑ from k=1 to 45 of (5k - 1) c. ∑ from k=1 to 75 of 2k² d. ∑ from n=1 to 50 of (1 + n²) e. ∑ from m=1 to 75 of (2m + 2)/3 f. ∑ from j=1 to 20 of (3j - 4) g. ∑ from p=1 to 35 of (2p + p²) h. ∑ from n=0 to 40 of (n² + 3n - 1)

Calcula "x" si L₁ // L₂.

For the following data set: (a) Compute the least-squares regression line. Round the answers to at least four decimal places. Regression line equation: (b) Which point is an outlier?

Write each complex number in the form a + b i. Round approximate answers to the nearest tenth. 37. √2(cos 45° + i sin 45°)

Find the value of y. 384 = 6 × 4^y (2 marks) y =

Solve the equation. 4(x+6) = 3(x-8) + x

Find the value of x, y, and z in the parallelogram below.

QUESTION 3 3.1 The first two terms of an infinite geometric sequence are 8 and 8/√2. Prove, without the use of a calculator, that the sum of the series to infinity is 16 + 8√2. 3.2 The following geometric series is given: x = 5 + 15 + 45 + ... to 20 terms. 3.2.1 Write the series in sigma notation. 3.2.2 Calculate the value of x.

Find the length of ×

Data la semicirconferenza di diametro AB uguale 2r costruiamo il triangolo equilatero ABC. Siano D ed E le intersezioni rispettivamente di BC e CA con la semicirconferenza. Sull'arco BD determiniamo un punto F in modo che sia FB² + FD² = (4 - 2√3)r²

Find the eigenvalues and eigenvectors of the matrix A = [1 0; 1 2].

Simplify answers and show your work. 2) (4 points) Write an equation for the function graphed.

19. ∑ from n=1 to ∞ of (4^(n+1) / (3^n - 2))

Solve the problem. f(x) = √(x + 3) a. Graph f(x) b. Write an equation for f⁻¹(x) c. Write the domain of f⁻¹ in interval notation

1.3 Given: P = (1 - a) and T = (1 + a)(1 + a²)(1 + a⁴)...(1 + a⁵¹²) Determine the value of P × T in terms of a.

Select two points to draw two rays to form an angle measuring 80 degrees. For each blank, fill in the bubble before the point that is correct. Draw a ray from point A to point [(A) T (B) U]. Draw a second ray from point A to point [(A) W (B) X (C) Y (D) Z].

12 In trapezium ABCD, ABD and ACD are right-angled triangles. a) Find the area of triangle ABD. b) Hence find the height of the trapezium. c) Find the area of the trapezium. d) Find the area of triangle ABC. e) Show that triangle AED is 108 m² larger than triangle BEC.

A septic tank has the shape shown to the right. How many gallons does it hold? (1 ft³ ≈ 7.48 gallons) The tank holds gal. (Round to the nearest gallon as needed.)

Find the total outside surface area and the volume of the solid.

Classify the conic section defined by each equation. Then write its standard equation. x² + 6x - 8y + 9 = 0 4x² - 9y² + 8x + 36y - 68 = 0 4x² + 16y² - 8x + 64y = 28 y² - 3y - 4x + 3 = 0 3x² + 5y² + 18x - 20y + 2 = 0 4y² - 36x² - 72x + 8y = 176

Joe and Jeetesh are buying a present for their friend which costs £20. Their contributions will be in the ratio of 1:3. How much will Jeetesh contribute? £ ☐

The probability that a complex assembly line works correctly depends on whether the line worked correctly the last time it was used. There is a 0.6 chance that the line will work correctly if it worked correctly the time before, and a 0.2 chance that it will work correctly if it did not work correctly the time before. Set up a transition matrix with this information and find the long-range probability that the line will work correctly. Let the first state be the assembly line working correctly, and the second be that the assembly line does not work correctly. The transition matrix is P = . (Type an integer or decimal for each matrix element.) The long-range probability that the line will work correctly is . (Type an integer or a simplified fraction.)

Find the total outside surface area and volume of the solid object. Assume that the base is regular. The total outside surface area is m². (Round to three significant digits.) The volume is m³. (Round to three significant digits.)

1. Use the given vectors to sketch the following: a. a + b b. a - b c. 3a - 2b

1. Three pipes can fill a pool in twelve hours. A drain can empty the full pool in eighteen hours. How many hours will it take to fill a quarter of the pool if the three pipes and the drain are open? A) 9 B) 15/2 C) 1/9 D) 1/6

Maximizing the Viewing Angle A billboard that is 30 ft wide is placed 60 ft from a highway as shown in the figure. The billboard is easiest to read from the highway when the viewing angle α is larger than 7°. a) Show that α = tan⁻¹(90 / x) - tan⁻¹(60 / x). b) Graph the function in part (a). c) For what approximate values of x is α greater than 7°? d) For approximately how long does a motorist traveling at 35 mph have a viewing angle larger than 7°?

For the given functions, find (f ∘ g)(x) and (g ∘ f)(x) and the domain of each. f(x) = 3 / (1 - 7x), g(x) = 1 / x

How many milliliters of Mylanta suspension will the patient receive per day if the compounded product is taken as directed? (Answer must be numeric; round the final answer to the nearest WHOLE number.)

BASIC ELECTRICITY INDUCTOR WORKSHEET #3

Solve the system: [x', y'] = (1/t) * [[5, 1], [3, 3]] * [x, y] + [5, 5] with x(1) = [0, 2], X(t) = [[t^2, t^6], [-3t^2, t^6]]

b) 1000 ÷ -500(-2)^2 + 2(100-100)^0(-1)^3 + 1/2 - 2/3

A wire of length 100 cm is to be cut into two pieces. One piece is bent into a square, and the other is bent into a circle. (a) (2 points) How should the wire be cut to maximize the total area of the square and circle? (b) (2 points) How should the wire be cut to minimize the total area?

Mean: Median: Mode: Range: Coefficient of Variation: Interpretation: Standard Deviation work: Interpretation:

Topic 9: Graphing Polynomial Functions Solve the problem. f(x) = √(x + 3) a. Graph f(x) b. Write an equation for f⁻¹(x) c. Write the domain of f⁻¹ in interval notation

Знайдіть значення виразу y^(-8):(y^3)^(-2), якщо y=-2.

Write short answers. Consider the inverse tangent function, defined by y = tan⁻¹(x), or y = arctan(x). Complete parts (a)-(d). (a) What is its domain? (b) What is its range?

2. The amount of water consumed each week by Montana residences is normally distributed. A simple random sample of 10 residences was taken with a sample mean of 120.3 gallons and a standard deviation of 10.0 gallons. Test the claim at the 0.10 SL that the average amount of water consumed is not 125 gallons.

In Exercises 1-4, do the following tasks: (a) Sketch the graph y = f(x). (b) Find approximate values Ln for the length of the given graph using approximations of the graph by polygonal paths with n line segments for n = 2, 4, ..., 20 as in Classroom Discussion 7.1.3. Tabulate your results. (c) What is the value in your table that best approximates the length L? Explain. (d) Use integral calculus to compute the length L of the given graph. You may use your calculator to compute the definite integral corresponding to the length L, but you must first evaluate the integrand by hand. 1. f(x) = x³, 0 ≤ x ≤ 1 2. f(x) = 1/x, 1 ≤ x ≤ 3

Question 2: Round to the nearest tenth.

6. How many miles does the student drive in one week? Assume the student drives to campus and then back home each day they attend class. Round answer to the nearest tenth, if necessary. 7. The semester at RCCC is 16 weeks long. Using your answer from #6, how many total miles will the student drive in one semester? Again, assume the student drives to campus and then back home each day they attend class. Round answer to the nearest tenth, if necessary. 8. The student’s car gets 26.3 miles per gallon. Using your answer from #7, how many gallons of gas will this student use driving to and from campus for the entire semester? Round to the nearest tenth, if necessary.

Step 1: ABCD is a parallelogram Step 2: ∠CDA ≅ ∠BAD, ∠CAD ≅ ∠BDA Step 3: Reflexive Property Step 4: △CIDA ≅ △BAD

Solve the equation accurate to three decimal places. 3(8^(x-4)) = 38 Solve the equation accurate to three decimal places. (1 + 0.90/365)^(365t) = 2 Find the derivative of the function. y = 2^(-3x)

Consider the function: f(x) = (9x² + 25) / x Step 1. Find all critical points of the function. Separate multiple answers with cor

Find the absolute maximum and minimum values of the function f(x) = 5/(x-4) + 9 ln(x-4) on the interval [18/3, 7].

Find the resistance in a circuit where the voltage is 4+2i volts and the current is -4i amperes. The resistance R in an electrical circuit is given by the formula R=V/I, where V is the voltage, measured in volts, and I is the current in amperes. The resistance in the circuit is R= ohms. (Type your answer in the form a+bi. Use integers or fractions for any numbers in the expression.)

Find the particular solution of the following differential equation, given that the curve passes through the point (3,2). Give your answer in its simplest form: 12/x dy/dx = 6/y

1. Unfortunately a rookie error was made and a horizontal distance was observed that had not been corrected for atmospheric effects (ppm), prism/instrument index constant (mm) and instrument scale factor (ppm). Calculate what the distance would have been if all corrections were applied using the data below. (20 mks) Measured horizontal distance: 360.104 m Scale factor ppm correction: -5 ppm Atmospheric correction: 20 ppm Prism constant: -35 mm

Identify the prefix used for disaccharides: Each of the reactants in reaction A is a single sugar molecule, also called a monosaccharide. What prefix before saccharide would you use to describe sucrose?

Single Sample T-Test: A researcher would like to study the effect of alcohol on reaction time. It is known that under regular circumstances the distribution of reaction times is normal with μ = 195. A sample of 15 subjects is obtained. Reaction time is measured for each individual after consumption of alcohol. Their reaction times were: 210, 216, 211, 240, 217, 219, 221, 222, 222, 227, 228, 223, 230, 228, and 232. Use α = 0.05. Independent Sample T-Test: A researcher is interested in the anxiety levels of individuals who get in-home counseling vs those who get out-of-home counseling. The researcher measures participant anxiety scores by using questionnaire measured on a scale from 1-10. The researcher manages to gather a sample of 40 participants. Use α = 0.05 In-Home Out-of-Home 1 8 5 6 1 7 3 7 4 7 3 5 3 5 1 4 4 6 6 5 5 2 1 4 4 3 4 6 3 7 6 5 7 4 7 3 7 8 8 7

Let b be any whole number from 1 through 9. Describe a strategy for adding each pair of numbers. (a) 9+b (b) b+10 (c) I b+b

Find the product. (x+5)(x^2+3x+9) (x+5)(x^2+3x+9)= (Simplify your answer.)

In a survey of women in the United States (ages 20-29), the mean height was 64.1 inches with a population standard deviation of 2.71 inches. Women's heights are normally distributed. a) What height represents the 95th percentile? b) What height represents the first quartile?

f(x)=4/(x^3-x)

Ten randomly selected cars were filled with either regular or premium gas (the decision was made based on a coin toss) and then driven on the freeway for the entirety of the tank of gas. The next day, each car was filled with whichever type of gas that was not used the previous day and then driven on the freeway for the entirety of the tank of gas. The mileage for each day was recorded and is summarized in the table below. MPG of 10 cars (regular/premium): 13/19, 20/22, 21/24, 23/25, 22/25, 27/26, 25/26, 27/28, 28/32, 22/24. Car 1 Car 2 Car 3 Car 4 Car 5 Car 6 Car 7 Car 8 Car 9 Car 10 Regular 16 20 21 23 22 27 25 27 28 22 Premium 19 22 24 25 25 26 26 28 32 24 You will be constructing a 90% confidence interval estimate of the difference between the mean efficiency of the car using regular and premium gas. You may assume that both samples are drawn from normally distributed populations. Question 1 Construct the 90% confidence interval estimate mean difference between the mileage from cars using regular and premium gas. Round your answer to 2 decimal places. < difference between the means <

Derive the reduced modulus of elasticity Er for an idealized I-section shown in Fig. P2.12, in which it is assumed that one-half of the cross-section area is concentrated in each flange and the area of the web is disregarded.

The table below shows the fraction of games won (to the nearest thousandth) by six professional teams in the east coast and west coast leagues for the 2016 season. The lists include the teams with the best and worst win-loss records in both leagues. Complete parts (a) through (e) below. East coast teams 0.429 0.466 0.484 0.522 0.584 0.637 West coast teams 0.361 0.414 0.500 0.543 0.582 0.586 The standard deviation for the west coast teams is 0.093. d. Apply the range rule of thumb to estimate the standard deviation of each of the data sets. How well does the rule work in each case? Briefly discuss why it does or does not work well. Using the range rule of thumb the standard deviation for the east coast teams is approximately 0.052. Using the range rule of thumb the standard deviation for the west coast teams is approximately

Find the missing dimension of the regular hexagon shown to the right. Round to three significant digits if necessary. The missing dimension is approximately (1) in.

Find the area of the figure given to the right. Round to three significant digits if necessary.

8. A board that is 22 inches long is cut into two pieces. The longer piece is 4 inches longer than the other piece. How long are the pieces?

Question 8 (Multiple Choice Worth 2 points) (Volume of Rectangular Prisms MC) A coach needs to fill a rectangular container with water to have available for karate practice. If the dimensions of the container are 30 inches by 24 inches by 25.8 inches, what is the maximum amount of water that the rectangular container will hold? 18,576 in^3 9,288 in^3 4,226.4 in^3 2,113.2 in^3

The body temperatures of a group of healthy adults have a bell-shaped distribution with a mean of 98.35°F and a standard deviation of 0.56°F. Using the empirical rule, find each approximate percentage below. a. What is the approximate percentage of healthy adults with body temperatures within 1 standard deviation of the mean, or between 97.79°F and 98.91°F? b. What is the approximate percentage of healthy adults with body temperatures between 97.23°F and 99.47°F?

Find the intervals where f(x) = (log 2 x) / x is increasing and where it is decreasing.

An angle, θ, has a reference angle of π/6 radians, and the angle θ is between π and 3π/2. Determine the exact angle measure of θ in radians.

You were asked to find all absolute extrema for the function (f(x)=4 x^3+30 x^2+48 x) on the interval ([-9,8]). Now that we know that (f'(x)=12 x^2+60 x+48), we can find the critical points. Find the values of where (f'(x)=0) and the values of (x) where (f'(x)) does not exist. Discard any solution that is outside ([-9,8]). Separate multiple answers with a comma where necessary.

A company created a new container in the shape of a triangular prism that will hold sunflower seeds. The container will be made from cardboard. How many square inches of cardboard are needed to make one container? Assume there are no overlapping areas.

Determine two other, different positive angles that are coterminal with the angle ( phi=frac7 pi10 )

Construct a table of values for the function. (Round your answers to three decimal places.) f(x) = 2^(x+1) + 3 x -2 -1 0 1 2 f(x) 3.5 5 Sketch the graph of the function.

1. Given the polynomial function f(x) = x^4 - 5x^3 - 7x^2 + 10x + 14 A. State the coordinates of the x-intercepts. B. State the coordinates of the relative maximums. C. State the coordinates of the relative minimums. D. State the range of the function using interval notation.

Use the graph of y=f(x) to find the limits: Step 1 of 2 : Find lim x→1− f(x).

Simplify. 8 sqrt(45)

81x^3 + 100x = 180x^2

А6 Найдите наименьшее целое отрицательное решение системы неравенств (2x+1)/4-(x-3)/8>-5 4(x+3)-7 >= 5(x-3) А7 Найдите значение выражения ((m/(m-6)-(2m)/(m^2-12m+36)) * (36-m^2)/(m-8)+12m/(m-6) при m=2 А8 Плиточник планирует уложить 168 м^2 плитки. Если он будет укладывать на 2 м^2 в день больше, чем запланировал, то закончит работу на 2 дня раньше. Сколько квадратных метров плитки в день планирует укладывать плиточник?

Sketch the graph of the polynomial function. f(x)=2x^4+3x^3-8x^2+3x Choose the correct graph below. A. B. C. D.

Definizione di funzione pari e dispari - Teorema fondamentale dell'aritmetica - Definizione di logaritmo - Definizione di funzione inversa e significato geometrico (simmetria rispetto alla bisettrice del I e III quadrante) - Definizione di funzioni monotone - Definizione di intorno - Definizione di massimo e minimo assoluto - Definizione di massimo e minimo locale - Definizione di maggiorante e minorante - Definizione di estremo superiore e estremo inferiore - Definizione di successione - Definizione di funzione limitata - Definizione di punto di accumulazione e punto isolato - Definizione di limite - Definizione di limite destro e sinistro - Teorema di unicità del limite - Definizione di successione geometrica - Definizione di successione monotona - Teorema (esistenza del limite per successioni monotone) - Teorema (esistenza del limite per funzioni monotone) - Teorema del prodotto tra una successione limitata e una tendente a 0 - Teorema del confronto - Teorema della permanenza del segno - Definizione di infiniti e infinitesimi - Confronto tra infiniti e infinitesimi - Teorema di cancellazione per infiniti - Teorema di cancellazione per infinitesimi - Definizione di funzione continua - Definizione di funzione continua da destra o da sinistra - Teorema (continua se e solo se continua da destra e da sinistra) - Definizione di funzione discontinua e tipi di discontinuità - Teorema degli zeri - Teorema dei valori intermedi (o di Darboux) - Teorema di Weirstrass - Teorema invertibilità e continuità - Definizione di derivata - Significato geometrico del rapporto incrementale coefficiente angolare della retta secante che passa per A e B - Significato geometrico di derivata coefficiente angolare della retta tangente al grafico - Definizione di derivata destra e sinistra - Punto di cuspide, punto angoloso e punto di flesso - Teorema (se è derivabile in un punto allora è continua in quel punto) + dimostrazione

A silo (base not included) is to be constructed in the form of a cylinder surmounted by a hemisphere. The cost of construction per square unit of surface area is 4 times as great for the hemisphere as it is for the cylindrical sidewall. Determine the dimensions to be used if the volume is fixed and the cost of construction is to be kept to a minimum. Neglect the thickness of the silo and waste in construction. If r is the radius of the hemisphere, h the height of the cylinder, and V the volume, then r= and h= . (Type exact answers, using π as needed.)

A integral [ intQ frac99 x+74 y1+8 x+6 y d x wedge d y ] sobre o quadrilátero Q de vértices [ (0,0) quad(6,-8) quad(-370,495) quad(-364,487) ] é da forma ln (N) para algum inteiro N. Determine N.

In Exercises 1-10, approximate each number using a calculator. 10. e^(-0.75) Round your answer to three decimal places. 1. 2^(3.4) 2. 3^(2.4) 3. 3^(sqrt(5)) 4. 5^(sqrt(3)) 5. 4^(-1.5) 6. 6^(-1.2) 7. e^(2.3) 8. e^(3.4)

Graph the function defined by y=k(x) on an appropriate viewing window. k(x)=9(x-0.5)(x+0.4)(x+0.1)(x-0.2) Please select the graph of k(x).

Question 2: Write a formula for the following polynomial function. You need to show JUSTIFICATION to your answer.

Find the B-matrix for the transformation x ↦ A x, where B=b1, b2. A=[ [ -6 1 ] [ 3 1 ] ], b1=[ [ -1 ] [ -1 ] ], b2=[ [ 1 ] [ 2 ] ] The B-matrix of the given transformation is .

Problem 2 (6 Points) You are given f(x)=(x^10-x-2)/(x+1) and f(x) is defined for all values except x ≠ -1. Using the equation of f(x) and WITHOUT graphing, check whether or not x=-1 is a vertical asymptote or a removable discontinuity. You will need to reference what must be true about f(x) for there to be a removable discontinuity at x=-1 and show all algebraic work!

Question Part 3 of 3 Derivatives (1) Solve the following initial value problem. The second derivative of s with respect to t is equal to -k (k constant), with the first derivative of s with respect to t equal to 66 and s equals 0 when t equals 0. (2) Find the value of t that makes the first derivative of s with respect to t equal to 0. (The answer will involve k.) (3) Find the value of k that makes s equal to 242 for the value of t found in step (2). (1) s equals 66t minus k times t squared over 2 (2) t equals 66 over k, when the first derivative of s with respect to t equals 0 (3) When s equals 242 for the value of t found in step (2), k equals (8712 minus 66 squared) over 484.

Use Cramer's Rule to solve the system: 2x1 + x2 - x3 = 1 3x1 + 2x2 + 2x3 = 13 4x1 - 2x2 + 3x3 = 9

The production function for a print shop is q=2000 * min(L, 3K), where q is the number of sheets printed per hour, L is the number of workers, and K is the number of printers. For example, if L=8 and K=2, then min(L, 3K)=6 and q=12,000. Draw the isoquants for this production function when q=2000, q=6000, and when q=12,000, you should draw three isoquants. Note what are K and L at each vertex.

Calcule as integrais indefinidas: (a) ∫(x+3) dx

Let A=PDP^-1 and P and D as shown below. Compute A^4. P=[ 1 4 2 7 ], D=[ 2 0 0 3 ] A^4= (Simplify your answer.)

Fill in the blanks below to find the products: 10 × 3/4 = 10 × □ ÷ = □ = 10 × 3/4 = 10 ÷ - × = Why are these equivalent?

log7 9 + log7 4

Solve the system of equations using Cramer's Rule 4x + 8y = 20 -4x + 2y = -30

Identify the function whose graph appears above. It is either: f(x) = A tan(x) + k or it is f(x) = A cot(x) + k.

Find the y-intercept of the function 5y-3x=15. (0,-3) (0,3) (3,0) (-3,0)

Rationalize the denominator of the expression. [ fracsqrta+sqrtbsqrta-sqrtb ]

Simplify the expression. [ frac8 a^2-35 a b-25 b^28 a b^2+5 b^3 ]

(a) Lena makes fruit salad using a ratio of 2 blueberries to 10 strawberries. Give the unit rates for this relationship. One unit rate: strawberries for each blueberry Another unit rate: (Choose one) for each (Choose one) (b) How many blueberries are needed if 15 strawberries are used?

A city's population in the year x=1956 was y=3,424,500. In 1977 the population was 3,428,700. Compute the slope of the population growth (or decline) and choose the most accurate statement from the following: The population is increasing at a rate of 100 people per year. The population is decreasing at a rate of 200 people per year. The population is decreasing at a rate of 400 people per year. The population is increasing at a rate of 400 people per year. The population is decreasing at a rate of 100 people per year. The population is increasing at a rate of 200 people per year.

Write the following ratio using two other notations. 4 to 5 Use only the numbers above (not any others).

(2) a=1/(3-2√2) とする。 (1) a の分世を住理化し、筒出にせよ。 (2) a の小改部分を b とするとも、光，bの值を求めよ、また、 a^2-b^2 の慎を求めよ。（3） b を(2)で氷めた値とし、 p は定教とする。 x にいての不等式 p<x<p+4b (1) か (䭃点 25) pの傎の施囲を求めよ。

(-9h^4 + 27h^3) / h^2

Is the point (2,10) a solution of the equation y=2x+1?

Solve the system by substitution. Verify your solution using a graphing calculator. y=4(x-4) y=-3(x+3) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution is (Simplify your answer. Type an ordered pair.) B. The solution set is the infinite set of solutions of the equation y=4(x-4). C. The solution set is the empty set.

Find the values of (x)

Determine the surface area of this composite object, which is a right cylinder and a hemisphere, to the nearest tenth of a square metre. HINT: One end of the cylinder is covered, so should not be included in the final answer.

Una encuesta sobre 520 personas reveló los siguientes datos acerca del consumo de dos productos A y B: 410 personas consumían por lo menos uno de los dos productos. 290 personas consumían A. 75 personas consumían A pero no B. a. ¿Qué porcentaje de personas consumia B? b. ¿Qué porcentaje de personas consumía sólo B? c. ¿Qué porcentaje de personas consumía los dos productos? d. ¿Qué porcentaje de personas no consumía ninguno de los dos productos?

Lesson 6: Connecting Similarity and Transformations Cool Down: Forward and Backwards? Determine if each statement must be true, could possibly be true, or definitely can't be true. Explain or show your reasoning. 1. Congruent figures are similar. 2. Similar figures are congruent.

Solve the following equation: 3.4(s-5)-2.1=8.1 s=

Question 6 Choose the equation representing the graph below. f(x)=1+√x f(x)=√(1-x) f(x)=√(x-1) None of these choices f(x)=-√x+1

Which of the following are irrational numbers? Select all correct answers. Select all that apply: √11 0.1414141414 ... 0.8282282228 ... √18

When the right half of a histogram is a mirror image of the left half, the histogram is (Choose one) . symmetric unimodal skewed right > skewed left

Equations and Inequalities Finding the roots of a quadratic equation of the form ax^2+bx=0 Solve for x. 6 x^2=12 x If there is more than one solution, separate them with commas. If there is no solution, click on "No solution". x=

Which expression is equivalent to sqrt(128 x^5 y^6 / 2 x^7 y^5) ? Assume x>0 and y>0. x sqrt(y) / 8 y sqrt(x) / 8 8 sqrt(x) / y 8 sqrt(y) / x

Find the values of the variables in the equation. [ left[ beginarrayll -9 7 -8 0 endarray right] = left[ beginarrayrr -9 x y z endarray right] ] [ beginarrayl x=7 y=-8 z=0 endarray ]

Completely factor the given polynomial, if possible. If the polynomial cannot be factored, indicate "Not Factorable". cq + cu + qx + ux

Write the given inequality using interval notation, and illustrate the inequality using the real number line. x < -2 Use interval notation to express the inequality. What is the resulting interval? Choose the graph that illustrates the inequality on the real number line. A. B. C. D.

Complete the following table by stating whether the polynomial is a monomial, binomial, or trinomial; then list its terms (entered as a comma-separated list) and state its degree. Polynomial Type Terms Degree -8 Select- Complete the following table by stating whether the polynomial is a monomial, binomial, or trinomial; then list its terms (entered as a comma-separated list) and state its degree. Polynomial Type Terms Degree x-x^2+x^4-x^5- Select-

Week 2: Ch 11 (Part 1) Solving a Systems Classifying systems of linear equations System A Line 1: y=-x-2 Line 2: y=-x-3 This system of equations is: consistent dependent consistent independent inconsistent This means the system has: a unique solution

There are approximately 39.37 inches in 1 meter. How many meters are there in 239 inches?

4b[2a^2-5(3ab-2b^2)]+29ab^2

Using the digits 0,1,2, ... 8,9, determine how many 8-digit lock combinations are possible according to the following criteria. Zero cannot be used for the first digit; digits may be repeated. The number of possible 8-digit lock combinations is .

2x^7+3x^6-12x^3+9 is Select an answer 2x^4+7/x^3-3x^2+12 is Select an answer 7x^3 is Select an answer 19x^6-8x^2+10 is Select an answer 5x^8+2 is Select an answer

Find the slope. m=(7-3)/(7-5) Select one: a. -2 b. 2 c. 5 d. 6

What does FOIL stand for when factoring? Factoring, Out, Inside, Later Reynolds Wrap First, Outer, Inner, Last Greatest common factors

Describe the sampling distribution of hatp based on large samples of size n-that is, given the mean, the standard deviation, and the (approximate) shape of the distribution of hatp when large samples of size n are (repeatedly) selected from the binomial distribution with a probability of success p. Let q=1-p.

Select the correct answer. What are the solutions of the quadratic equation below? 2 x^2 - 2 x - 9 = 0 A. (-1 ± √19)/2 B. (3 ± √19)/2 C. (1 ± √19)/2 D. (1 ± 3√19)/2

Use the properties of logarithms to condense the following expression. [ (1/2) ln x+ln (x^2-1)-ln (x+1) ]

y=1/2 x-1 y=1/2 x+5 How many solutions does the system of equations have? no solution one solution infinitely many solutions

Look at this diagram: If P R and S U are parallel lines and m angle P Q O=132°, what is m angle R Q O?

Evaluate the expression without using a calculator. [ (2^2 cdot 4)^2 ]

Which of the figures below are congruent? A B C D (A) B and C (B) A and C (C) B and D (D) A and D

Determine the slope of the equation 4x + 1/2 y = -6

Express in simplest radical form. 6 sqrt(175) + 7 sqrt(28)

Determine whether the equation defines y as a function of x. 2x-3y=5 The equation defines y as a function of x. The equation does not define y as a function of x. Determine whether the equation defines y as a function of x. x^2+(y-5)^2=6 The equation defines y as a function of x. The equation does not define y as a function of x.

Find the indicated side of the right triangle.

Simplify. 5(-y-4 z)-2(-5 z-6 y)

Simplify. Assume all variables are positive. [ sqrtfrac9 x^32 y^2= ]

Multiply: 8 · 5/2 Give your answer as a fraction, reduced to lowest terms

Test: Chapter 1-Appendix-A Question list Question 1 Question 2 Question 3 Question 4 Question 5 Question 6 Question 7 Question 8 The graph shows a relationship between price, x, and quantity demanded, y. Use the graph to answer the question. This function is perfectly inelastic. The slope of this relationship at point A is

Which conic section is formed when a plane intersects the central axis of a double-napped cone at a 90° angle?

Final Exam Find the area. Area of square=[?] in^2 Area of triangle= square in^2 Remember: Asquare=bh 18 in Area of Figure = square in^2

Graphs, Functions, and Systems Choosing a graph to fit a narrative: Basic (a) Kaitlin fills her pool with water. (b) Lamar walks from home to school.

L .3 proving triangles congruent by SSS and SAS WZ R is the midpoint of QS. Complete the proof that triangle RSU is congruent to triangle RQT. 1. R is the midpoint of QS - Given 2. QT is congruent to SU - Given 3. RT is congruent to RU - Given 4.

Solve for x in 4 cos ^2(x)=1 x=-60^circ x=60^circ x=120^circ x=-60^circ, 60^circ x=60^circ, 120^circ

For the exponential function f(x)=4 * 6^x, what is the value of f(-3)?

A tree casts a 25-foot shadow on a sunny day, as shown in the diagram below. If the angle of elevation from the tip of the shadow to the top of the tree is 32 degrees, what is the height of the tree to the nearest tenth of a foot?

Greatest Common Factor (GCF) - Quiz - Level F Marcus collects donations and sends care packages to troops overseas. He has 36 bars of soap and 24 toothbrushes and wants to arrange the items so the packages are identical. What is the greatest number of packages that Marcus can make using all the soap and toothbrushes? What is the greatest number of packages of soap and toothbrushes that Marcus can make? Marcus can make at most packages.

(5.7 × 10^21) × (1.2 × 10^-18)

In due villaggi dell'Amazzonia la popolazione di uno era i 5/6 della popolazione dell'altro. Una grave epidemia costrinse a emigrare 70 abitanti di ogni villaggio, per cui attualmente il primo villaggio ha i 4/5 degli abitanti del secondo. Quanti abitanti ha oggi ciascun villaggio?

Use the distributive property to rewrite each expression. 6(7+8) 6(7+8)= (Type an expression. Do not simplify.)

Which undefined term is used to define an angle?

2000 ml =? L

Which describes the system of equations below? 3x-10y=-4 20x-y=-20 consistent and dependent inconsistent consistent and independent Submit

Geometry ≥+2.3 Proving triangles congruent by SSS and SAS WZ Y is the midpoint of UW and VX. Complete the proof that triangle UXY is congruent to triangle WVY. 1. Y is the midpoint of UW - Given 2. Y is the midpoint of VX - Given 3. VW is congruent to UX - Given 4. UY is congruent to WY - Definition of midpoint

Algebra 2 Sem1 Quiz 2.2.1 - Factoring Factor completely: 9 x^2 + 12 x + 4 a. (2 x + 3)^2 b. (3 x + 2)^2 c. (3 x + 2)(3 x - 2) d. (2 x + 3)(3 x + 2)

In right triangle XYZ, angle X and angle Z are complementary angles and cos(X) is 9/11. What is sin(Z) ? A. 11/9 B. 9/11 C. sqrt(20)/9 D. sqrt(20)/11

A triangle is half the side of a rectangle. The area by two. The formula for the area of a triangle can Example 1: Find the area of the triangle. A=(b b)+2 A=(8 * 8)+2 A=64 / 2 A=32 yd^2

A small hole in the wing of a space shuttle requires a 16.3 cm^2 patch. What is the patch's area in square kilometers (km^2) ? Be sure your answer has the correct number of significant figures. 1.63 x 10^-9 km^2 If the patching material costs NASA 2.85 / in^2, what is the cost of the patch to the nearest cent? Be sure your answer has the correct number of significant figures.

Workers at A La Mode Ice Cream Parlor hand churn batches of ice cream and put them in the freezer. The temperature of the ice cream x hours after a batch is put into the freezer is given by the function f(x). The temperature is measured in degrees Fahrenheit. What does f(6)=f(7) tell you? The temperature of the ice cream after 6 hours is the same as after 7 hours.

The sales of vinyl records have increased due to a revived popularity. In the year 2012, 50,000 records were sold. Every following year, the number of records sold were 1.1 times the number of records sold the previous year. From 2012 to the end of 2016, how many vinyl records were sold? A. 80,525 records B. 255,255 records C. 73,205 records D. 305,255 records

Question 19 of 25 The graph of the reciprocal parent function, f(x)=1/x, is shifted 7 units up and 2 units to the right to create the graph of g(x). What function is g(x) ? A. g(x)=1/(x+7)+2 B. g(x)=1/(x-2)+7 C. g(x)=1/(x-7)+2 D. g(x)=1/(x+2)+7

In a laboratory experiment, the population of bacteria in a petri dish started off at 850 and is growing exponentially at 8% per day. Write a function to represent the population of bacteria after t days, where the hourly rate of change can be found from a constant in the function. Round all coefficients in the function to four decimal places. Also, determine the percentage rate of change per hour, to the nearest hundredth of a percent.

Question 6 6 of 13 Evaluate and match each expression on the left to its value on the right, when x=4 and y=7. 12+x 3x+y 4y-10 1/2 xy 18 19 14 16

Find the mean, ( barx ), of the data. 3,4,5,7,10,12,15 ( overlinemathrmx=[?] )

Evaluate the following radical. [ sqrt[3]-216 ]

X is the midpoint of W. Complete the proof that triangle UWX is congruent to triangle UVX. - Statement - Reason 1. X is the midpoint of VW - Given 2. W perpendicular to UX - Given 3. angle UXV is congruent to angle UXW - All right angles are congruent 4. VX is congruent to WX - Definition of midpoint 5. UX is congruent to UX - Reflexive Property of Congruence 6. triangle UWX is congruent to triangle UVX -

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