Questions: 4x^2 + 9y^2 ≤ 36

4x^2 + 9y^2 ≤ 36
Transcript text: $4 x^{2}+9 y^{2} \leq 36$
failed

Solution

failed
failed

Solution Steps

Step 1: Identify the Type of Inequality

The given inequality is \(4x^{2} + 9y^{2} \leq 36\). This is an inequality representing an ellipse centered at the origin.

Step 2: Rewrite the Inequality in Standard Form

To rewrite the inequality in standard form, divide every term by 36:

\[ \frac{4x^{2}}{36} + \frac{9y^{2}}{36} \leq 1 \]

Simplify the fractions:

\[ \frac{x^{2}}{9} + \frac{y^{2}}{4} \leq 1 \]

Step 3: Identify the Characteristics of the Ellipse

The standard form of an ellipse is \(\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} \leq 1\), where \(a\) and \(b\) are the semi-major and semi-minor axes, respectively.

From \(\frac{x^{2}}{9} + \frac{y^{2}}{4} \leq 1\), we identify:

  • \(a^{2} = 9\) so \(a = 3\)
  • \(b^{2} = 4\) so \(b = 2\)

This means the ellipse is centered at the origin with a semi-major axis of 3 along the x-axis and a semi-minor axis of 2 along the y-axis.

Final Answer

The inequality \(4x^{2} + 9y^{2} \leq 36\) represents an ellipse centered at the origin with a semi-major axis of 3 along the x-axis and a semi-minor axis of 2 along the y-axis. The standard form of the inequality is:

\[ \boxed{\frac{x^{2}}{9} + \frac{y^{2}}{4} \leq 1} \]

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
a. The expression x^2 x^6 y^10 / x^3 y^4 can be rewritten in the form x^a y^b where: - a= - b= b. Which of the following expressions are equivalent to 2^4 * 5^3 ? Select all that apply 2^4 * 2 * 5^5 / 5^2 2^6 * 5^9 / 2^2 * 5^6 (2 * 5^2)(2^3 * 5) 2^4 * 5^2 * 5^6 / 5^5 2^7 * 5^3 / 2^3 * 5 (2^2 * 5)(2^2 * 5^3)
failedAnswered
Consider a home mortgage of 250,000 at a fixed APR of 6% for 30 years. a. Calculate the monthly payment. b. Determine the total amount paid over the term of the loan. c. Of the total amount paid, what percentage is paid toward the principal and what percentage is paid for interest.
failedAnswered
Find the x - and y-intercepts.
failedAnswered
4. Evaluate your Analysis entries. 1. Now put in bold any sentences in your Analysis column that are rephrasing the original line. 2. Put in bold any sentences that are explaining the meaning of the original line. 3. Put in bold any sentences that are adding facts/info to the original line. 4. Go through your Analysis column and highlight/underline the parts that demonstrate your critical thinking. 5. Which part of your analysis is making your own conclusion from the evidence?Does your RL include lines from the required sources and have complete citations (per the examples in the assignment instructions?)
failedAnswered
Which type of environmental scientist is likely to study methods of water conservation and decontamination? a. Hydrologist b. Toxicologist c. Oceanographer d. Ecologist