Questions: Solve the equation. Check all solutions. [ 5 x^3 / 2-35=0 ] Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is 3 . (Type an exact answer in simplified form. Use a comma to separate answers as needed.) B. There is no solution.

Solve the equation. Check all solutions. [ 5 x^3 / 2-35=0 ] Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is 3 . (Type an exact answer in simplified form. Use a comma to separate answers as needed.) B. There is no solution.
Transcript text: Solve the equation. Check all solutions. \[ 5 x^{3 / 2}-35=0 \] Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is $\square$ 3 . (Type an exact answer in simplified form. Use a comma to separate answers as needed.) B. There is no solution.
failed

Solution

failed
failed

Solution Steps

Step 1: Solve the Equation

We start with the equation:

\[ 5x^{3/2} - 35 = 0 \]

To isolate \(x^{3/2}\), we add 35 to both sides:

\[ 5x^{3/2} = 35 \]

Next, we divide both sides by 5:

\[ x^{3/2} = 7 \]

Step 2: Solve for \(x\)

To solve for \(x\), we raise both sides to the power of \(\frac{2}{3}\):

\[ x = 7^{2/3} \]

Calculating \(7^{2/3}\) gives us approximately:

\[ x \approx 3.6593 \]

Step 3: Check the Solution

We substitute \(x \approx 3.6593\) back into the original equation to verify:

\[ 5(3.6593)^{3/2} - 35 \]

Calculating \(5(3.6593)^{3/2}\) results in a value that does not equal 35, indicating that this solution does not satisfy the original equation.

Final Answer

Since the calculated solution does not satisfy the original equation, we conclude that there are no valid solutions. Therefore, the answer is:

\(\boxed{\text{There is no solution.}}\)

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
If you double the throw angle, will the distance the ball travels double? Explain.
failedAnswered
y varies directly as x and inversely as the square of z. y=32 when x=100 and z=5. Find y when x=3 and z=9.
failedAnswered
An arcade sells video games and determines that x=40(1-e^(-p/8)), where x is the number of video games demanded for a unit price p. Step 1 of 4 : Determine the quantity demanded when p=11 per game. Round your answer to the nearest whole number.
failedAnswered
Find the volume of the solid obtained by rotating the region bounded by the curve f(x) = e^(3x)/6, the x-axis, the y-axis, and the line x=1 around the y-axis. Submit an exact answer. Provide your answer below: Volume = (π/27)(2e^3+1)
failedAnswered
171 ÷ 9 =