/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 91 Find all values of \(x\) satisfy... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 91

Find all values of \(x\) satisfying the given conditions. $$y=(x+4)^{\frac{3}{2}} \text { and } y=8$$

Short Answer

Expert verified
The only value of \(x\) satisfying the given conditions is \(x = 0\).

Step by step solution

01

Equating the two functions

First, we need to set the two functions equal to each other to find where they intersect. That can be done by substituting \(y=8\) into the first function. This yields the following equation: \[8 = (x + 4)^{3/2}.\]
02

Solving for \(x\)

To isolate \(x\), we need to get rid of the 3/2 power on the right side of the equation. We can do this by squaring both sides, which yields the equation \[64 = (x + 4)^3.\] Then, taking the cube root of both sides gives us an equation in terms of \(x\): \[(x + 4) = \sqrt[3]{64}\].
03

Simplifying the final equation

Simplifying the equation \((x + 4) = \sqrt[3]{64}\) gives us \(x + 4 = 4\). Subtracting 4 from each side, we then find the value of \(x\), which is \(x = 0\).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Use the Pythagorean Theorem and the square root property to solve. Express answers in simplified radical form. Then find a decimal approximation to the nearest tenth. A rectangular park is 4 miles long and 2 miles wide. How long is a pedestrian route that runs diagonally across the park?

Solve for \(t: \quad s=-16 t^{2}+v_{0} t\).

Use the Pythagorean Theorem and the square root property to solve. Express answers in simplified radical form. Then find a decimal approximation to the nearest tenth. A baseball diamond is actually a square with 90 -foot sides. What is the distance from home plate to second base?

In Exercises 95鈥�102, use interval notation to represent all values of x satisfying the given conditions. $$ y=|2 x-5|+1 \text { and } y>9 $$

In Exercises 122鈥�133, use the strategy for solving word problems, modeling the verbal conditions of the problem with a linear inequality. A city commission has proposed two tax bills. The first bill requires that a homeowner pay 1800 dollar plus \(3 \%\) of the assessed home value in taxes. The second bill requires taxes of 200 dollar plus \(8 \%\) of the assessed home value. What price range of home assessment would make the first bill a better deal?
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Applied Mathematics

Read Explanation

Statistics

Read Explanation

Logic and Functions

Read Explanation

Pure Maths

Read Explanation

Geometry

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.