/*! 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 88 Will help you prepare for the ma... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Problem 88

Will help you prepare for the material covered in the next section. Consider the equation \(\frac{x^{2}}{16}-\frac{y^{2}}{9}=1\) a. Find the \(x\) -intercepts. b. Explain why there are no \(y\) -intercepts.

Short Answer

Expert verified
The x-intercepts are (-4,0) and (4,0), and there are no y-intercepts for the given equation.

Step by step solution

01

Finding the x-intercepts

To find the x-intercepts, we need to set \(y = 0\), and solve for \(x\). So, our equation becomes: \(\frac{x^{2}}{16}-\frac{0^{2}}{9}=1\). This simplifies to \(\frac{x^{2}}{16}=1\), which can be further simplified to \(x^{2}=16\). Solving for \(x\), we obtain \(x= \pm 4\). Hence, the x-intercepts are (-4,0) and (4,0).
02

Testing for y-intercepts

Next, we check for y-intercepts by setting \(x = 0\). This gives us \(\frac{0^{2}}{16}-\frac{y^{2}}{9}=1\), which simplifies to \(- \frac{y^{2}}{9} = 1\), after further simplification we get \(y^{2}=-9\). Since we cannot have a negative square, this equation has no real solutions, thus indicating that there are no y-intercepts for the given equation.

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

Find the solution set for each system by graphing both of the system's equations in the same rectangular coordinate system and finding points of intersection. Check all solutions in both equations. $$ \left\\{\begin{array}{r} (y-2)^{2}=x+4 \\ y=-\frac{1}{2} x \end{array}\right. $$

Find the vertex, focus, and directrix of each parabola with the given equation. Then graph the parabola. $$(y+4)^{2}=12(x+2)$$

Graph each semi ellipse. $$y=-\sqrt{16-4 x^{2}}$$

The reflector of a flashlight is in the shape of a parabolic surface. The casting has a diameter of 4 inches and a depth of 1 inch. How far from the vertex should the light bulb be placed?

In \(1992,\) a NASA team began a project called Spaceguard Survey, calling for an international watch for comets that might collide with Earth. Why is it more difficult to detect a possible "doomsday comet" with a hyperbolic orbit than one with an elliptical orbit?
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Statistics

Read Explanation

Pure Maths

Read Explanation

Geometry

Read Explanation

Decision Maths

Read Explanation

Logic and Functions

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.