Q. 20 In Problems 7鈥�22, solve each i... [FREE SOLUTION]

91影视

Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 3: Q. 20 (page 171)

In Problems 7鈥�22, solve each inequality.
$25 x^{2} + 16 < 40 x$

Short Answer

Expert verified

The inequality has no solution.

Step by step solution

Step 1. Given information

The given inequality is $25 x^{2} + 16 < 40 x$ .

Step 2. Find the Intercepts and Vertex

Express the inequality in standard form.

$25 x^{2} - 40 x + 16 < 0$

Factor the function $f (x) = 25 x^{2} - 40 x + 16$ .

localid="1646159236427" $f (x) = {(5 x - 4)}^{2}$

So, the x-intercept of the function is $(\frac{4}{5}, 0)$ .
The value of $f (0) = 16$ .
So, the y-intercept is $(0, 16)$ .
Find x -coordinate of the vertex by using the formula $x = \frac{- b}{2 a}$ .

$\begin{array}{rcl} x & = & \frac{40}{50} \\ = & \frac{4}{5} \end{array}$

The value of $f (\frac{4}{5}) = 0$ .
So, the vertex of the parabola is $(\frac{4}{5}, 0)$ .

Step 3. Graph the function

Plot $f (x)$ on a graph by using the intercepts and the vertex.

Step 4. Find the region below x-axis

The function $f (x)$ is on or above the horizontal axis, so the given inequality has no solution.

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x	$y = f (x)$
-2	-8
-1	-3
0	0
1	1
2	0

91影视

In Problems 7鈥�22, solve each inequality.
$25 x^{2} + 16 < 40 x$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find the Intercepts and Vertex

Step 3. Graph the function

Step 4. Find the region below x-axis

One App. One Place for Learning.

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91影视

In Problems 7鈥�22, solve each inequality.25x2+16<40x

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find the Intercepts and Vertex

Step 3. Graph the function

Step 4. Find the region below x-axis

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Mechanics Maths

Theoretical and Mathematical Physics

Decision Maths

Pure Maths

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

In Problems 7鈥�22, solve each inequality.
$25 x^{2} + 16 < 40 x$