Docsity
Docsity

Prepare for your exams
Prepare for your exams

Study with the several resources on Docsity


Earn points to download
Earn points to download

Earn points by helping other students or get them with a premium plan


Guidelines and tips
Guidelines and tips

Solutions Manual for Rational Exponents: Solving Equations and Simplifying Expressions, Study notes of Piano

Solutions for various problems related to rational exponents, including solving equations and simplifying expressions. The problems involve finding the radical or exponential form of given expressions, as well as determining the height of water in a weir given its length and flow rate. The document also includes problems on velocity of water flowing from an open rain barrel and the number of possible random walks with a given number of steps and directions.

Typology: Study notes

2021/2022

Uploaded on 09/27/2022

ekanaaa
ekanaaa 🇺🇸

4.3

(28)

268 documents

1 / 36

Toggle sidebar

This page cannot be seen from the preview

Don't miss anything!

bg1
Write each expression in radical form, or write each radical in exponential form.
1.
SOLUTION:
2.
SOLUTION:
3.
SOLUTION:
4.
SOLUTION:
Simplify.
5.
SOLUTION:
6.
SOLUTION:
7.
SOLUTION:
8.
SOLUTION:
9.
SOLUTION:
10.
SOLUTION:
11.
SOLUTION:
12.
SOLUTION:
Solve each equation.
13.
SOLUTION:
Therefore, the solution is 4.
14.
SOLUTION:
Therefore, the solution is 1.
15.
SOLUTION:
Therefore, the solution is 5.5.
16.CCSSTOOLSA weir is used to measure water flow in a channel. (Refer to the photo on page 410)
For a rectangular broad crested weir, the flow Q in cubic feet per second is related to the weir length L in feet and
height H of the water by . Find the water height for a weir that is 3 feet long and has flow of 38.4
cubic feet per second.
SOLUTION:
Therefore,thewaterheightfortheweiris4feet.
Write each expression in radical form, or write each radical in exponential form.
17.
SOLUTION:
18.
SOLUTION:
19.
SOLUTION:
20.
SOLUTION:
21.
SOLUTION:
22.
SOLUTION:
23.
SOLUTION:
24.
SOLUTION:
Simplify.
25.
SOLUTION:
26.
SOLUTION:
27.
SOLUTION:
28.
SOLUTION:
29.
SOLUTION:
30.
SOLUTION:
31.
SOLUTION:
32.
SOLUTION:
33.
SOLUTION:
34.
SOLUTION:
35.
SOLUTION:
36.
SOLUTION:
37.
SOLUTION:
38.
SOLUTION:
39.
SOLUTION:
40.
SOLUTION:
41.
SOLUTION:
42.
SOLUTION:
43.
SOLUTION:
44.
SOLUTION:
Solve each equation.
45.
SOLUTION:
Therefore, the solution is 5.
46.
SOLUTION:
Therefore, the solution is 2.
47.
SOLUTION:
Therefore, the solution is .
48.
SOLUTION:
Therefore, the solution is .
49.
SOLUTION:
Therefore, the solution is .
50.
SOLUTION:
Therefore, the solution is .
51.
SOLUTION:
Therefore, the solution is 8.
52.
SOLUTION:
Therefore, the solution is 2.
53.
SOLUTION:
Therefore, the solution is 8.
54.
SOLUTION:
Therefore, the solution is .
55.
SOLUTION:
Therefore, the solution is .
56.
SOLUTION:
Therefore, the solution is .
57.CONSERVATION Water collected in a rain barrel can be used to water plants and reduce city water use. Water
flowing from an open rain barrel has velocity , where v is in feet per second and h is the height of the
water in feet. Find the height of the water if it is flowing at 16 feet per second.
SOLUTION:
The height of the water is 4 feet.
58.ELECTRICITY The radius r in millimeters of a platinum wire L centimeters long with resistance 0.1 ohm is
.
How long is a wire with radius 0.236 millimeter?
SOLUTION:
So, the wire has a length of 16 centimeters.
Write each expression in radical form, or write each radical in exponential form.
59.
SOLUTION:
60.
SOLUTION:
61.
SOLUTION:
62.
SOLUTION:
63.
SOLUTION:
64.
SOLUTION:
65.
SOLUTION:
66.
SOLUTION:
Simplify.
67.
SOLUTION:
68.
SOLUTION:
69.
SOLUTION:
70.
SOLUTION:
71.
SOLUTION:
72.
SOLUTION:
73.
SOLUTION:
74.
SOLUTION:
75.
SOLUTION:
76.
SOLUTION:
77.
SOLUTION:
78.
SOLUTION:
Solve each equation.
79.
SOLUTION:
Therefore, the solution is 12.
80.
SOLUTION:
Therefore, the solution is 3.
81.
SOLUTION:
Therefore, the solution is 5.
82.
SOLUTION:
Therefore, the solution is .
83.
SOLUTION:
Therefore, the solution is .
84.
SOLUTION:
Therefore, the solution is 11.
85.CCSSMODELINGThe frequency f in hertz of the nth key on a piano is .
a.WhatisthefrequencyofConcertA?
b. Which note has a frequency of 220 Hz?
SOLUTION:
a. Replace n with 49 in the equation to determine the frequency of Concert A.
So, the frequency of Concert A is 440 hertz.
b. Replace f with 220 in the equation to determine the value of n.
So, the note with a frequency of 220 corresponds to the 37th note on the piano or the A below middle C.
86.RANDOM WALKS Suppose you go on a walk where you choose the direction of each step at random. The path
of a molecule in a liquid or a gas, the path of a foraging animal, and a fluctuating stock price are all modeled as
random walks. The number of possible random walks w of n steps where you choose one of d directions at each
step is .
a. How many steps have been taken in a 2-directionrandomwalkifthereare4096possiblewalks?
b. How many steps have been taken in a 4-directionrandomwalkifthereare65,536possiblewalks?
c.Ifawalkof7stepshas2187possiblewalks,howmanydirectionscouldbetakenateachstep?
SOLUTION:
a.Replace w with 4096 and d with 2 in the equation to determine the value of n.
So, in a 2-direction random walk having 4096 possible walks there have been 12 steps taken.
b. Replace w with 65,536 and d with 4 in the equation to determine the value of n.
So, in a 4-direction random walk having 65,536 possible walks there have been 8 steps taken.
c. Replace n with 7 and w with 2187 in the equation to determine the value of d.
So, in 2187 possible walks of 7 steps there could be 3 directions taken at each step.
87.SOCCER The radius r of a ball that holds V cubic units of air is modeled by .
What are the possible volumes of each size soccer ball?
SOLUTION:
Size 3: d = 7.3 in.. r = 3.65
Size 3: d= 7.6 in., r = 3.8
Size 4: d = 8.0 in.. r = 4.0
Size 4: d= 8.3 in., r = 4.15
Size 5: d = 8.6 in.. r = 4.3
Size 5: d= 9.0 in., r = 4.5
Volume of size 3 soccer balls vary from 204.0 to 230.2 cubic inches. Volume of size 4 soccer balls vary from 268.5
to 299.9 cubic inches. Volume of size 5 soccer balls vary from 333.6 to 382.4 cubic inches.
88.MULTIPLE REPRESENTATIONS In this problem, you will explore the graph of an exponential function.
a. TABULAR Copy and complete the table below.
b. GRAPHICAL Graph f(x) by plotting the points and connecting them with a smooth curve.
c. VERBAL Describe the shape of the graph of f(x). What are its key features? Is it linear?
SOLUTION:
a.
b.
c. The graph of f(x) = 4x is a curve. It has no x-intercept, a y-intercept of 1, the domain is all real numbers, the
range is all positive real numbers, it is increasing over the entire domain, as x approaches infinity f(x) approaches
infinity, as x approaches negative infinity f(x) approaches 0. The graph is not linear.
89.OPEN ENDED Write two different expressions with rational exponents equal to .
SOLUTION:
Sample answer:
First:
Second:
Thus can be represented by and .
90.CCSS ARGUMENTS Determine whether each statement is always, sometimes, or never true.
Assume that x is a nonnegative real number. Explain your reasoning.
a.
b.
c.
d.
e.
f.
SOLUTION:
a. Sometimes istrue.Itisonlytruewhenx = 1.
b. Sometimes istrue.Itisonlytruewhenx = 1.
c. Sometimes istrue.Itisonlytruewhenx = 1.
d. is always true by definition of .
e. isalwaystruesince = = x1 or x.
f. Sometimes istrue.Itisonlytruewhenx = 1.
91.CHALLENGE For what values of x is ?
SOLUTION:
Thus, the expressions will be equal for x = 1, 0, 1.
92.ERROR ANALYSIS Anna and Jamal are solving . Is either of them correct?
Explain your reasoning.
SOLUTION:
Anna is correct. Jamal did not write the expressions with equal bases before applying the Power Property of
Equality.
93.WRITING IN MATH Explain why 2 is the principal fourth root of 16.
SOLUTION:
Sample answer: 2 is the principal fourth root of 16 because 2 is positive and 24 = 16.
94.What is the value of ?
A 5
B 11
C 25
D 35
SOLUTION:
Therefore, the correct choice is D.
95.At a movie theater, the costs for various numbers of popcorn and hot dogs are shown.
Which pair of equations can be used to find p, the cost of a box of popcorn, and h, the cost of a hot dog?
F
G
H
J
SOLUTION:
Let p be the cost of a box of popcorn and h the cost of a hot dog. Then p + h = 8.50 and 2p + 4h = 21.6.
The correct choice is G.
96.SHORT RESPONSE Find the dimensions of the rectangle if its perimeter is 52 inches.
SOLUTION:
Therefore, the dimensions of the rectangle are 17.5 inches by 8.5 inches.
97.If 34 = 9x, then x=
A 1
B 2
C 4
D 5
SOLUTION:
So, the correct choice is B.
Simplifyeachexpression.Assumethatnodenominatorequalszero.
98.
SOLUTION:
99.
SOLUTION:
100.
SOLUTION:
101.
SOLUTION:
102.
SOLUTION:
103.
SOLUTION:
104.GARDENING Felipe is planting a flower garden that is shaped like a trapezoid as shown. 3
Use the formula to find the area of the garden.
SOLUTION:
Replace h with 3a, b1 with 6a, and b2 with 4a in the formula to determine the value of A.
Therefore, the area of the garden is 15a2 square units.
Write each equation in slope-intercept form.
105.
SOLUTION:
So, in slope-intercept form the equation is y = 3x 1.
106.
SOLUTION:
So, in slope-intercept form the equation is y = 6x+11.
107.
SOLUTION:
So, in slope-intercept form the equation is y = 2x 12.
108.
SOLUTION:
So, in slope-intercept form the equation is .
109.
SOLUTION:
So, in slope-intercept form the equation is .
110.
SOLUTION:
So, in slope-intercept form the equation is .
Find each power.
111.103
SOLUTION:
112.105
SOLUTION:
113.101
SOLUTION:
114.
SOLUTION:
eSolutionsManual-PoweredbyCogneroPage1
7-3 Rational Exponents
pf3
pf4
pf5
pf8
pf9
pfa
pfd
pfe
pff
pf12
pf13
pf14
pf15
pf16
pf17
pf18
pf19
pf1a
pf1b
pf1c
pf1d
pf1e
pf1f
pf20
pf21
pf22
pf23
pf24

Partial preview of the text

Download Solutions Manual for Rational Exponents: Solving Equations and Simplifying Expressions and more Study notes Piano in PDF only on Docsity!

Write each expression in radical form, or write each radical in exponential form.

SOLUTION:

SOLUTION:

SOLUTION:

SOLUTION: Simplify.

SOLUTION:

SOLUTION:

SOLUTION:

eSolutions Manual - Powered by Cognero Page 1

SOLUTION:

SOLUTION:

SOLUTION:

SOLUTION:

SOLUTION:

eSolutions Manual - Powered by Cognero Page 2

Therefore, the solution is 1.

SOLUTION: Therefore, the solution is 5.5.

  1. CCSS TOOLS A weir is used to measure water flow in a channel. (Refer to the photo on page 410) For a rectangular broad crested weir, the flow Q in cubic feet per second is related to the weir length L in feet and height H of the water by. Find the water height for a weir that is 3 feet long and has flow of 38. cubic feet per second. SOLUTION: Therefore, the water height for the weir is 4 feet. Write each expression in radical form, or write each radical in exponential form.
  2. SOLUTION:
  3. SOLUTION: eSolutions Manual - Powered by Cognero Page 4

SOLUTION:

SOLUTION:

SOLUTION:

SOLUTION:

SOLUTION:

SOLUTION:

SOLUTION:

SOLUTION:

Simplify.

SOLUTION:

SOLUTION: eSolutions Manual - Powered by Cognero Page 5 7 - 3 Rational Exponents

SOLUTION:

SOLUTION:

SOLUTION:

SOLUTION:

SOLUTION:

SOLUTION:

eSolutions Manual - Powered by Cognero Page 7

SOLUTION:

SOLUTION:

SOLUTION:

SOLUTION:

SOLUTION:

eSolutions Manual - Powered by Cognero Page 8

Solve each equation.

SOLUTION: Therefore, the solution is 5.

SOLUTION: Therefore, the solution is 2.

SOLUTION: Therefore, the solution is.

SOLUTION: Therefore, the solution is.

SOLUTION: eSolutions Manual - Powered by Cognero Page 10

Therefore, the solution is.

SOLUTION: Therefore, the solution is.

SOLUTION: Therefore, the solution is.

SOLUTION: Therefore, the solution is 8.

SOLUTION: Therefore, the solution is 2. eSolutions Manual - Powered by Cognero Page 11

Therefore, the solution is.

SOLUTION: Therefore, the solution is.

SOLUTION: Therefore, the solution is.

  1. CONSERVATION Water collected in a rain barrel can be used to water plants and reduce city water use. Water flowing from an open rain barrel has velocity , where v is in feet per second and h is the height of the water in feet. Find the height of the water if it is flowing at 16 feet per second. SOLUTION: The height of the water is 4 feet.
  2. ELECTRICITY^ The radius r in millimeters of a platinum wire L centimeters long with resistance 0.1 ohm is . eSolutions Manual - Powered by Cognero Page 13

The height of the water is 4 feet.

  1. ELECTRICITY^ The radius r in millimeters of a platinum wire L centimeters long with resistance 0.1 ohm is . How long is a wire with radius 0.236 millimeter? SOLUTION: So, the wire has a length of 16 centimeters. Write each expression in radical form, or write each radical in exponential form.
  2. SOLUTION:
  3. SOLUTION:
  4. SOLUTION:
  5. SOLUTION:

eSolutions Manual - Powered by Cognero Page 14

SOLUTION:

SOLUTION:

SOLUTION:

SOLUTION:

SOLUTION:

SOLUTION:

eSolutions Manual - Powered by Cognero Page 16 7 - 3 Rational Exponents

SOLUTION:

SOLUTION:

SOLUTION:

SOLUTION:

eSolutions Manual - Powered by Cognero Page 17

SOLUTION:

Solve each equation.

SOLUTION: Therefore, the solution is 12.

SOLUTION: Therefore, the solution is 3.

SOLUTION: eSolutions Manual - Powered by Cognero Page 19

Therefore, the solution is 3.

SOLUTION: Therefore, the solution is – 5.

SOLUTION: Therefore, the solution is.

SOLUTION: Therefore, the solution is.

eSolutions SOLUTION: Manual - Powered by Cognero Page 20