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Algebra Worksheets
Practice Problems
4 3 π r 3
3V 4 π r 3
3 V 4 π r 3
r 3 3 V 4 π
r 3 V 4 π 3
[Solve the formula forr
r 3 × 1 4 1 7 4 × 2 2 7 3
r 3 × 9 9 × 7 4 × 2 2 × 7 3
r 2 7 8 3
r
The radius of the sphere is 1.5 m.
E 1 2 m v 2
2E m v 2
2 E v 2 m
[Solve the equation form
m 2 × 3000 40 × 40
[Substitute:E v
m 2 × 7 5 4 0
The mass of the body is 3.75 kg.
1 3 r h
3V = πr h
[Multiply both sides by 3.]
3 V π r 2 h
[Divide both sides byπ r
h 3 V π r 2
[Symmetry property.]
The solution ish 3 V π r 2 r
[Ifr
p l b
p 2 l b
[Divide both sides by 2.]
p 2 l b
[Subtractl
b p 2 l
[Symmetry property.]
v u at
v u at
[Subtractu
v - u t a
[Divide both sides byt
a v - u t
[Symmetry property.]
The solution isa v - u t t
[The solution must exclude values of a variable that make the denominator zero.]
1 f 1 u 1 v
1 f 1 v 1 u
[Subtract1 v
v - f f v 1 u
[Simplify.]
f v v - f u
s r r h
s 2 π r r h
[Divide both sides by 2πr
s 2 π r r h
[Subtractr
h s 2 π r r r
[Symmetry property.]
1 0 0 I R T
PRT = 100I
[Multiply RT on both sides.]
P R T 1 0 0
[Divide both sides by 100.]
I =P R T 1 0 0
[Symmetry property.]
π R s h
V π h R s
[Divide both sides byπ h
V π h s
[SubtractR
R V π h s
[Multiply both sides by -1.]
s R V π h
y mx c
y c mx
[Subtractc
y - c x m
[Divide both sides byx
Algebra Worksheets
- Page 1
1.
The volume of a sphere is given by the formula V = . Find the radius of a sphere whose volume is m3?
| a. | 15 m | ||
| b. | 17 m | ||
| c. | 1.7 m | ||
 | d. | 1.5 m |
Solution:
V =[Solve the formula for
The radius of the sphere is 1.5 m.
Correct answer : (4)
2.
The kinetic energy, E, of a body moving with a velocity is given by the equation E = , where is the mass of the body. Find the mass of a body moving with a velocity 40 m/s and having an energy of 3000 N.
| a. | 4.05 kg | ||
| b. | 3.75 kg | |
| c. | 3.65 kg | ||
| d. | 6.75 kg |
Solution:
2
[Solve the equation for
[Substitute:
The mass of the body is 3.75 kg.
Correct answer : (2)
3.
Solve the formula V = 2 for the variable . Indicate any restrictions on the values of the variables.
| a. | = , V ≠ 0 | ||
| b. | = , ≠ 0 | ||
| c. | = , ≠ 0 | |
| d. | = , ≠ 0 |
Solution:
V =3V = π
[Multiply both sides by 3.]
[Divide both sides by
[Symmetry property.]
The solution is
[If
Correct answer : (3)
4.
Solve the formula = 2( + ) for .
| a. | = + | ||
| b. | = | ||
| c. | = | ||
| d. | = - |
Solution:
[Divide both sides by 2.]
[Subtract
[Symmetry property.]
Correct answer : (4)
5.
Solve the formula = + for . Indicate any restrictions on the values of the variables.
| a. | = , ≠ 0 | ||
| b. | = , ≠ 0 | |
| c. | = ( + ), ≠ 0 | ||
| d. | = + , ≠ 0 |
Solution:
[Subtract
[Divide both sides by
[Symmetry property.]
The solution is
[The solution must exclude values of a variable that make the denominator zero.]
Correct answer : (2)
6.
Solve = + for .
| a. | = | ||
| b. | = - - | ||
| c. | = | ||
| d. | = |
Solution:
[Subtract
[Simplify.]
Correct answer : (4)
7.
Solve = 2π( + ) for and indicate any restrictions on the values of the variables.
| a. | = 4, ≠ 0 | ||
| b. | = , ≠ 0 | ||
| c. | = 2π | ||
| d. | = - , ≠ 0 |
Solution:
[Divide both sides by 2π
[Subtract
[Symmetry property.]
Correct answer : (4)
8.
Solve P = for I.
| a. | I = | ||
| b. | I = 100PRT | ||
| c. | I = | |
| d. | I = 100 + PRT |
Solution:
P =PRT = 100I
[Multiply RT on both sides.]
[Divide both sides by 100.]
I =
[Symmetry property.]
Correct answer : (3)
9.
Solve V = ( - ) for .
| a. | = + | ||
| b. | = | ||
| c. | = - | |
| d. | = - |
Solution:
V =[Divide both sides by
[Subtract
[Multiply both sides by -1.]
Correct answer : (3)
10.
Solve = + for .
| a. | = + | ||
| b. | = ( + ) | ||
| c. | = | |
| d. | = |
Solution:
[Subtract
[Divide both sides by
Correct answer : (3)