Word Problems
Logs and Exponents
Factoring and solving
Simplifying
Odds and Ends
100
A certain gas will escape from a storage tank according to the formula e=130sqrt(p) where e represents the amount escaping in cubic meters per minute at atmospheric pressure, and p represents the pressure in kilopascals. How much gas is escaping when the pressure is 484 kilopascals? Round your answer to the nearest whole number.
2860 cubic meters
100
Simplify
(18e^5)/(3e^2)
6e3
100
Factor
49x2-16
(7x+4)(7x-4)
100
Simplify x^24*x^11
x35
100
Evaluate (32)3
729
200
Use the formula R=log_10I , where R is the measurement of the Richter scale and I is the intensity, to find the Richter scale measurement of an earthquake with intensity 53,000,000.
7.7243
200
Solve for x to the nearest hundredth: 4.85x = 17
x = 1.79
200
Solve 3(x+7)2+17=59
-7+-sqrt(14)
200
Simplify
(x3+2x-1)-(2x2+4x-2)
x3-2x2-2x+1
200
Graph the function y=2sqrt(x)
300
If $3000 is invested at a rate of 10% compounded continuously, find the balance in the account after 7 years. Use the formula A = Pert
$6041.26
300
Simplify log416x
2x
300
Solve x^3-5x^2=0
x = 5, 0
300
Simplify 8sqrt(8)-4sqrt(18)
4sqrt(2)
300
Y varies jointly with x and the square of t. Write an equation that represents this.
y=kxt2
400
The volume of a sphere can be given by the formula V = 4.18879r3. You have to design a spherical container that will hold a volume of 55 cubic inches. What should the radius of your container be?
2.36 in
400
Solve the equation log2(x+8)=4
x=8
400
Solve the equation 3 sqrt(5x+4)+5=6
-3/5
400
Simplify (-3c3d4e6)2
9c6d8e12
400
Find the inverse of the function f(x)=(2x+5)/3
f^-1(x)=3/2x-5/2
500
The value M in dollars of a laptop t years after 2012 can be estimated by the formula M(t)=800/t+100 . In what year will the laptop be worth $300? What does the value of the laptop approach as time passes?
2016. $100
500
Solve the equation log6x + log6(x+16)=2
x = 2, -18 is extraneous
500
Solve by factoring 3x2+5x-12=0
x=4/3, -3
500
Simplify 2sqrt605*sqrt(55)
110sqrt(11)
500
Let f(x)=2x3-5 and g(x)=3x2. Find f(g(x)) and state the domain.
f(g(x))=54x6-5. Domain is all real numbers.