Algebra
5x^3-11=614
5
F(x)=2x^2-3x+1. When F(x)=10, what is x?
x=3
What is the exact value of sin(7pi/6)?
-1/2
Find the limit of e8+2x-x^3 as x approaches infinity.
0
sin(x2)+c
Factor x^2+11x+24
(x+3)(x+5)
Identify the transformations to this function: f(x)=3(2-x)^2-5
Vertically stretched by a factor of 3, reflected over the y-axis, shifted right 2 units, shifted down 5 units
Find all exact values for x from [0,2pi):
Sqrt(3)-2sin(x)=0x=pi/3, x=2pi/3
y=cbrt(1-8z)
-(8/3)(1-8z)^(-2/3)
Evaluate the integral of 4x*cos(2-3x)dx
-(4/3)x*sin(2-3x)+(4/9)cos(2-3x)+c
(3/(x-5))-(20/(x^2-25))=(-2/(x+5))
3
Find the domain of f(x)=sqrt(x-2)
(2, infinity)
x3-4x2+x+6 divided by x-2 is
x2-2x-3
Find the equation of the tangent line to f(x)=(1+12sqrt(x))(4-x2) at x=9
f’(x)=-820x+4531
Evaluate the integral of 10x/(4x2-8x+9)dx
(5/4)ln|4(x-1)2+5|+sqrt(5)*arctan((2x-2)/sqrt(5))+c
Given 3x+y=-8 and -4x-y=6, what are x and y?
x=14, y=-50
Simplify sqrt(192)
8sqrt(3)
Jack and Jill are standing at the seashore 10 miles apart. The coastline is a straight line between them. They can see the same ship in the water, with the angle between the coastline and the line between Jack and the ship being 35 degrees. The angle between the coastline and the line between Jill and the ship is 45 degrees. How far is Jack from the ship?
10sin(45°)/sin(100°)
Two people are at an elevator. At the same time, one of them starts to walk away from the elevator at a rate of 2 ft/sec, and the other starts going up the elevator at a rate of 7 ft/sec. What rate is the distance between the two people changing 15 seconds later? A calculator is allowed; round to four decimal places.
7.2801
Find the surface area of the object obtained by rotating 𝑦 =sin(2𝑥) , 0<=x<=pi/8, about the x-axis. Calculators are allowed; round to four decimal places.
1.8215
Spot the mistake
A=B
A*A=A*B
A2=AB
A2+A2=AB+A2
2A2=AB+A2
2A2-2AB=AB+A2-2AB
2A2-2AB=A2-AB
2(A2-AB)=1(A2-AB)
2=1A new company starts out with 3 million dollars. It is estimated to grow at a continuous rate of 6%, and after 2 years, it has 4.6 million dollars. How many years after the 2 year mark will it take for the company to reach 7 million dollars? Answer exactly
ln(7/3)/(0.06ln(b)) where b=the .12th root of 4.6/3
Draw the trigonometric functions on the unit circle.
See picture on my phone
An 80 cm piece of wire is cut into two pieces. One piece is bent into an equilateral triangle and the other will be bent into a rectangle with one side 4 times the length of the other side. Determine where, if anywhere, the wire should be cut to maximize the area enclosed by the two figures.
The wire should not be cut; all of the wire should be bent into an equilateral triangle in order to maximize the area.
Find the hydrostatic force on a trapezoidal object submerged in water, with the surface of the object aligning with the surface of the water. The object is 3 meters tall, the top is 4 meters long, and the bottom is 7 meters long.
264,870N