6th grade
c+14=25
11
Solve for x: 3x + 15 = 45$
x=10
Solve for b1 in the area of a trapezoid formula:
A=1/2h(b1+b2)
b1= 2a/h - b2
Solve for x: log2(x)+log2(x-2)=3
4
Find dy/dx for the following equation:x^3 + y^3 = 6xy
dy/dx=2y-x^2/y^2-2x
38.2=c+27.2
11
A ladder leans against a wall. The base of the ladder is 6 feet from the wall, and the ladder reaches 8 feet up the wall. How long is the ladder?
10 feet
Let $b$ = boat speed and $c$ = current speed.
Upstream: $3(b - c) = 36 ---> b - c = 12$
Downstream: $2(b + c) = 36 ---> b + c = 18$
Boat = 15 mph, Current = 3 mph
what is the exact value of sin(3.14..../3
square root of 3 divided by 2
find the determinant of matrix A
|1 3 2|
|4 1 3| =A
|2 5 2|
17
A farmer has a total of 160 animals where the ratio of goats to sheep is $3:5$. If the farmer sells 20 sheep, what is the new ratio of goats to sheep in simplest form?
3:4
what grade would this be :You have 5 apples, you dividee those apples by 7 and you get cut apples. What would you need to multiply to get x+7 apples and x is 30 percent of the original apples
11.9
If f(x) = x^2 - 3x + 5, find f(-2)
15
Find the derivative (f'(x)) of the following function: f(x)=(3x^2 -5)^4
24x(3x^2 -5)^3
Evaluate the indefinite integral:
loop x cos(x) dx
x sin(x) + cos(x) + C
A rectangle has a length that is 4 inches longer than twice its width ($w$). If the total perimeter of the rectangle is 56 inches, what are the dimensions of the rectangle?
Width = 8 inches, Length = 20 inches
X+y=15
Y+z=22
x+z=19
x = 6, y = 9, z = 13$
x^2-10x+13=0
x= 5-+ 2 square root 3
1. Integration by Parts (The "Double Loop")
Find the indefinite integral of the following. This requires using Integration by Parts twice because the function "loops" back to its original form.
e^x(cos(x)+sin(x))/2 +c
Evaluate the following integral along the entire real line:
infinite loop -infinite 1 / x^4 + 1 dx
3.14159..../The square root of 2
After a 25% discount is applied to a video game, a 10% sales tax is added to the "sale price," making the final cost $49.50. What was the original price of the game before the discount and tax?
$60
Simplify the following expression to a single integer:
(-2)^5 x (-2)^-3 / (-2)^-2
16
If a 15-foot ramp rises 3 feet off the ground, what is the angle of elevation (0) of the ramp?
roughly equal to 11.5 degrees
Related Rates (The Conical Tank)
A conical water tank has a height of 10 meters and a top radius of 4 meters. Water is being pumped into the tank at a constant rate of 2m^3/min
How fast is the water level rising when the water is exactly 5 meters deep?
dh/dt=1/2x3.14.... is roughly 0.159 m/min
Find all functions f :R-->R such that for all x,y ER:
f(x^2 + f(y))=y+(f(x))^2
f(x)= x