Polynomials
The profit function, p(x), is found by subtracting the cost function, c(x), from the revenue function, r(x). Given p(x) = -15x2 + 600x + 60 and r(x) = -0.4x2 + 130x + 1200, find the cost function.
c(x) = 14.6x2 - 470x + 1140
Write x3/2 in radical form.
sqrt(x3)
The function N(x) = 90*(0.86)x + 69 can be used to predict the temperature of a cup of hot chocolate in degrees Fahrenheit after x minutes. What is the approximate average rate of change of the temperature of the hot chocolate, in degrees per minute, over the interval [0, 6]? Round to the nearest hundredth.
-8.93
Relative to the graph of y = 3*sin(x), the transformation that occurred to produce the graph of y = 3*sin(x + pi/3) is
Which function has the greatest y-intercept?
(1) f(x) = 4*sin(2x)
(2) g(x) = 3x4 + 2x3 + 7
(3) h(x) = 5*e2x + 3
(4) j(x) = 6log2(3x + 4)
(4) j(x) = 6log2(3x + 4)
Find the zeros of this function: y = 2d4 + 6d3 - 18d2 - 54d
0, 3, -3
Explain why 813/4 = 27.
The 4th root of 81 is 3, and 33 = 27.
The inverse f-1(x) of the function f(x) = log8(x-5) is
f-1(x) = 8x + 5
A person's lung capacity can be modeled by the function C(t) = 250*sin(pi*t) + 2450, where C(t) represents the volume in mL present in the lungs after t seconds. State the maximum value of this function over one full cycle, and explain how you found that value.
The heights of women in the United States are normally distributed with a mean of 64 inches and a standard deviation of 2.75 inches. The percent of women whose heights are between 64 and 69.5 inches, to the nearest whole percent, is
48
If (a3+27) = (a+3)*(a2+ma+9), find the value of m.
m = -3
The solution set for the equation sqrt(56 - x) = x
{7}
Solve 3.8*31.5t = 16 algebraically. Round to the nearest hundredth.
0.87
If an angle is in standard position whose terminal side passes through the point (-3, 4), identify whether the following functions would be positive or negative:
sec(x)
csc(x)
cot(x)
sec(x) < 0, or negative
csc(x) > 0, or positive
cot(x) < 0, or negative
Can f(x) = x2 + 1 be classified as an even function? Justify your answer algebraically (NOT graphically).
Yes. Because f(-x) = (-x)2 + 1 = x2 + 1, which is the same as f(x).
The result of the expression (x+2)2+4(x+2)+3 when it is rewritten as the product of two binomials.
(x+5)(x+3)
If (6 - ki)2 = 27 - 36i, the value of k is
k = 3
Julia deposits $2000 into a savings account that earns 4% interest per year. This savings account can be modeled by an exponential function y = 2000*(1.04)t, where t is the time in years. Write an equation that represents the amount of money in her savings account in terms of the monthly growth rate. Round to the nearest thousandth.
y = 2000* (1.003)12t
If the cosine of an angle is - 3/4 and the angle is in Quadrant III, then the sine of that angle is
-sqrt(7)/4
The sum of the first 20 terms of the series -2, 6, -18, 54,... is
1,743,392,200
The completely factored form of x8-y8 is
(x4+y4)(x2+y2)(x+y)(x-y)
Written in a + bi form, the solutions to the equation 5x2 - 2x + 13 = 9 are
(1/5) +/- (sqrt(19)/5) i
Determine, to the nearest tenth of a year, how long it would take an investment to double at a 3.75% interest rate, compounded continuously.
18.5
Given tan(theta) = -4/3 where pi/2 < theta < pi, then the value of sec(theta) is
-5/3
Solve the following system of equations:
x + 2y - z = 1
-x - 3y + 2z = 0
2x - 4y + z = 10
x = 3
y = -1
z = 0