MA 150 final exam

given cot=3/4 and sec<0, which of the following are true?

III only

evaluate cos(7pi/13) to 4 decimal places

-0.1205

evaluate (gof)(6)

-4

Rationalize the root in the following expression. (50-x)/(sqrtx)-(sqrt50)

-sqrt(x)-sqrt(50)

for the equation -2tan(6x)=0.9551, how many solutions will exist in the interval [0,2pi)?

12

evaluate 2f(4)-5g(3)

13

Given the following piecewise function, find the value of 3f(0)+5f(2)

16

Solve the following equation for x to one decimal place, ln(x-3)=2.75

18.6

the diameter D of a tumor, in millimeters, t days after it is detected is given by D(t)=56e^0.0361t. after how many days will the diameter of the tumor double?

19 days

the growth of a certain strain of bacteria can be modeled by N(t)=N0e^kt, where N0 is the initial number of bacteria, t is the time elapsed in minutes. the doubling time for the growth of the bacteria is 54 minutes. Suppose that there are 4000 bacteria initially present. After how many minutes will there be 47,000 bacteria?

192 minutes

convert the angle x=23*41'15'' to decimal form

23.6575*

The weight of a certain breed of dog is a linear function of time, t, in months, for 2<_t<_16. If the dog has a weight of 3 pounds at 4 months, and a weight of 7 pounds at 10 months, estimate the weight of the dog after 14 months.

9.7 lbs

convert x=3pi/7 to degrees, minutes, seconds

77*8'34''

Given f(x)=5e^0.9x+4.25, evaluate f(3) to four decimal places

78.6487

At what point does the graph of f(x)=(2x-3)/(5x+2) cross its horizontal asymptote?

it does not cross the horizontal asymptote

express the following as a single logarithm, ln(xy^2)-3lnx+5lny

ln(y^7/x^2)

find the general solution to the equation 4cos^2x=3

pi/6 +pi(n), 5pi/6+pi(n)

in which quadrants will the solutions of the equation tanx=7.3535 in the interval [0,360) lie?

quadrants I and III

the volume V enclosed by a sphere, in cubic feet, is a function of the radius of the sphere r, when measured in feet. This relation is expressed by the formula V(r)=4/3pir^3 for r>0. Find the value of the radius r when the volume is V=288pi

r=6 feet

Which of the following could be the graph of y=-5cos(pix/3)

starts at -4, goes up to 4

Solve the equation for the exact value of x, 2^3x-1=5^x+6

x=(6ln5+ln2)/(3ln2-ln5)

solve the equation for x on the interval [0,2pi), sec^2x+2=3secx

x=0,pi/3,5pi/3

find an actue angle x to the nearest 0.1* that solves the equation 3cotx=5.32

x=29.4*

which of the following values of x satisfy the equation cscx=2?

x=5pi/6

Which of the following is a zero of h(x)=2x^2-20x+32

x=8

solve the following equation for x, lnx+ln(x-3)=ln(9x-27)

x=9

Find the standard equation of a parabola with a vertex at (2,1) passing through the point (-3,2)

y=1/25(x-2)^2+1

find the slant asymptote of the rational function f(x)=(3x^2-5x+1)/(x-2)

y=3x+1

find the zeros and y-intercept of the rational function, f(x)=(x^2-5x+6)/(x^2-x-2)

zeros: x=3, y-int: (0,-3)

Factor the expression and simplify as much as possible. (4x+5)^-8...

(x+9)^2(3x-4)/(4x+5)^9

If you invest $15,000 in an account at an annual interest rate of 4.5% compounded continuously, find the balance in the account after 8 years.

$21,499.94

Simplify the following expression, ((2/3x+1)-2)/((4/3x+1)+5)

(-6x)/(9+15x)

find all intervals on which the function f(x)>0, f(x)=-3(x-4)^2(x+1)^3

(-INF,-1)

find the domain of the function f(x)=(x^2-2x-3)/(x^2+6x+5)

(-INF,-5)U(-5,-1)U(-1,INF)

for the function f(x)=sin(x/6), find all intervals where f(x)<0 on the interval (0,24pi)

(6pi,12pi)U(18pi,24pi)

evaluate cos(-19pi/3)

1/2

Find and simplify the difference quotient f(2+h)-f(2)/h, where f(x)=2x^2+3x+5

2h+11

find all value of x in the interval [0.2pi) that satisfy the equation secx+2=0

2pi/3, 4pi/3

The population of turtles on a certain island is modeled by P(t)=0.045t^2+0.67t+12, where P(t) is the population and t is the time in years since 2010. Find the population of turtles in the year 2025.

32

on a citrus farm, the average annual yield of oranges is 88 pounds per tree when the number of trees is 26 per acre. For each additional tree over 26, the annual yield per tree decreases by 2 pounds per tree. How many orange trees should be planted per acre to maximize the number of pounds of oranges per acre:

35 trees

a box is to be created from a piece of cardboard measuring 40 inches by 40 inches by cutting out identical squares with sides of length x from each corner and folding up the sides. Find an expression for the volume of the box V as a function of x.

V(x)=x(40-2x)^2

find the domain of the function f(x)=(2x/3-sqrt(x+1))

[-1,8)U(8,INF)

Given f(x)=sqrt(5-x) and g(x)=sqrt(x+4), find the domain of (fog)(x)

[-4,21]

find the amplitude and period of the graph of y=-4cos(x/6)

amplitude is 4, period of pi/6

Find the inverse function f^-1(x) of the function f(x)=(13x+20)/(4x+15)

f^-1(x)=(20-15x)/(4x-13)