Expert: Sherman D. - 6/13/2005

Question
1. The daily cost,C(in dollars), to produce x portable 12inch TV given by C(x)= X^2 -80x+2000. How   many TVs should be produced to minimize the cost

2.A person 60feet from the base of vertical flagpole. If the angle of elevation to the top of the pole is 27 degree, how tall is the flagpole.

3. Find all h(t)= -16t^2+ 96t+100, find the time at which the ball reaches it's maximum height.
100ft high
96ft per second

4. The number N of bacteria present in a culture at time t(in hours) obeys the function N(t)=1000e^0.01t. What will be the number of bacteria be after 5 hours?(Round to the nearest whole number)

Answer
1.)
The daily cost,C(in dollars), to produce x portable 12inch TV given by C(x)= x^2 - 80x + 2000. How many TVs should be produced to minimize the cost

to find this out, just use this formula
x = -b/(2a), then substitute that in for x

x = (-(-80))/(2(1))
x = 80/2
x = 40

C(40) = (40)^2 - 80(40) + 2000
C(40) = 1600 - 3200 + 2000
C(40) = -1600 + 2000
C(40) = 400

So the answer is 40 TVs.

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2.)
A person 60feet from the base of vertical flagpole. If the angle of elevation to the top of the pole is 27 degree, how tall is the flagpole.

tan(27) = x/60
x = 60tan(27)
x = 30.57152697

ANS : About 30.57 feet tall.

You can also do is this way

Sine Rule
c/sin(27) = 60/sin(90 - 27)
c/(sin(27)) = 60/(sin(63))
c = (60(sin(27)))/(sin(63))
c = 30.57

where as side c is the side you are looking for.

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3.) Find all h(t) = -16t^2 + 96t + 100, find the time at which the ball reaches it's maximum height.
100ft high
96ft per second

t = -b/2a
t = (-96)/(2(-16))
t = (-96)/(-32)
t = 3

h(3) = -16(3)^2 + 96(3) + 100
h(3) = -16(9) + 288 + 100
h(3) = -144 + 288 + 100
h(3) = 144 + 100
h(3) = 244

ANS : 3seconds

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4.) The number N of bacteria present in a culture at time t(in hours) obeys the function N(t)=1000e^0.01t. What will be the number of bacteria be after 5 hours?(Round to the nearest whole

N(t) = 1000e^(.01t)
N(5) = 1000e^(.01 * 5)
N(5) = 1000e^(.05)
N(5) = 1000 * 1.051271096
N(5) = 1051.271096

ANS : 1051 bacteria