A bicyclist pedals at a rate of 120 rpm. The diameter of the pedal sprocket is 20 cm. The diameter of the rear wheel sprocket is 8 cm. The diameter of the rear bicycle tire is 70 cm.

a) What is the angular velocity (in rad) of the rear sprocket?

b) What is the linear velocity of the chain in cm per min

c) What is the speed of the bicycle in cm per min?

Formulate a system of equations for the situation below and solve.

A manufacturer of women's blouses makes three types of blouses: sleeveless, short-sleeve, and long-sleeve. The time (in minutes) required by each department to produce a dozen blouses of each type is shown in the following table.

The cutting, sewing, and packaging departments have available a maximum of 73.5, 150, and 44 labor-hours, respectively, per day. How many dozens of each type of blouse can be produced each day if the plant is operated at full capacity?

Use the given conditions to write an equation for the line in? point-slope form and in? slope-intercept form.

Passing through (-5,-6) and parallel to the line whose equation is y= -5x+1

______________________________________________________________________________________________________________________________________________

Write an equation for the line in? point-slope form.

_______

(Simplify your answer. Use integers or fractions for any numbers in the? equation.)

Write an equation for the line in? slope-intercept form.

________

(Simplify your answer. Use integers or fractions for any numbers in the? equation.)

Find the local maximum and minimum values of the function.

Tell the intervals where the graph of the function is increasing and decreasing

f(x)= 2x^3 +3x^2 - 12x

Use an appropriate comparison test to determine the convergence/divergence of the following series:

a.)∑ n= (1)/(√n−1) (Upper limit of the sigma is ∞ and the lower limit of the sigma is n=2)

b.) ∑ n=n(n+1)/(n^2+1) (n-1) (Upper limit of sigma is ∞ and the lower limit of sigma is n=2)

c.) ∑ n= cos^2(n)/ (n^3/2) (Upper limit of sigma is ∞ and the lower limit of sigma is n=1)

d.) ∑ 5^n/(√n4^n) (Upper limit of sigma is ∞ and the lower limit of sigma is n=1)

e.) ∑ n (1)/(In(In(n))) (Upper limit of sigma is ∞ and the lower limit of the sigma is n=3)

f.) ∑ (n+2^n)/(n^2*2^n) (Upper limit of sigma is ∞ and the lower limit of the sigma is n=1)

g.) ∑ (1)/(1^2+2^2+ 3^2+...+n^2) (Upper limit of sigma is ∞ and the lower limit of the sigma is n=1)

evaluate the indefinite integral

sqrt(4-x^2)

A cheetah can run at 105 ft/s, but only for 7 seconds. The cheetah is at (0,0) when it sees an antelope which is moving accoording to the parametric equation (x,y)= (-39+40t , 228+30t), where t is in seconds and (x,y) are measured in feet. If the cheetah started to run at t=0 it could catch the antelope. How many seconds can the cheetah afford to wait before starting? Assume that the cheetah does not change direction when it runs.

Which of the following is the volume of the region bounded by x * 2 + y * 2 = 4 cylinders, z = 0 and z = 4 - x planes?

Find the absolute maximum value and absolute minimum value, if any, of the function g(x) = x √(4 − x2) on the interval [−2, 2].

Find the Taylor series for f ( x ) centered at the given value of a . (Assume that f has a power series expansion. Do not show that R n ( x ) → 0 . f ( x ) = 2 /x , a = − 4

integration of ((8(x+a))/(x^2+a^2))dx. using trig. sub.

Use Lagrange multipliers to find the absolute extrema of f(x,y) = x² + y² - 2x - 4y + 5 on the region x² + y² <= 9.

            i) A bowl collects 1.67 cm height of water in its first week in a dewdrop. Each week the height of the water increases by 4% more than it did the week before. By how much does it increase in nine weeks, including the first week?

ii) 1000 tickets were sold. Adult tickets cost GHC8.50, children's cost GHC4.50, and a total of GHC7300 was collected. How many tickets of each kind were sold?              

A ferris wheel is 50 meters in diameter and boarded from a platform that is 5 meters above the ground. The six o'clock position on the ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 4 minutes. The function h = f(t) gives your height in meters above the ground t minutes after the wheel begins to turn.

What is the Amplitude in meters=
What is the Midline( y=) in meters=
What is the Period in minuets=
How High are you off of the ground after 2 minutes-in meters=

Round your answers to the three decimal places.

A dock is 1 meter above water. Suppose you stand on the edge of the dock and pull a rope attached to a boat at the constant rate of a 1m/s. Assume the boat remains at water level. At what speed is the boat approaching the dock when it is 10 meters from the dock? 15 meters from the dock? Isn’t it surprising that the boats speed is not constant ?

At 10 meters x’=
At 15 meters x’=