Hello everybody,

I am just wanting to check my answers to the following questions, and if i am wrong could somebody please point out how to do it correctly?

A satellite orbiting the Earth is rotating twice a minute. As the satellite turns

an instrument on the side of the satellite is periodically heated the by the sun

then cools as it moves into the shady side of the satellite. The instrument

reaches a maximum temperature of 50◦C and a minimum temperature of -

10◦C. Supposing that t = 0 corresponds to the time the temperature of the

instrument is at its highest write down a trigonometric function that captures

this behaviour. Sketch the temperature of the instrument over one minute (that

is two revolutions of the satellite).

Function = Function: f(t) = 30cos2t Is that correct?

The volume of water in a tank at a particular time (measured in seconds) is

given by V (t) = 2t(1 - t)m3. Find the rate of change of the volume of water

in the tank from first principles (i.e. using the definition of the rate of change -

which is a limit).

I got -2m^3/s.

Consider the function f(x) = -x2+3x-1. Find the equation of the tangent to

the graph of f(x) at x = 2. [NOTE: when calculating f′(2), use first principles.]

f(x) = -x^2+3x-1

f(2) = 1

f '(x) = -2x+3

f '(2) = -1

tangent line: y = -1x + b -- substitute (2,1) into equation to solve for b

y = -x + 3

Consider the trigonometric function f(t) = 4 - 2 cos(2piet).

What is the amplitude of f(t)?

What is the period of f(t)?

What are the maximum and minimum values attained by f(t)?

Sketch the graph of f(t) for t 2 [0; 2].

Can somebody help me out with this one please?

Thank you in advance for any help .