- #1

- 52

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Differentiate x(t) = pi / t

^{2}

pi x(t) = t

^{-2}

= pi (t

^{-2})

= -2pi t

^{-3}

2)

Differentiate x(t) = 1 / (At

^{3}+ B)

= (At

^{3}+ B)

^{-2}x (2At

^{2})

= (-2At

^{2}) / (At

^{3}+ B)

3)

Differentiate x(t) = [A sqrt(t+B)]

^{4}

= [A (t+B)

^{1/2}]

^{4}

= A

^{4}(t + B)

^{2}

= 2A

^{4}(t + B)

4)

The nebraska board of grain are designing new portable grain silos. they have enough sheet material to make 2000 cylinderical containers, each of fixed surface area 54m

^{2}(this includesthe cylinder ends). calculate in terms of pi the maximum volume of grain that could be stored in total?

my answer is = for 1 container V is 30.46m

^{3}, so for 2000 containers (30.46 x 2000) = 60920m

^{3}is this correct

5)

The height h(x) in meters above the ground of a parachute varies with her horizontal distance x in meters from a landing target on the ground as h(x) = 50sin

^{-1}(0.1x). What is the rate of change of h with respect to x = 6m?

my answer is (25 / 4) is this correct