Compose a 1250 words assignment on calculus and questions. Needs to be plagiarism free! 3) C  .If  .and , then when is ? You must show your work to receive credit.

fg(x)) = a(cx + d) + bacx + ad +b

g(f(x)) = c(ax + b) + dacx + bc +d

When , . bc + d = ad + b

This is only true when f(d) . = g(b)

f(d) = ad + b

g(b) = bc + d

Hence Option C is the correct answer.

4) B Two scientists positioned at  .and  .are 3 miles apart simultaneously measure the angle of elevation of a hot air balloon to be  .and , respectively. Suppose the balloon is directly above a point on the line segment connecting  .and . Find the elevation of the balloon.

We can draw the triangle that fits this situation. Then we can form simultaneous equations using the sin rule:

(3-x)/sin 40 = h / sin 50

x / sin 30 = h / sin 60

by manipulating the second equation, we get x = 0.577h

Substitute this in equation 1 and we get

3 – 0.577h = 0.84y

3 = 1.417h

h = 3/1.417 = 2.1 miles

hence the correct answer is option B.

5) A  . .True/False. It  .is continuous at then  .and  .is both continuous . If true, then explain why. if false, give a counterexample.

This comes from the properties of limits. The limit of the product of two functions is the product of the limits. Since both the functions have a limit at x=0 and are continuous, their product is also continuous.