Answer:
v ≈ (3.28512, 20.74146)
Step-by-step explanation:
v = 21(cos(81°), sin(81°))
v ≈ (3.28512, 20.74146) . . . . (x, y) components
The notation varies among authors. The vector can be written as ...
(r, θ) = (21, 81°)
r∠θ = 21∠81°
r cis θ = 21 cis 81°
v = 21·e^(i·9π/20)
(x, y) ≈ (3.28512, 20.74146)
v = 3.28512i +20.74146j . . . . perhaps this is the vector notation you want (i and j are unit vectors in the x- and y-directions, respectively)
Choices A and B have typos in them, so its not clear what you're trying to say for those parts. However, the domain of 
is 
meaning that x can be 0 or larger. In other words, we can't have x be negative. Similarly, y is the same story because has the inverse 
, but only when , so therefore 
as well. In short you can say both x and y are nonnegative.
To summarize so far, the domain is and the range is
Since x = 0 and y = 0 are the smallest x and y values possible, this means (x,y) = (0,0) is the left-most point or where the graph starts. This is the origin. Choice C is a true statement.
Choice D on the other hand is <u>not</u> a true statement. Graph out and you'll see that a straight line does not form, but instead a nonlinear curve that grows forever. That growth gradually diminishes as x gets larger. Algebraically you can pick three points from the function and show that the slopes are different. Say the three points are P, Q and R. If you can show that slope of PQ does not equal slope of QR, then the function is not linear.
<u>Part</u><u> </u><u>(</u><u>a</u><u>)</u>
Using the quotient rule, the blank is 11/5.
<u>Part</u><u> </u><u>(</u><u>b</u><u>)</u>
Using the product rule, the blank is 9.
<u>Part</u><u> </u><u>(</u><u>c</u><u>)</u>
Using the power rule, the blank is 5.
