Answer:
a) See the file below, b) ![s = \int\limits^{0.5\pi}_{-0.25\pi} {[\left( 3\cdot \cos t\right)^{2}+\left(-5\cdot \sin t \right)^{2}]} \, dx](https://tex.z-dn.net/?f=s%20%3D%20%5Cint%5Climits%5E%7B0.5%5Cpi%7D_%7B-0.25%5Cpi%7D%20%7B%5B%5Cleft%28%203%5Ccdot%20%5Ccos%20t%5Cright%29%5E%7B2%7D%2B%5Cleft%28-5%5Ccdot%20%5Csin%20t%20%5Cright%29%5E%7B2%7D%5D%7D%20%5C%2C%20dx)
, c) 
Step-by-step explanation:
a) Points moves clockwise as t increases. See the curve in the file attached below. The parametric equations describe an ellipse.
b) The arc length formula is:
c) The perimeter of that arc is approximately:
Answer:
dz / dt = -50
Step-by-step explanation:
To solve the chain rule must apply, we have all the necessary values to make the calculation, as follows:
using the chain rule, we find:
dz / dt = (∂z / ∂x) * (∂x / ∂t) + (∂z / ∂y) * (∂y / ∂t)
Evaluating when t = 9, we have to:
fx (6, 4) * g '(9) + fy (6, 4) * h '(9)
We know that g '(9) = −6; h '(9) = 4; fx (6, 4) = 9; fy (6, 4) = 1
Replacing:
(9 * -6) + (1 * 4) = -50
Por lo tanto dz / dt = -50
The 2 marked angles are alternate angles and so they are equal.
Therefore:- 3x + 5 = 65
3x = 60
x = 20 (answer)
9 points = 1 questions
40 points = ? questions
40/9=4.4 questions or just 4 questions
apologies if my answers are wrong
