<u>Answer-</u> Length of the curve of intersection is 13.5191 sq.units
<u>Solution-</u>
As the equation of the cylinder is in rectangular for, so we have to convert it into parametric form with
x = cos t, y = 2 sin t (∵ 4x² + y² = 4 ⇒ 4cos²t + 4sin²t = 4, then it will satisfy the equation)
Then, substituting these values in the plane equation to get the z parameter,
cos t + 2sin t + z = 2
⇒ z = 2 - cos t - 2sin t
∴ 


As it is a full revolution around the original cylinder is from 0 to 2π, so we have to integrate from 0 to 2π
∴ Arc length



Now evaluating the integral using calculator,

Answer:
D
Step-by-step explanation:
The average rate of change of f(x) in the closed interval [ a, b ] is

Here { a, b ] = [ - 1, 2 ], thus
f(b) = 4 ← from (2, 4 )
f(a) =
← from (- 1,
) , thus
average rate of change =
=
=
→ D
Answer:
18.
a) 6k + 2y
b) 2x^2 + 2x
c) 16h
19. 4.5 cm
20.
a) x > 4.5
b) x >= 32
Step-by-step explanation:
Max cost of 15 bats = 15 x 35 = $535
Min cost of 15 bats = 15 x 20 = $300
Max cost of 12 gloves = 12 x 60 = $720
Mix cost of 12 gloves = 12 x 30 = $360
Min total cost = 360 + 300 = $660
Max total cost = 535 + 720 = $1255
The range is from $660 to $1255
=============> Answer (A) is out of the range