Answer:
(e) csc x − cot x − ln(1 + cos x) + C
(c) 0
Step-by-step explanation:
(e) ∫ (1 + sin x) / (1 + cos x) dx
Split the integral.
∫ 1 / (1 + cos x) dx + ∫ sin x / (1 + cos x) dx
Multiply top and bottom of first integral by the conjugate, 1 − cos x.
∫ (1 − cos x) / (1 − cos²x) dx + ∫ sin x / (1 + cos x) dx
Pythagorean identity.
∫ (1 − cos x) / (sin²x) dx + ∫ sin x / (1 + cos x) dx
Divide.
∫ (csc²x − cot x csc x) dx + ∫ sin x / (1 + cos x) dx
Integrate.
csc x − cot x − ln(1 + cos x) + C
(c) ∫₋₇⁷ erf(x) dx
= ∫₋₇⁰ erf(x) dx + ∫₀⁷ erf(x) dx
The error function is odd (erf(-x) = -erf(x)), so:
= -∫₀⁷ erf(x) dx + ∫₀⁷ erf(x) dx
= 0
J.
x represents the minutes and y shows how many gallons over that time.
I believe that when finding the radius of a circle you half the diameter, but when finding the circumference of a circle you need to multiply the diameter (14cm) by pi.
So 14xpi= 43.98229715
But it can be simplified/ rounded to 44cm.
Of course I might be incorrect so do please correct me if I am wrong.
Answer:
a) 4410
b) 4189.5
Step-by-step explanation:
To find the volume of the pool, multiply the length, width, and depth:
21*35*6=4410ft^3
95% capacity would be equal to 0.95*4410=4189.5ft^3
120 ways. More details in attachment.
