Answer:
f'(x) = -f(x) = 9xy² - 6x²y + 5x³
Step-by-step explanation:
f(x) = –9xy² + 6x²y – 5x³
additive inverse: f'(x) = -f(x) = 9xy² - 6x²y + 5x³
f(x) + f'(x) = f(x) -f(x) = (–9xy² + 6x²y – 5x³) + (9xy² - 6x²y + 5x³) = 0
Since the legs are the same length, we know that the remaining two angles must be the same.
120+2x=180
2x=60
x=30
Final answer: x=30 degrees
Answer:
x=5
Step-by-step explanation:
x+5 = -3x+25
Add 3x to each side
x+3x+5 = -3x+3x+25
4x +5 = 25
Subtract 5 from each side
4x+5-5 = 25-5
4x = 20
Divide each side by 4
4x/4 = 20/4
x =5
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
Answer:
Step-by-step explanation:
10, 24 and 38 are composite numbers.
(10 can be divided by 5 and 2; 24 can be divided by 8, 3, 12 and 2; 38 can be divided by 19 and 2).
The others are prime numbers.
