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: there are 25 red flowers in Sakura's garden.
Step-by-step explanation:
In Sakura's garden, for every 5 red flowers, there are 10 yellow flowers. This means that if there are 10 red flowers, there would be 20 yellow flowers. if there are 20 red flowers, there would be 40 yellow flowers. Therefore, the ratio of red flowers to yellow flowers in the garden is
5/10 = 10/20 £= 20/40 = 1/2 = 1:2
Total ratio = 2 + 1 = 3
If there are 75 total red and yellow flowers, then the total number of red flowers are in Sakura's garden would be
1/3 × 75 = 25
Answer:
The Schusters will have to pay $2,034 in the sixth month.
Step-by-step explanation:
Since Carpet King is trying to increase sales, and it has instituted a new promotion by which all purchases can be paid on the installment plan with no interest, as long as the total is paid in full within six months, and there is a $20 minimum monthly payment required, if the Schuster family buys carpeting for $2,134 and makes only the minimum payment for five months, to determine how much will they have to pay in the sixth month, the following calculation must be performed:
2134 - (5 x 20) = X
2134 - 100 = X
2034 = X
Therefore, the Schusters will have to pay $ 2,034 in the sixth month.
