9514 1404 393
Answer:
Step-by-step explanation:
a) The 36000 -23000 = 13000 difference in salary is being made up at the rate of 3000 -2000 = 1000 per year. It will take 13000/1000 = 13 years for the salaries to be the same.
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b) After 13 years, the salary will be ...
23000 +13(3000) = 23000 +39000 = 62,000 . . . dollars
36000 +13(2000) = 36000 +26000 = 62,000 . . . dollars
Answer:
1) 1/6, 1/3, 1/2, 3/4
2) 3/10, 2/5, 7/10, 4/5
3) 1/4. 7/12. 2/3, 5/6
4) 4/15. 11/30, 2/5, 7/10
Step-by-step explanation: Either convert all in a set to a common denominator, or convert to decimal fractions.
Answer:
aⁿ=4(−1)ⁿ⁻¹/3ⁿ
Step-by-step explanation:
use the formula an=a1rⁿ⁻¹
aⁿ=4(−1)ⁿ⁻¹/3ⁿ
Answer:
∫((cos(x)*dx)/(√(1+sin(x)))) = 2√(1 + sin(x)) + c.
Step-by-step explanation:
In order to solve this question, it is important to notice that the derivative of the expression (1 + sin(x)) is present in the numerator, which is cos(x). This means that the question can be solved using the u-substitution method.
Let u = 1 + sin(x).
This means du/dx = cos(x). This implies dx = du/cos(x).
Substitute u = 1 + sin(x) and dx = du/cos(x) in the integral.
∫((cos(x)*dx)/(√(1+sin(x)))) = ∫((cos(x)*du)/(cos(x)*√(u))) = ∫((du)/(√(u)))
= ∫(u^(-1/2) * du). Integrating:
(u^(-1/2+1))/(-1/2+1) + c = (u^(1/2))/(1/2) + c = 2u^(1/2) + c = 2√u + c.
Put u = 1 + sin(x). Therefore, 2√(1 + sin(x)) + c. Therefore:
∫((cos(x)*dx)/(√(1+sin(x)))) = 2√(1 + sin(x)) + c!!!
