Calculator = -0.176091259
the final temperature was -2 F, and that reflects a drop of 13 units, so
-2------0------------------------------------------------------+11.
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!!!
p = number of items sold (note: this is not the profit)
1 item sells for $855, so p items sell for 855p dollars
Subtract off the cost of 6780 and we have the expression 855p-6780 which is the profit for that given month.
Now plug in p = 250 because 250 items were sold in that given month
855*p - 6780 = 855*250 - 6780 = 206,970
The company earns $206,970 in profit for that month. Apply 15% to this value
15% of 206,970 = (15/100)*206,970 = 0.15*206,970 = 31,045.50
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Answer: $31,045.50 which is choice C
