Answer:
⅔ √(x + 1) (x − 2) + C
Step-by-step explanation:
∫ x / √(x + 1) dx
Add and subtract 1 to the numerator.
∫ (x + 1 − 1) / √(x + 1) dx
Split the fraction.
∫ [ (x + 1) / √(x + 1) − 1 / √(x + 1) ] dx
∫ [ √(x + 1) − 1 / √(x + 1) ] dx
Rewrite with exponents.
∫ [ (x + 1)^½ − (x + 1)^-½ ] dx
Use u-substitution.
u = x + 1, du = dx
∫ (u^½ − u^-½) du
Integrate using power rule.
⅔ u^(3/2) − 2 u^½ + C
Factor.
u^½ (⅔ u − 2) + C
⅓ u^½ (2 u − 6) + C
Substitute back.
⅓ (x + 1)^½ (2 (x + 1) − 6) + C
Simplify.
⅓ √(x + 1) (2x + 2 − 6) + C
⅓ √(x + 1) (2x − 4) + C
⅔ √(x + 1) (x − 2) + C
2 - 0.5n= 3n+16
----------------------- subtract 2 from both sides
-2 -2
-0.5n = 3n+14
----------------------- then subtract -3n from both sides as well
-3n -3n
-3.5n = 14
--------------- divide -3.5 on each side
-3.5 -3.5
simplify
Answer: n= -4
I will assume that we are trying to find the slope between (-9,2) and (9, 2)
The slope's equation ⇒
<u>Let's set the variables</u>:
(x1, y1) --> (-9, 2)
(x2, y2) --> (9, 2)
<u>Now let's plug them in:</u>
<u>Thus the slope of the line is 0.</u>
Hope that helps!
Based on the value of the annuity, the amount it earns, and the compounding period, the money paid to Nathan each month will be B. $5,840.62.
<h3>How much will Nathan be paid monthly?</h3>
The amount Nathan will be paid is an annuity because it is constant.
First find the monthly interest and the compounding period in months:
= 4.8/12 months
= 0.4%
Number of compounding periods:
= 20 x 12
= 240 months
The monthly payment is:
Present value of annuity = Annuity x ( 1 - (1 + rate) ^ -number of periods) / rate
900,000 = A x ( 1 - (1 + 0.4%)⁻²⁴⁰) / 0.375%
900,000 = A x 154.0932
A = 900,000 / 154.0932
= $5,840.62.
Find out more on the present value of an annuity at brainly.com/question/25792915.
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1 3/5 x 2 3/4
= 8/5 x 11/4
= 22/5
= 4 2/5 (4 and 2/5)