CAN SOMEONE PLEASE HELP ME !

Use partial fraction expansion to evaluate: LaTeX: \int\frac{x-1}{x^2+3x+2}dx ∫ x − 1 x 2 + 3 x + 2 d x a. LaTeX: -2\ln\left|x+1

ohaa [14]

$\frac{x-1}{x^2+3x+2}\\\frac{x-1}{(x+1)(x+2)}\\\frac{x-1}{(x+1)(x+2)}=\frac{A}{x+2}+\frac{B}{x+1}\\x-1=A(x+1)+B(x+2)\\\\\text{ Let } x=-1 \text{ then } -2=A(0)+B(-1+2) \text{ which means } B=-2\\\\\text{ Instead of choose } x \text{ to be -1, let's now set it equal to -2 to find } A\\\\-3=A(-1)+B(-2+2)\\-3=-A\\A=3\\\\ \text{ So your integral becomes } \\\int \frac{3}{x+2} dx+\int \frac{-2}{x+1} dx\\3 \ln|x+2|-2\ln|x+1|+C\\\\or\\-2\ln|x+1|+3\ln|x+2|+C$

8 0

3 years ago

Your friend attempted to factor an expression as shown. Find the error in your friends work. Then factor the expression correctl

loris [4]

Answer:

Third step is incorrect. The correct factored form is (x-1)(2x-5).

Step-by-step explanation:

The given expression is

$2x^2-7x+5$

We need to find the factored form of this expression.

Step 1: Given

$2x^2-7x+5$

Step 2: Splitting the middle term method, the middle term can be written as (-5x-2x).

$2x^2-5x-2x+5$

$(2x^2-5x)+(-2x+5)$

Step 3: Taking out common factors from each parenthesis.

$x(2x-5)-1(2x-5)$

Step 4: Taking out common factors.

$(x-1)(2x-5)$

Therefore, the third step is incorrect. The correct factored form is (x-1)(2x-5).

3 0

2 years ago

An ore ship is traveling west toward Duluth on Lake Superior at 18 miles per hour. The bearing of Split Rock Lighthouse is 285de

goblinko [34]

We are given
v = 18 m/hr west
θ1 = 285°
θ2 = 340°

After 1 hours, the distance traveled by the ship is
dv = 18 mi

The distance between the ship and the lighthouse is
d = 18 / cos 340
Solve for d

5 0

3 years ago

Sam invests a sum of money in a retirement account with a fixed annual interest rate of 7%

Zolol [24]

Answer:

The initial amount of investment was $7,822

Step-by-step explanation:

The formula for compound interest, including principal sum is:

$A=P(1+\frac{r}{n})^{nt}$ , where

A is the future value of the investment/loan, including interest

P is the principal investment amount

r is the annual interest rate (decimal)

n is the number of times that interest is compounded per unit t

t is the time the money is invested or borrowed for

Let us use this rule to solve the question

∵ Sam invests a sum of money in a retirement account with a fixed

annual interest rate of 7% compounded quarterly

∴ r = 7% = $\frac{7}{100}$ = 0.07

∴ n = 4 ⇒ compounded quarterly

∵ After 13 years, the balance reaches $19,280.02

∴ A = 19,280.02

∴ t = 13

Substitute these values in the rule above to find P

∵ $19,280.02=P(1+\frac{0.07}{4})^{4(13)}$

∴ $19,280.02=P(1.0175)^{52}$

→ Divide both sides by $(1.0175)^{52}$

∴ 7,821.99888 = P

→ Round it to the nearest dollar

∴ 7,822 = P

∴ P = $7,822

∴ The initial amount of investment was $7,822.

8 0

3 years ago

An architect is recreating the blueprint for a deck with an existing scale factor of 1in.=2ft. Using 12in by 8in. The architect

NemiM [27]

Answer:

New scale factor is 1 inch = 3 ft.

New width of the blueprint = (16/3) inches = 5.3333 inches

Step-by-step explanation:

Initial scale factor is 1 inch = 2 ft

And the architect draws a blueprint of 12 inches by 8 inches.

Converting to real life scale using 1 inch = 2 ft

Length = 12 inches = 12 × 2 ft = 24 ft

Width = 8 inches = 8 × 2 ft = 16 ft.

New scale factor turns the length to 8 inches

Scale factor = (length in the drawing)/(real life length)

Scale factor = (8 inches)/(24 ft) = (1 inch)/(3 ft)

Hence, new scale factor is 1 inch = 3 ft.

New width of the blue print

3 ft in real life = 1 inch on paper

16 ft in real life = (16/3) inches on paper

New width of the blueprint = (16/3) inches = 5.333 inches

3 0

3 years ago