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Nataly [62]
3 years ago
5

Resolve (7x+19)/(x+1)(x+5) into partial fraction​

Business
1 answer:
Volgvan3 years ago
5 0

Answer:

\dfrac{7x+19}{(x+1)(x+5)}=\dfrac{3}{x+1}+\dfrac{4}{x+5}

Explanation:

The given expression is  

\dfrac{7x+19}{(x+1)(x+5)}

We need to resolve this into partial fraction.

The form of the partial fraction decomposition is

\dfrac{7x+19}{(x+1)(x+5)}=\dfrac{A}{x+1}+\dfrac{B}{x+5}        ...(1)

\dfrac{7x+19}{(x+1)(x+5)}=\dfrac{A(x+5)+B(x+1)}{(x+1)(x+5)}

7x+19=Ax+5A+Bx+B

7x+19=(A+B)x+(5A+B)

On comparing both sides, we get

A+B=7      ...(2)

5A+B=19    ...(3)

Subtract (2) from (3), we get

4A=12

A=3

Put A=3 in (1).

3+B=7

B=4

Put A=3 and B=4 in (1).

\dfrac{7x+19}{(x+1)(x+5)}=\dfrac{3}{x+1}+\dfrac{4}{x+5}

Therefore, \dfrac{7x+19}{(x+1)(x+5)}=\dfrac{3}{x+1}+\dfrac{4}{x+5} .

You might be interested in
Both Bond Bill and Bond Ted have 10.4 percent coupons, make semiannual payments, and are priced at par value. Bond Bill has 5 ye
AURORKA [14]

Answer:

Ans,

a) If interest rates suddenly rise by 3 percent, Bill´s bond would drop by -20.02%  and Ted´s bond would go down by -36.07%

.

b) If rates were to suddenly fall by 3 percent, Bill´s bond would rise by 26.79%

and Ted´s bond would rise too by 86.47%

.

Explanation:

Hi, first let´s go ahead and establish the stable scenario, for that we are going to use the information of the problem but we need to add the discount rate of the bond or yield, which is the missing information. All this so this concept can be explained in a better way, so for this example we´ll say that the yield of both bonds is 10% compounded semi-annually, the same units as the coupon. Now we have to use the following formula.

Price=\frac{Coupon((1+Yield)^{n}-1) }{Yield(1+Yield)^{n} } +\frac{FaceValue}{(1+Yield)^{n} }

Where:

Coupon = (%Coupon/2)*FaceValue= (0.104/2)*1,000=52

Yield = we are going to assume 10% annual, that is 5% semi-annual

n = Payment periods (For Bill n=5*2=10, for Ted, n=22*2=44)

So, let´s see what is the price of each bond if the yield was 10% annual compounded semi-annually.

Price(Bill)=\frac{52((1+0.05)^{10}-1) }{0.05(1+0.05)^{10} } +\frac{1,000}{(1+0.05)^{10} } =1,015.44

In Ted´s case, that is:

Price(Ted)=\frac{52((1+0.05)^{44}-1) }{0.05(1+0.05)^{44} } +\frac{1,000}{(1+0.05)^{44} } = 1,035.33

Now, if the interest rate (Yield) suddenly goes up by 3%, this is what happens to Bill´s Bond

Price(Bill)=\frac{52((1+0.08)^{10}-1) }{0.08(1+0.08)^{10} } +\frac{1,000}{(1+0.08)^{10} } = 812.12

If yield goes down by 3%, this is the new price of Bill´s bond.

Price(Bill)=\frac{52((1+0.02)^{10}-1) }{0.02(1+0.02)^{10} } +\frac{1,000}{(1+0.02)^{10} } =  1,287.44

Now, in the case of Ted, this is what happens to the price if the yield goes up.

Price(Ted)=\frac{52((1+0.08)^{44}-1) }{0.08(1+0.08)^{44} } +\frac{1,000}{(1+0.08)^{44} } =  661.84

If it goes down by 3%, this would be the price for Ted´s bond.

Price(Ted)=\frac{52((1+0.02)^{44}-1) }{0.02(1+0.02)^{44} } +\frac{1,000}{(1+0.02)^{44} } =   1,930.56

Now, in percentage, what we need to use is the following formula.

Change=\frac{(VariationValue-BaseValue)}{BaseValue} x100

For example, in the case of Bill´s bond, which yield went up by 3%, this is what we should do.

Change=\frac{(812.12-1,015.44)}{1,015.44} x100=-20.02Percent

So, the price variation is -20.02% if the yield rises by 3%.

This are the results of the prices and calculations for you to answer this question. Best of luck.

                         Bill        Ted                       % (Bill)       %(Ted)

Base Price     $1,015.44    $1,035.33    

(+) 3% Yield  $812.12          $661.84      -20.02%          -36.07%

(-) 3% Yield  $1,287.44     $1,930.56       26.79%            86.47%

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Angela's monthly disposable income is ​$2 comma 3682,368. She has monthly expenses of ​$2 comma 1272,127 ​(including recreationa
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Answer:

12.88%

Explanation:

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monthly expenses including recreational expenses ($2,127)

net cash flow $241

after expenses are reduced by $64, her net cash flow will increase to $305

Angela's monthly savings rate = (net cash flow / disposable income) x 100 = $305 / $2,368 = 12.88%

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Hilton Brews is a company producing instant mixes for all kinds of beverages. It notices that the market for tea has risen due t
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Answer:

Hilton Brews

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B. Diversification.

Explanation:

Diversification strategy is the corporate strategy that Hilton Brews has adopted to take advantage of the increased health benefits of teas by introducing a new line of organically grown and processed teas.  Diversification strategy is different from other corporate growth strategies which Hilton Brews could have adopted, including market expansion, market penetration, and product development.

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