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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} .

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8 0
1 year ago
Jeremy is a business student at ABC University. He is currently enrolled for 18 credits, mostly of quantitative courses with hig
kenny6666 [7]

Answer: work overload

Explanation:

From the question, we are informed that Jeremy is a business student at ABC University and that he is currently enrolled for 18 credits, mostly of quantitative courses with high workloads.

We are further told that he also works 25 hours a week as a bartender. This shows that Jeremy has many works he's doing and the likely cause of his stress is work overload. He's performing too much tasks.

5 0
4 years ago
In 2015, the city of Berkeley instituted a tax on sugar-sweetened sodas. Suppose that the tax increased the price of a typical s
DedPeter [7]

Answer:

(g) Between 0 and -S7.5k because residents can substitute to other products

Explanation:

Data given in the question

Increase in price of typical soda = 10 cents

Total consumed = 150,000 sodas [er day

Dropped quantity = 75,000 sodas

So by considering the above information, the per day compensating variation of the tax varies from 0 and - 7,500

Since the sugar sweetened sodas is treated as a normal goods. Moreover, people can substitute the other goods also if there is an increase in a price of the good

The -7,500 is come from = (-75,000 × 0.10)

The options are as follows

(a) Greater than -$15k because soda is a luxury good with income (b) -$15k because that is the old consumption level times the value of the tax (c) Between -S7.5k and -$15k because soda is a luxury good elasticity > 1 with income elasticity >1 (d) Between -$7.5k arti -$15k because residents can substitute to other products (e) -$7.5k because that is the new consumption level times the value of the tax ()-$7.5k because that is the change in consumption times the value of the tax (g) Between 0 and -S7.5k because residents can substitute to other products (h) Between 0 and -$7.5k because because beverages are typically necessity goods with 6) Nothing because there was no effect on income G) It is impossible to say without knowing consumers' marginal rate of substitution income elasticity less than 1

8 0
4 years ago
A person puts $100.00 into a savings account with 2.4% annual interest rate (computed continuously). The value of such an invest
andre [41]

Answer:

It will take up to 3 years for the total interest to exceed $5.00

Explanation:

The future value of an investment whose interest is compounded continuously can be expressed as;

A=P e^(rt)

where;

A=future value of the investment

P=initial value of investment

r=annual interest rate

t=number of years

In our case;

A=Initial value+interest=(100+5)=$105

P=$100

r=2.4%=2.4/100=0.024

t=unknown

replacing;

105=100 e^(0.024 t)

e^(0.024 t)=105/100

e^(0.024 t)=1.05

ln {e^(0.024t)}=ln 1.05

0.024 t ln e=ln 1.05

but ln e=1

0.024 t=ln 1.05

t=ln 1.05/0.024

t=2.03 years rounded up=3 year

It will take up to 3 years for the total interest to exceed $5.00

4 0
4 years ago
You decide to invest in a period annuity that offers 4.5% APR compounded monthly for 20 years. How much money will you need to i
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$553,229.03 this is the answer for APEX
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