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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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The purpose of having a minimum wage is to _____. a. Educate workers about what they could be making b. Guarantee that workers a
vagabundo [1.1K]

Answer:

The purpose of having a minimum wage is to guarantee that workers are paid fairly and not exploited.

Answer:b

3 0
3 years ago
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Keenan has won the lottery for $10,000,000. He is offered a cash payment now of $7,500,000, or 10 annual payments of $1,000,000.
Katarina [22]

Answer:

a) 5,6%

b)$16 191 937.48

Explanation:

Download docx
7 0
3 years ago
Douglas can afford 240$ a month for five years for a car loan. If the APR is 8.5%, how much can he afford to borrow to purchase
SVETLANKA909090 [29]

Answer:

Douglas can afford 21697.88 to borrow to purchase a car.

Explanation:

As the formula for calculating present value is given as:

PV = PMT * ( (1-(1+r)^-n) / r )

As Douglas can afford 240$ a month for five years for a car loan so

it means that payment = 240 $

As the APR is 8.5% which means after dividing by 12 the rate per month = 8.5%/12

Total number of Months = 5*12

Total number of Months = 60

Putting these values into the above formula, we get

PV = PMT * ( (1-(1+r)^-n) / r )

PV = 240 * ( (1-(1+8.5%/12)^-60) / (8.5%/12) )

PV = 11697.88

As the down payment = 10,000 so the total value of car

= 11697.88+10000

= 21697.88

Douglas can afford 21697.88 to borrow to purchase a car.

8 0
3 years ago
Widget Inc. manufactures widgets. The company has the capacity to produce​ 100,000 widgets per​ year, but it currently produces
gayaneshka [121]

Answer:

$62,100

Explanation:

Given that,

Sales price per unit = $ 40

Variable costs per​ unit:

Manufacturing = $ 23

Marketing and administrative = $ 8

Total fixed​ costs:

Manufacturing = $ 76,000  

Marketing and administrative = $24,000

Total incremental costs:

= Variable manufacturing + Variable marketing and administrative

= (6,900 × $23) + (6,900 × $8)

= $158,700 + $55,200

= $213,900

Incremental income:

= Incremental revenue - Total incremental costs

= (6,900 × $40) - $213,900

= $276,000 - $213,900

= $62,100

Therefore, the operating income increases by $62,100.

7 0
3 years ago
What is an example of a situation in which the cost of capacity is substantially more than the cost of waiting? What would the w
labwork [276]

Answer:

<em>Cost of Capacity, Cost of Waiting</em> and <em>Waiting Lines</em> which are concepts indicated in the question speaks to Queuing Theory under Operations Management.

The goal of studying this theory simply relates to Optimizing Efficiency.

Let's define the concepts highlighted in the question.

Capacity cost is defined as the total amount of expenses incurred by an organization to provide for or increase its ability to conduct business operations. It can also be referred to as the <em>cost of service</em>.

Cost of Waiting on the hand within the context indicated above is how much it costs a business to keep customers waiting.

The more customers leave without making a purchase or do not return because of frustrating wait times, the higher the waiting cost.

Waiting Line -  This is simply a line of people waiting to be attended to, or access a product or service. It could also refer to Assembly Line. Or simply, <em>a queue.</em>

Explanation:

Cost of Waiting plus Cost of Service equals Total Cost.

<u><em>An optimized situation</em></u><u> is where the total cost is at it's lowest</u>. Reducing capacity may reduce costs of service, but cause an upward spike loss of sales due to lost customers.

Excessive capacity, on the other hand, will reduce the loss of sales due to the loss of customers but lead to an increase in operating costs.

To answer the questions, an example of a situation in which the cost of capacity is substantially more than the cost of waiting is given below:

a) If One ATM can serve 3 customer in 2 Minutes, and ATM users arrive the ATM Gallery at the rate of 3 customers every 4 minutes, then haveing 5 ATM Machines installed at such a location would translate to higher cost of capacity in relation to cost of waiting (Assuming that the cost of purchasing the machines and profit accruable from the ATM use charges are not factors under consideration)

b) the waiting line in such a condition would be substantially smaller than an optimised gallery or close to zero

Cheers!

3 0
3 years ago
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