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3 years ago

When CP = Rs 1250 and SP = Rs 1500, find profit or loss percent ?

Mathematics

1 answer:

Alex Ar [27]3 years ago

6 0

Answer:

profit=20%

Step-by-step explanation:

profit%=sp-cp/cp×100%

=1500-1250/1250×100

=250/1250×100

=20%

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A 75-gallon tank is filled with brine (water nearly saturated with salt; used as a preservative) holding 11 pounds of salt in so

Debora [2.8K]

Let $A(t)$ = amount of salt (in pounds) in the tank at time $t$ (in minutes). Then $A(0) = 11$ .

Salt flows in at a rate

$\left(0.6\dfrac{\rm lb}{\rm gal}\right) \left(3\dfrac{\rm gal}{\rm min}\right) = \dfrac95 \dfrac{\rm lb}{\rm min}$

and flows out at a rate

$\left(\dfrac{A(t)\,\rm lb}{75\,\rm gal + \left(3\frac{\rm gal}{\rm min} - 3.25\frac{\rm gal}{\rm min}\right)t}\right) \left(3.25\dfrac{\rm gal}{\rm min}\right) = \dfrac{13A(t)}{300-t} \dfrac{\rm lb}{\rm min}$

where 4 quarts = 1 gallon so 13 quarts = 3.25 gallon.

Then the net rate of salt flow is given by the differential equation

$\dfrac{dA}{dt} = \dfrac95 - \dfrac{13A}{300-t}$

which I'll solve with the integrating factor method.

$\dfrac{dA}{dt} + \dfrac{13}{300-t} A = \dfrac95$

$-\dfrac1{(300-t)^{13}} \dfrac{dA}{dt} - \dfrac{13}{(300-t)^{14}} A = -\dfrac9{5(300-t)^{13}}$

$\dfrac d{dt} \left(-\dfrac1{(300-t)^{13}} A\right) = -\dfrac9{5(300-t)^{13}}$

Integrate both sides. By the fundamental theorem of calculus,

$\displaystyle -\dfrac1{(300-t)^{13}} A = -\dfrac1{(300-t)^{13}} A\bigg|_{t=0} - \frac95 \int_0^t \frac{du}{(300-u)^{13}}$

$\displaystyle -\dfrac1{(300-t)^{13}} A = -\dfrac{11}{300^{13}} - \frac95 \times \dfrac1{12} \left(\frac1{(300-t)^{12}} - \frac1{300^{12}}\right)$

$\displaystyle -\dfrac1{(300-t)^{13}} A = \dfrac{34}{300^{13}} - \frac3{20}\frac1{(300-t)^{12}}$

$\displaystyle A = \frac3{20} (300-t) - \dfrac{34}{300^{13}}(300-t)^{13}$

$\displaystyle A = 45 \left(1 - \frac t{300}\right) - 34 \left(1 - \frac t{300}\right)^{13}$

After 1 hour = 60 minutes, the tank will contain

$A(60) = 45 \left(1 - \dfrac {60}{300}\right) - 34 \left(1 - \dfrac {60}{300}\right)^{13} = 45\left(\dfrac45\right) - 34 \left(\dfrac45\right)^{13} \approx 34.131$

pounds of salt.

7 0

2 years ago

A person invests 10000 dollars in a bank. The bank pays 4.5% interest compounded

Greeley [361]

The person would have to leave the money in the bank for 7.8 years for it to reach 13,500 dollars.

Step-by-step explanation:

Step 1; First we must calculate how much interest is generated for a single year. The annual interest rate is 4.5% i.e. 4.5% of 10,000 dollars which equals 0.045 × 10,000 = 450 dollars a year. As the years pass, more and more will be put into the account due to interest.

Step 2; For there to be 13,500 dollars in the bank account we need to calculate how much money is added due to interest.

The money needed to be added through interest = 13,500 - 10,000 = 3,500 dollars.

So we need to determine how long it will take for the bank to add 3,500 dollars by adding 450 dollars a year.

The number of years to reach 13,500 dollars = $\frac{3,500}{450}$ = 7.777 years. By rounding this value to the nearest tenth, we get 7.8 years.

7 0

3 years ago

Ira bought a tennis racquet that cost $112. The sales tax rate is 9 percent. What is the total amount that she paid?

zvonat [6]

Wouldnt 9% bc 9 cents ?

5 0

3 years ago

Professor Goodheart has two exams, exam 1 and exam 2. The exam 1 weights 40% and the exam 2 weights 60% of the final grades. Put

garri49 [273]

Answer:

Imperfect substitutes

explanation:

The choices above are not perfect substitutes, meaning they can not be perfectly or directly replace the other. Imperfect substitutes are close substitutes but not perfect substitutes. Unlike perfect substitutes, imperfect substitutes satisfies same utility but has different characteristics and therefore not entirely substitutable. For example, while one may want to have the 40 marks too, he'd rather have 60 marks even if the criteria for a 60 mark score was increasingly hard.

8 0

3 years ago

50 POINTS!! PLEASE HELP ASAP

natita [175]

Answer:

D. Miko found an incorrect quotient and checked her work using multiplication incorrectly

Step-by-step explanation:

We are given the equation

$\frac{5}{\frac{5}{3} }$