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3 years ago

Find the square root of 167281 by division method

Mathematics

1 answer:

tensa zangetsu [6.8K]3 years ago

6 0

Answer:

square root of 167281 is 409

Here's the Step-by-step explanation using division:

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a medium apple has 72 calories. This is 3/4 of the calories in a medium banana. How many calories does a medium banana have?

qaws [65]

The banana had 54 calories

8 0

3 years ago

Write and solve a system of linear equations: The larger of two numbers is 18 more than 5 times the smaller. If 3 times the larg

marshall27 [118]

Answer:

8 and -2

Step-by-step explanation:

Let the numbers be l and s.

We have equations:

l = 5s + 18

3l + 4s = 16

Solve for s by substituting l into the second equation:

3(5s + 18) + 4s = 16

15s + 54 + 4s = 16

19s = 16 - 54

19s = -38

s = -38/19

s = -2

Find the value of l:

l = 5(-2) + 18

l = -10 + 18

l = 8

3 0

2 years ago

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

1 year ago

deposited $175 each month the balance of the savings account in 5 years will be $12,100.how much of the final balance will come

Ugo [173]

Answer:

$1,600

Step-by-step explanation:

To find out how much of the final balance will come from the interest earned, you have to determine the total value of the deposits made and subtract this from the balance the account will have after 5 years.

amount deposited each month: $175

months: 12*5= 60

Total amount deposited: $175*60= $10,500

Interests: $12,100-$10,500= $1,600

According to this, the amount of the final balance that will come from the interest earned is $1,600.

4 0

2 years ago

Write an equality that represents the graph below:<br><br> (help me quick please)

insens350 [35]

Answer:

Step-by-step explanation:

It's a solid dot that's going left, so it's less than or equal to. What integer is it on? -2. So it is either less than or equal to -2.

4 0

2 years ago

Read 2 more answers