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musickatia [10]
3 years ago
12

What is (4p-1) squared

Mathematics
1 answer:
ahrayia [7]3 years ago
5 0


(4p-1)(4p-1)

=16p^2 - 4p - 4p +1

=16p^2 -8p +1 (That's your answer)

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A 1000-liter (L) tank contains 500 L of water with a salt concentration of 10 g/L. Water with a salt concentration of 50 g/L flo
djverab [1.8K]

Answer:

a) y(t)=50000-49990e^{\frac{-2t}{25}}

b) 31690.7 g/L

Step-by-step explanation:

By definition, we have that the change rate of salt in the tank is \frac{dy}{dt}=R_{i}-R_{o}, where R_{i} is the rate of salt entering and R_{o} is the rate of salt going outside.

Then we have, R_{i}=80\frac{L}{min}*50\frac{g}{L}=4000\frac{g}{min}, and

R_{o}=40\frac{L}{min}*\frac{y}{500} \frac{g}{L}=\frac{2y}{25}\frac{g}{min}

So we obtain.  \frac{dy}{dt}=4000-\frac{2y}{25}, then

\frac{dy}{dt}+\frac{2y}{25}=4000, and using the integrating factor e^{\int {\frac{2}{25}} \, dt=e^{\frac{2t}{25}, therefore  (\frac{dy }{dt}+\frac{2y}{25}}=4000)e^{\frac{2t}{25}, we get   \frac{d}{dt}(y*e^{\frac{2t}{25}})= 4000 e^{\frac{2t}{25}, after integrating both sides y*e^{\frac{2t}{25}}= 50000 e^{\frac{2t}{25}}+C, therefore y(t)= 50000 +Ce^{\frac{-2t}{25}}, to find C we know that the tank initially contains a salt concentration of 10 g/L, that means the initial conditions y(0)=10, so 10= 50000+Ce^{\frac{-0*2}{25}}

10=50000+C\\C=10-50000=-49990

Finally we can write an expression for the amount of salt in the tank at any time t, it is y(t)=50000-49990e^{\frac{-2t}{25}}

b) The tank will overflow due Rin>Rout, at a rate of 80 L/min-40L/min=40L/min, due we have 500 L to overflow \frac{500L}{40L/min} =\frac{25}{2} min=t, so we can evualuate the expression of a) y(25/2)=50000-49990e^{\frac{-2}{25}\frac{25}{2}}=50000-49990e^{-1}=31690.7, is the salt concentration when the tank overflows

4 0
3 years ago
X^3+y^3=???????????????
omeli [17]

Answer:

Well since we don't know what X or Y is, then we can't answer this question.

Step-by-step explanation:

6 0
2 years ago
A circle has a radius of 13in . find the radian measure of the central angle ? that intercepts an arc of length 15in
steposvetlana [31]
Find the circumference which is 2*3.14*13 and then usethe central angle formula
7 0
3 years ago
A car travels 120 miles in 2.5 hours (with a constant speed). What is the car's
kipiarov [429]

Answer:

48

Step-by-step explanation:

120 divided by 2.5 = 40

5 0
3 years ago
Read 2 more answers
THE QUESTION IS DOWN BELOW.<br>major points when given branliest
emmainna [20.7K]

The ratios are Surface area ⇒ 4 : 25 Height ⇒ 2 : 5 and Volume ⇒ 8 : 125

<h3>How to determine the ratios?</h3>

The scale factor is given as:

m : n = 2 : 5

For the area, we take the square of the ratios.

i.e.

Area = 2^2 : 5^2

Evaluate

Area = 4 : 25

For the volume, we take the cube of the ratios.

i.e.

Volume = 2^3 : 5^3

Evaluate

Volume = 8 : 125

The given scale factor can be used for the height of the model and the original bicycle

Hence, the ratios are

Surface area ⇒ 4 : 25

Height ⇒ 2 : 5

Volume ⇒ 8 : 125

Read more about ratios at:

brainly.com/question/13419413

#SPJ1

7 0
1 year ago
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