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xz_007 [3.2K]
3 years ago
10

A triangle has sides of (2x), (x - 7) and (3x - 20).

Mathematics
1 answer:
LiRa [457]3 years ago
7 0
2x+x-7+3x-20=87cm
6x-27=87
6x=114
x=19
Therefore the sides are:12cm, 38cm, and 37cm
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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
An equation and the steps it are shown below: 4x
Svetlanka [38]

You have to give every thing that the problem says for me to be able to figure it out.

6 0
3 years ago
for a different punch recipe, the equation,s=4c represents the number of cups of seltzer,s, that you need for,c, cups of cranber
asambeis [7]

Answer:

4

Step-by-step explanation:

If two variables are proportional then

y\propto x

y=kx    ...(i)

where, k is constant of proportionality.

The given equation is

s=4c       ...(ii)

where,

s = number of cups of seltzer.

c = cups of cranberry juice.

On comparing (i) and (ii), we get

Independent variable: x=c

Dependent variable: y=s

Constant of proportionality: k=4

Therefore, the constant of proportionality is 4.

8 0
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Please help me ASAP
miskamm [114]

Answer:

540 m so yaaaaàaaaaaaaaaaaaaaaa

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2 years ago
Explain why the equation 5丨x丨-7=7 has only one solution?
Rama09 [41]
The answer to this question that you have me would be 5|x|-7=7 will equal to x=2
6 0
3 years ago
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