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joja [24]
3 years ago
13

In ΔABC, if AB = 10 and BC = 6, AC can NOT be equal to

Mathematics
1 answer:
Goshia [24]3 years ago
6 0

Answer:

16

Step-by-step explanation:

adding any two sides of a triangle is allways greater than the third side

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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
Help pls (10 POINTS) What fraction is less than the fraction represented by the model?​
goblinko [34]

Answer:

2/4

Step-by-step explanation:

It’s very easy

6 0
2 years ago
1439<br> 31<br> a. 71.9<br> b. 62<br> c. 56.3<br> d. 42.4<br> Solve for x
Tcecarenko [31]

Answer:

C26 is also a Category of EAD (Employment Authorization Document) provided to immigrant workers in U.S. These are dependents of H1b visa holders commonly referred to as H4-EAD.

Step-by-step explanation:

3 0
2 years ago
Help me please thanks
Tcecarenko [31]

Answer:

+/- x over 12

Step-by-step explanation:

5 0
2 years ago
Read 2 more answers
Is 8 a solution to 3 over 4 x = 6
SSSSS [86.1K]

Answer:

Yes, 8 is a solution

Step-by-step explanation:

<u>Step 1:  Check if solution</u>

<u />\frac{3}{4} x = 6

\frac{3}{4} (8) = 6

\frac{24}{4} = 6

6=6

Answer:  Yes, 8 is a solution

6 0
3 years ago
Read 2 more answers
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