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alex41 [277]
3 years ago
7

Please help i need it now:)

Mathematics
1 answer:
NikAS [45]3 years ago
4 0
A: 40

B:400

C:4000

D:40000
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A tank holds 300 gallons of water and 100 pounds of salt. A saline solution with concentration 1 lb salt/gal is added at a rate
Shkiper50 [21]

The amount of salt in the tank changes with rate according to

Q'(t)=\left(1\dfrac{\rm lb}{\rm gal}\right)\left(4\dfrac{\rm gal}{\rm min}\right)-\left(\dfrac{Q(t)}{300+(4-1)t}\dfrac{\rm lb}{\rm gal}\right)\left(1\dfrac{\rm gal}{\rm min}\right)

\implies Q'+\dfrac Q{300+3t}=4

which is a linear ODE in Q(t). Multiplying both sides by (300+3t)^{1/3} gives

(300+3t)^{1/3}Q'+(300+3t)^{-2/3}Q=4(300+3t)^{1/3}

so that the left side condenses into the derivative of a product,

\big((300+3t)^{1/3}Q\big)'=4(300+3t)^{1/3}

Integrate both sides and solve for Q(t) to get

(300+3t)^{1/3}Q=(300+3t)^{4/3}+C

\implies Q(t)=300+3t+C(300+3t)^{-1/3}

Given that Q(0)=100, we find

100=300+C\cdot300^{-1/3}\implies C=-200\cdot300^{1/3}

and we get the particular solution

Q(t)=300+3t-200\cdot300^{1/3}(300+3t)^{-1/3}

\boxed{Q(t)=300+3t-2\cdot100^{4/3}(100+t)^{-1/3}}

5 0
3 years ago
2X(X+y) + 2y(3X-y)<br> Please help me
tankabanditka [31]

Answer:

2x^2 + 8xy - 2y^2

Step-by-step explanation:

2X(X+y) + 2y(3X-y)

2x^2 + 2xy + 6yx - 2y^2

2x^2 + 8xy - 2y^2

7 0
3 years ago
Need help asap please ​
nalin [4]

Answer:

15 yd^2

Step-by-step explanation:

a= 1/2bh

a= 1/2(3)10

a= 1/2(30)

a= 15

8 0
4 years ago
Read 2 more answers
Divide: 407:10<br> Guys I need help I don’t know how to do divide SOMEONE HELP ME QUICKLY!!!
katen-ka-za [31]

Answer:

40

7 Remainder

7 0
3 years ago
Read 2 more answers
In the function f(x) = 5(x2 − 4x + ____) + 15, what number belongs in the blank to complete the square?
Georgia [21]
If you would like to find the number which belongs in the blank to complete the square, you can calculate this using the following steps:

f(x) = 5(x^2 - 4x + a) + 15
a ... the number = ?

<span>x^2 - 4x + a = (x - 2)^2 = x^2 - 4x + 4
</span>a = 4

The correct result would be 4.
5 0
3 years ago
Read 2 more answers
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