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2 years ago

Find the x- and y-intercepts of the linear function. -8 - 2x + 4y = 0

Mathematics

1 answer:

almond37 [142]2 years ago

4 0

Answer: x-2y=-4

Step-by-step explanation:

Move the constant to the righthand side and change its sign (-2x=4y+8)
Change the signs on both sides of the equation (x-2y=-4)
Divide both sides of the equation by 2 (-x+2y=4)
<u><em>Solution: x-2y=-4</em></u>

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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

Which equation shows the value of -2/5-(-9/15)

enot [183]

Answer:

Step-by-step explanation:

-2/5 - (-9/15) = -2/5 + 9/15.

both of those equations are equivalent.

hope this helps.

7 0

2 years ago

Read 2 more answers

The diameter of the attic is 18ft and its height is 18ft. What's is the volume of the space in the attic

Svet_ta [14]

I attached an image with the complete question.

Answer:
volume of attic = 1526.04 ft³

Explanation:
Volume of cone can be calculated using the following rule:
Volume = $\frac{1}{3}$ * area of base * height
Volume = $\frac{1}{3}$ * π * radius² * height
We are given that:
π = 3.14
radius = 18/2 = 9 ft
height = 18 ft

Substitute in the equation to get the volume as follows:
Volume = $\frac{1}{3}$ * 3.14 * (9)^2 * (18) = 1526.04 ft³

Hope this helps :)

5 0

3 years ago

Which angles are pairs of corresponding angles? check all that Apply.

miskamm [114]

Answer:

k i all uc la if u do this now nu will fry ud hedbhedbhgebcyhegfyebc

Step-by-step explanation:

bcyhebvcvbehcbe nhbdwgef che bhcb hsg ge hdbhuj eh

4 0

3 years ago

Factor 7u-14!!????????

Whitepunk [10]

U=2 Becuase you have to get u bye itself

5 0

2 years ago