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3 years ago

How to get the y intercept in a word problem

Mathematics

1 answer:

saw5 [17]3 years ago

5 0

You have to equal x to zero than solve

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A filter filled with liquid is in the shape of a vertex-down cone with a height of 9 inches and a diameter of 6 inches at its op

Alina [70]

Answer: Level of the liquid dropping at 28.28 inch/second when the liquid is 2 inches deep.

Step-by-step explanation:

Since we have given that

Height = 9 inches

Diameter = 6 inches

Radius = 3 inches

So, $\dfrac{r}{h}=\dfrac{3}{9}=\dfrac{1}{3}\\\\r=\dfrac{1}{3}h$

Volume of cone is given by

$V=\dfrac{1}{3}\pi r^2h\\\\V=\dfrac{1}{3}\pi \dfrac{1}{9}h^2\times h\\\\V=\dfrac{1}{27}\pi h^3$

By differentiating with respect to time t, we get that

$\dfrac{dv}{dt}=\dfrac{1}{27}\pi \times 3\times h^2\dfrac{dh}{dt}=\dfrac{1}{9}\pi h^2\dfrac{dh}{dt}$

Now, the liquid drips out the bottom of the filter at the constant rate of 4 cubic inches per second, ie $\dfrac{dv}{dt}=-4\ in^3$

and h = 2 inches deep.

$-4=\dfrac{1}{9}\times \pi\times (2)^2\dfrac{dh}{dt}\\\\-9\pi =\dfrac{dh}{dt}\\\\-28.28=\dfrac{dh}{dt}$

Hence, level of the liquid dropping at 28.28 inch/second when the liquid is 2 inches deep.

7 0

3 years ago

Help me I really need to get this done

posledela

Answer:

It’s the second one

Step-by-step explanation:

6 0

2 years ago

I need help desperitly

topjm [15]

Number one is 12. There is 12 cubes.

8 0

3 years ago

How much water should be added to 3 gallons of pure acid in order to obtain the 15% acid solution? HELP DUE BY TOMMOROW MORNING

Pani-rosa [81]

3 gallons of acid = 100% concentration acid
? (water+acid) gallons = 15 concentration acid

Note: Every gallon of water added reduces the percentage concentration of acid. Therefore, the relationship is inverse proportionality.

Solution:

Total number of gallons (water+acid) = (3*100)/15 = 20 gallons
Therefore, gallons of water = 20-3 = 17 gallons

5 0

3 years ago

Tina’s age, y, is 5 years more than her brother Tim’s age, x.

gogolik [260]

If you are asking for an equation for this statement, it would be y = x + 5

3 0

3 years ago

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