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3 years ago

Can someone please help me

Mathematics

1 answer:

ICE Princess25 [194]3 years ago

7 0

Answer:

Step-by-step explanation:

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A water tank is in the shape of a right circular cone as shown above. The diameter of the cone is 10 feet, and the height is 15

Vsevolod [243]

Answer:

The rate at which the height of the water tank is changing is approximately 0.4244 ft/hour

Step-by-step explanation:

The given parameters are;

The diameter of the cone = 10 feet

The height of the cone = 15 feet

The rate at which water is leaking from the tank, (dV/dt) = 12 ft³/h

The volume of water in the tank = 27·π cubic feet

The volume V of a right circular cone with radius r and height h = 1/3×π×r²×h

The rate of change of the volume, dV, with time dt is given as follows;

The radius of the cone when the volume of the water in the tank is 27·π cubic feet is given as follows;

1/3×π×r²×h = 27·π ft³

The ratio of the height to the radius of the cone is h/r = 15/5 = 3

h/r = 3

∴ r =h/3

The volume of the cone, V = 1/3×π×r²×h = 1/3×π×(h/3)²×h = 1/27×π×h³ = h³/27×π

dV/dt = dV/dh × dh/dt

Which gives;

12 = d(h³/27×π)/dh × dh/dt = π×h²/9 × dh/dt

dh/dt = 12/(π×h²/9)

At 27·π ft³ = 1/27×π×h³ ft³, we have;

27 = 1/27×h³

27² = h³

h = ∛27² = 9

∴ dh/dt = 12/(π×h²/9) = 12/(π×9²/9) = 12/(π×9) = 4/(3·π) ≈ 0.4244 ft/hour

The rate at which the height of the water tank is changing ≈ 0.4244 ft/hour.

6 0

3 years ago

− 4x − 7y = 15<br> 4x − 2y = − 6

BartSMP [9]

Answer:

x= -2 y= -1

Step-by-step explanation:

5 0

3 years ago

2) What is the area of the figure?

Lina20 [59]

Answer:

9+7+4+5= 25

Step-by-step explanation:

add up everything then get ur answer

8 0

3 years ago

Let g(x) = 4x − 4 + |x + 6|. find all values of a which satisfy the equation g(a) = 3a + 2. (enter your answers as a comma-separ

Leya [2.2K]

Try this explanation, if it is possible check it in other sources:

let 'z' common variable for g(x) and g(a).

Then 4z-4+|z+6|=3z+2; ⇔ z-6+|z+6|=0; ⇔ z∈(-oo;-6)∩{0}.

All the additional details are in the attachment.

answer: (-oo;-6)∩{0}

5 0

3 years ago

Find the equation in slope-intercept form that describes a line through (2, 4) with slope 0

Blizzard [7]

Answer:

y = 4

Step-by-step explanation:

We are to find an equation of a line that passes through (2,4) and has a slope of 0.

Taking another point (x,y) on the line.

Slope of a straight line = change in y ÷ change in x.

i.e $\frac{y - 4}{x - 2} = 0$

y - 4 = 0(x - 2)

y - 4 = 0

y = 4 (the equation of our line)

3 0

3 years ago

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