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anzhelika [568]

2 years ago

6

The radius of a cone is decreasing at a constant rate of 7 inches per second, and the volume is decreasing at a rate of 948 cubi

c inches per second. At the instant when the radius of the cone is 99 inches and the volume is 525 cubic inches, what is the rate of change of the height? The volume of a cone can be found with the equation V=13πr2h.V=31πr2h. Round your answer to three decimal places.

1 answer:

nadezda [96]2 years ago

8 0

Answer:

Step-by-step explanation:

We have volume of cone as

$V=\frac{1}{3} \pi r^2 h$

and for a cone always r/h = constant

Given that r' = rate of change of radius = -7 inches/sec

(Negative sign because decresing)

V' =- 948 in^3/sec

Radius = 99 inches and volume = 525 inches

Height at this instant = $\frac{525}{\frac{1}{3} \pi (99)^2} \\=\frac{0.1607}{\pi}$

Let us differentiate the volume equation with respect to t using product rule

$V=\frac{1}{3} \pi r^2 h\\V' = \frac{1}{3} \pi[2rhr'+r^2 h']\\-948 = \frac{1}{3} \pi[2(99)(-7)(\frac{0.1607}{\pi})+99^2 h']\\$

$-948 = \frac{1}{3} \pi[2(99)(-7)(\frac{0.1607}{\pi})+99^2 h']\\-948 = 33(3.14)(-2.25/3.14 + 99 h')\\-9.149=-0.72+99h'\\-8.429 = 99h'\\h' = 0.08514$

Rate of change of height = 0.08514 in/sec

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Gelneren [198K]

Answer:

General equation of line : $y = mx+c$ --1

Where m is the slope or unit rate

Table 1)

p d

1 3

2 6

4 12

d = Number of dollars (i.e.y axis)

p = number of pound(i.e. x axis)

First find the slope

First calculate the slope of given points

$m = \frac{y_2-y_1}{x_2-x_1}$ ---A

$(x_1,y_1)=(1,3)$

$(x_2,y_2)=(2,6)$

Substitute values in A

$m = \frac{6-3}{2-1}$

$m = 3$

Thus the unit rate is 3 dollars per pound.

So, It matches the box 1 (Refer the attached figure)

Equation 1 : $p=3d$

$\frac{p}{3}=d$

Since p is the x coordinate and d is the y coordinate

On Comparing with 1

$m = \frac{1}{3}$

Thus the unit rate is $\frac{1}{3}$ dollars per pound

So, It matches the box 2 (Refer the attached figure)

Equation 2 : $\frac{1}{3}d=3p$

$d=9p$

Since p is the x coordinate and d is the y coordinate

On Comparing with 1

$m =9$

Thus the unit rate is 9 dollars per pound

So, It matches the box 3 (Refer the attached figure)

Table 2)

p d

1/9 1

1 9

2 18

d = Number of dollars (i.e.y axis)

p = number of pound(i.e. x axis)

$(x_1,y_1)=(\frac{1}{9},1)$

$(x_2,y_2)=(1,9)$

Substitute values in A

$m = \frac{9-1}{1-\frac{1}{9}}$

$m = \frac{8}{frac{8}{9}}$

$m = 9$

Thus the unit rate is 9 dollars per pound

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3 0

3 years ago

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PLSSS HELP PANICKING

devlian [24]

Answer:

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Step-by-step explanation:

a systems of equations can be made from the information on the problem

x+y=48

x=2y+3

since x= 2y+3 substitute 2y+3 in the firat equation to get:

(2y+3)+y=48 -> 3y+3=48 -> 3y=45 -> y=15

plug in 15 for y in the second equation to solve for x

x+15 =48 --> x=33

8 0

2 years ago

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grigory [225]

Answer:

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2 years ago

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Hitman42 [59]

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2 years ago

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kvv77 [185]

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2 years ago

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