Mathematics, 26.03.2021 05:40 sjackson0625p8w1a0

The radius of a right circular cone is increasing at a rate of 1.9 in/s while its height is decreasing at a rate of 2.2 in/s. At what rate is the volume of the cone changing when the radius is 134 in. and the height is 136 in.

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Answer from: probablyacommunist

Volume of the cone is increasing at the rate $9916\pi \frac{in^3}{s}$ .

Step-by-step explanation:

Given: The radius of a right circular cone is increasing at a rate of 1.9 in/s while its height is decreasing at a rate of 2.2 in/s.

To find: The rate at which volume of the cone changing when the radius is 134 in. and the height is 136 in.

Solution:

We have,

$\frac{dr}{dt} =1.9 \:\text{in/s}$ , $\frac{dh}{dt}=-2.2\:\text{in/s}$ , $r=134 \:\text{in}$ , $h=136\:\text{in}$

Now, let be the volume of the cone.

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

Differentiate with respect to .

$\frac{dv}{dt} =\frac{1}{3}\pi \left [ r^2\frac{dh}{dt}+h\left ( 2r \right )\frac{dr}{dt} \right ]$

Now, on substituting the values, we get

$\frac{dv}{dt} =\frac{1}{3}\pi\left [ \left ( 134 \right )^2\left ( -2.2 \right )+\left ( 136\right )\left ( 2 \right )\left ( 134 \right )\left ( 1.9 \right ) \right ]$

$\frac{dv}{dt} =\frac{1}{3}\pi\left [ -39503.2+69251.2 \right ]$

$\frac{dv}{dt} =\frac{1}{3}\pi\left [ 29748 \right ]$

$\frac{dv}{dt} =9916\pi \frac{in^3}{s}$

Hence, the volume of the cone is increasing at the rate $9916\pi \frac{in^3}{s}$ .

Answer from: Quest

answer:

payment just for service

→

87.12

payment for service including tax

→

94.09

explanation:

service only with 20% tip

→

72.6

(

100

)

87.12

in the opening of the question the word 'service' is associated only with the pretax value.

the closing part of the question asks: how much did she pay for the

service

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so technically the answer is

→

72.6

(

100

)

87.12

however, the intention of the question provider may have been that your answer is to be

87.12

(

100

)

94.09

to 2 decimal places.

payment just for service

→

87.12

payment for service including tax

→

94.09

tony b

mar 21, 2017

answer:

trying to explain it another way

explanation:

service charge

→

72.60

20% tip

100

72.60

14.52

−−−−−−

←

add

87.12

tax

100

87.12

6.97

−−−−−

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add

94.09

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