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3 years ago

Solve the system by substitution. y = 4x – 8 Y = 2x

Mathematics

1 answer:

enyata [817]3 years ago

4 0

first one if u solve for y is y=4x-8

solve for x is x =y/4+2

second one is if u solve for y is y=2x

if u solve for x is x =y/2

Step-by-step explanation:

hope this help

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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

musickatia [10]

Answer:

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 $V$ be the volume of the cone.

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

Differentiate with respect to $t$ .

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

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 $9916\pi \frac{in^3}{s}$ .

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Step-by-step explanation:

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