This questions worth 25 points to whoever helps me with it!

Mathematics

1 answer:

Anastasy [175]3 years ago

7 0

V=1750(1/5)^3

V=1750/125

V=14 ft^3

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Gravel is being dumped from a conveyor belt at a rate of 20 ft3/min, and its coarseness is such that it forms a pile in the shap

11Alexandr11 [23.1K]

Answer:

0.25 feet per minute

Step-by-step explanation:

Gravel is being dumped from a conveyor belt at a rate of 20 ft3/min. Since we are told that the shape formed is a cone, the rate of change of the volume of the cone.

$\dfrac{dV}{dt}=20$ ft^3/min$

$\text{Volume of a cone}=\dfrac{1}{3}\pi r^2 h$

Since base diameter = Height of the Cone

Radius of the Cone = h/2

Therefore,

$\text{Volume of the cone}=\dfrac{\pi h}{3} (\dfrac{h}{2}) ^2 \\V=\dfrac{\pi h^3}{12}$

$\text{Rate of Change of the Volume}, \dfrac{dV}{dt}=\dfrac{3\pi h^2}{12}\dfrac{dh}{dt}$

Therefore: $\dfrac{3\pi h^2}{12}\dfrac{dh}{dt}=20$

We want to determine how fast is the height of the pile is increasing when the pile is 10 feet high.

$h=10$ feet$\\\\\dfrac{3\pi *10^2}{12}\dfrac{dh}{dt}=20\\25\pi \dfrac{dh}{dt}=20\\ \dfrac{dh}{dt}= \dfrac{20}{25\pi}\\ \dfrac{dh}{dt}=0.25$ feet per minute (to two decimal places.)$

When the pile is 10 feet high, the height of the pile is increasing at a rate of 0.25 feet per minute

5 0

3 years ago

7x - 2 = 2y 3x = 2y - 1

77julia77 [94]

7x - 2 = 2y
7x = 2y + 2
so
7x = 2y + 2
3x = 2y - 1
----------------subtract
4x = 3
x = 3/4

7x - 2 = 2y
7(3/4) - 2 = 2y
21/4 - 2 = 2y
21/4 - 8/4 = 2y
13/4 = 2y
so
y = 13/4 * 1/2
y = 13/8

answer
(3/4, 13/8)

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4 years ago

Please help! if anybody is good at equivalent polynomial expressions please help!!

scoundrel [369]

The one you have highlighted is correct

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3 years ago

A line has a slope of –3 and a y-intercept of (0, –1). What is the equation of the line that is parallel to the given line and p

elena-s [515]

The equation of the parallel line is y= -3x -3

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4 years ago