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2 years ago

6. Find the equation of the line that goes through the point (5,1) and has a slope of 0.

Mathematics

1 answer:

alekssr [168]2 years ago

8 0

Answer:

y = 1

Step-by-step explanation:

a line with a slope of zero is a horizontal line parallel to the x- axis with equation

y = c ( c is the value of the y- coordinates the line passes through )

the line passes through (5, 1 ) with y- coordinate 1 , then

y = 1 ← is the equation of the line

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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

inessss [21]

Answer:

The height of cone is decreasing at a rate of 0.085131 inch per second.

Step-by-step explanation:

We are given the following information in the question:

The radius of a cone is decreasing at a constant rate.

$\displaystyle\frac{dr}{dt} = -7\text{ inch per second}$

The volume is decreasing at a constant rate.

$\displaystyle\frac{dV}{dt} = -948\text{ cubic inch per second}$

Instant radius = 99 inch

Instant Volume = 525 cubic inches

We have to find the rate of change of height with respect to time.

Volume of cone =

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

Instant volume =

$525 = \displaystyle\frac{1}{3}\pi r^2h = \frac{1}{3}\pi (99)^2h\\\\\text{Instant heigth} = h = \frac{525\times 3}{\pi(99)^2}$

Differentiating with respect to t,

$\displaystyle\frac{dV}{dt} = \frac{1}{3}\pi \bigg(2r\frac{dr}{dt}h + r^2\frac{dh}{dt}\bigg)$

Putting all the values, we get,

$\displaystyle\frac{dV}{dt} = \frac{1}{3}\pi \bigg(2r\frac{dr}{dt}h + r^2\frac{dh}{dt}\bigg)\\\\-948 = \frac{1}{3}\pi\bigg(2(99)(-7)(\frac{525\times 3}{\pi(99)^2}) + (99)(99)\frac{dh}{dt}\bigg)\\\\\frac{-948\times 3}{\pi} + \frac{2\times 7\times 525\times 3}{99\times \pi} = (99)^2\frac{dh}{dt}\\\\\frac{1}{(99)^2}\bigg(\frac{-948\times 3}{\pi} + \frac{2\times 7\times 525\times 3}{99\times \pi}\bigg) = \frac{dh}{dt}\\\\\frac{dh}{dt} = -0.085131$

Thus, the height of cone is decreasing at a rate of 0.085131 inch per second.

3 0

3 years ago

What is the solution of the inequality shown<br> below?<br> y-1 > 0

kipiarov [429]

Answer:

y>1

Step-by-step explanation:

y-1 > 0

Add 1 to each side

y-1 +1> 0+1

y>1

7 0

3 years ago

What's the slope (0,4) and (-8,-1)

Tju [1.3M]

slope = y2-y1 over x2-x1

-1 - 4= -5

-8-0 - -8

so you get -5/-8

negative divided by negative = positive

slope = 5/8

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3 years ago

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A repairman charged $93.06. The price included 2 hours of labor and a $40 service charge.

NISA [10]

Answer:

$26.53

Step-by-step explanation:

93.06-40=53.06

53.06÷2=26.53

<h2><u><em>Could I please have Brainliest?</em></u></h2>

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3 years ago

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AlladinOne [14]

Answer:

the awnser is 24

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3 years ago