Write an equation in slope intercept form for a line that passed through the two points below (-4,7), (8,1)

A trough is 8 feet long and has perpendicular cross section in the shape of an isosceles triangle (point down) with base 1 foot

murzikaleks [220]

Answer:

Dh/dt = 0.082 ft/min

Step-by-step explanation:

As a perpendicular cross section of the trough is in the shape of an isosceles triangle the trough has a circular cone shape wit base of 1 feet and height h = 2 feet.

The volume of a circular cone is:

V(c) = 1/3 * π*r²*h

Then differentiating on both sides of the equation we get:

DV(c)/dt = 1/3* π*r² * Dh/dt (1)

We know that DV(c) / dt is 1 ft³ / 5 min or 1/5 ft³/min

and we are were asked how fast is the water rising when the water is 1/2 foot deep. We need to know what is the value of r at that moment

By proportion we know

r/h ( at the top of the cone 0,5/ 2) is equal to r/0.5 when water is 1/2 foot deep

Then r/h = 0,5/2 = r/0.5

r = (0,5)*( 0.5) / 2 ⇒ r = 0,125 ft

Then in equation (1) we got

(1/5) / 1/3* π*r² = Dh/dt

Dh/dt = 1/ 5*0.01635

Dh/dt = 0.082 ft/min

4 0

3 years ago

Which is a better estimate for the weight of a dresser?<br> 45 grams or 45 kilograms

STatiana [176]

45 grams is about 1/4 cup of water or maybe 1/4 cup of flour or uncooked rice would be 45 grams. Anyway it's not much.

Unless the dresser is made of paper, 45 grams is not enough. 45 kg though large (that's roughly 100 pounds if that's what you think in), the dresser might be found in the apartment where Sherlock Holmes lives. (The dresser is a piece of victorian furniture) it is much closer to what a modern dresser would weigh.

5 0

3 years ago

Draw a histogram for the intervals 17-19, 20-22, 23-25, and 26-28 using the following data: 19, 19, 27, 20, 27, 26, 25, 26, 18,

snow_lady [41]

Intervals are given to us

19, 19, 27, 20, 27, 26, 25, 26, 18, 27, 20, 24, 19, 21, 27, 23, 21, 17, 22, 22

From the given data we need to create a frequency table

From 17 - 19 there are 5 numbers. they are 19,19,19, 18, 17

From 20 -22 there are 6 numbers . they are 20, 20, 21, 21, 22, 22

From 23 - 25 there are 3 numbers. they are 23, 24, 25

From 26 to 28 there are 6 numbers . they are 27, 27, 26, 26, 27, 27

Histogram is attached below

4 0

3 years ago

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DO,K = (5, 0) (10, 0) The scale factor is 1/2 2 5

Lapatulllka [165]

If the preimage point is (5,0) and the image point is (10,0)
then the scale factor is k = 2

Basically the coordinates of the old point have doubled (multiplied by 2)

x = 5 is the old x coordinate
x = 10 is the new x coordinate (5*2 = 10)

y = 0 is the old y coordinate
y = 0 is the new y coordinate (0*2 = 0, no change)

3 0

3 years ago

PLEASE HELP HELPPPPPPPPP

professor190 [17]

Answer:

x+2y=- 7

x-2y =9

Step-by-step explanation:

Solving Steps

2x+4y=-14

x-2y=9

Divide both sides

(2x+4y) ÷2=-14=2

{x-2y=9

Remove the parentheses

Divide

2x÷2+4y÷2=-7

x-2y =9

Divide

Solution

x+2y=- 7

x-2y =9

5 0

2 years ago

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