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3 years ago

Can you please show me the steps and solution to this problem?

1 answer:

4 0

M = - 7 - 3 / - 2 - 4
m = - 10 / - 6
m = 10/6
m = 5/3

y = 5/3x + c , (4,3)
3 = 5/3(4) + c
12 = 20 + 4c
4c = - 8
c = - 2
y = 5/3x - 2

i am a mathematics teacher. if anything to ask please pm me

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A sphere and a cylinder have the same radius and height. The volume of the cylinder is 21m. what is the volume of the sphere.

Goshia [24]

Answer:

The volume of the sphere is 14m³

Step-by-step explanation:

Given

Volume of the cylinder = $21m^3$

Required

Volume of the sphere

Given that the volume of the cylinder is 21, the first step is to solve for the radius of the cylinder;

<em>Using the volume formula of a cylinder</em>

The formula goes thus

$V = \pi r^2h$

Substitute 21 for V; this gives

$21 = \pi r^2h$

Divide both sides by h

$\frac{21}{h} = \frac{\pi r^2h}{h}$

$\frac{21}{h} = \pi r^2$

The next step is to solve for the volume of the sphere using the following formula;

$V = \frac{4}{3}\pi r^3$

Divide both sides by r

$\frac{V}{r} = \frac{4}{3r}\pi r^3$

Expand Expression

$\frac{V}{r} = \frac{4}{3}\pi r^2$

Substitute $\frac{21}{h} = \pi r^2$

$\frac{V}{r} = \frac{4}{3} * \frac{21}{h}$

$\frac{V}{r} = \frac{84}{3h}$

$\frac{V}{r} = \frac{28}{h}$

Multiply both sided by r

$r * \frac{V}{r} = \frac{28}{h} * r$

$V = \frac{28r}{h}$ ------ equation 1

From the question, we were given that the height of the cylinder and the sphere have equal value;

This implies that the height of the cylinder equals the diameter of the sphere. In other words

$h = D$ , where D represents diameter of the sphere

Recall that $D = 2r$

So, $h = D = 2r$

$h = 2r$

Substitute 2r for h in equation 1

$V = \frac{28r}{2r}$

$V = \frac{28}{2}$

$V = 14$

Hence, the volume of the sphere is 14m³

4 0

3 years ago

Read 2 more answers

The equation of a parabola is 18(y−5)2=x+3 . What are the coordinates of the focus? (−3, 7) (−5, 5) (−1, 5) (−3, 3)

aleksandrvk [35]

18(y-5)^2=x+3

do the algebra to make it into =x form

x=18y^2-180y+447

then you take the form of the focus, you can do the math

(-215/72, 5)

6 0

3 years ago

99 points AND BRAINLIEST answer to the person who can do this for me. I WILL REPORT ANY DUMB ANSWERS! PLEASE HELP ASAP!

Evgen [1.6K]

ΔADC ≅ ΔBCD (SAS congruency)

∠AED ≅ ∠BEC (opposite angles)

ΔAED ≅ ΔBEC (ASA congruency)

Therefore DE <span>≅ CE (corresponding sides of the two congruent triangles AED and BEC)</span>

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3 years ago

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Expression for six minus b

Zanzabum

Answer:

6-b

Step-by-step explanation:

I hope this helps, and have a great day! :D

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2 years ago

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