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2 years ago

I need serious help. Please

Mathematics

2 answers:

Juli2301 [7.4K]2 years ago

7 0

By definition of supplementary angles, m<1 + m<2 = 180 (a)
and m<2 + m<3 = 180 (b)
Then, m<1 + m<2 = m<2 + m<3 by definition of supplementary angles (c)
Subtract m<2 from each side. You get m<1 = m<3 (d) or <1 =~ <3 (e)

Leto [7]2 years ago

5 0

A is 180 degrees, B is 180 degrees, C is definition of complementary angle, D is 180-angle 2, and E is angle 3.

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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

Question 2 (essay worth 10 points)

Sliva [168]

The sample space for the arrangement of a jazz CD (J), a pop CD (P), and a rock CD (R) is {JPR, JRP, PJR, PRJ, RJP, RPJ}.

<h3>What is permutation and combination?</h3>

A permutation is the number of different ways a set can be organized; order matters in permutations, but not in combinations.

We have:

Minni is arranging 3 different music CDs in a row on a shelf.

Three CDs are a jazz cd (j), a pop cd (p), and a rock cd (r).

The sample space means all the possible ways to arrange the CDs.

Total arramgement = 3! = 3×2×1 = 6

The sample space for the arrangement of a jazz CD (J), a pop CD (P), and a rock CD (R) is:

{JPR, JRP, PJR, PRJ, RJP, RPJ}

Thus, the sample space for the arrangement of a jazz CD (J), a pop CD (P), and a rock CD (R) is {JPR, JRP, PJR, PRJ, RJP, RPJ}.

Learn more about permutation and combination here:

brainly.com/question/2295036

#SPJ1

4 0

1 year ago

Which number line shows the solutions to 1/2 x -2 > 0

Mkey [24]

Answer:

The top choice

Step-by-step explanation:

1/2 x -2 > 0

Add 2 to each side

1/2 x -2+2 > 0+2

1/2 x > 2

Multiply each side by 2

1/2 x *2 > 2*2

x > 4

There is an open circle at 4 and the line goes to the right

5 0

2 years ago

Read 2 more answers

Click on the table(s) of values that represent a function.

GrogVix [38]

Answer:

Data set 1

Step-by-step explanation:

Because for every x there is only one y

6 0

2 years ago

Need help :))))))))

tatiyna

easy

No need to explain

6 0

2 years ago