Write the facts family numbers 15,5,and 3

The volume of a hemisphere is 144 pi. Find the radius and total surface area.

sineoko [7]

Formula of the Volume of a hemisphere:
V = $\frac{2}{3}$ $\pi$ r³
144 $\pi$ = $\frac{2}{3}$ $\pi$ r³
Multiply by 3 to cancel fraction in the right side
144 $\pi$ × 3 = 2 $\pi$ r³
432 $\pi$ = 2 $\pi$ r³
Divide by 2 $\pi$ on either sides to isolate r³
$\frac{432 \pi }{2 \pi }$ = $\frac{2 \pi }{2 \pi }$ r³
2 $\pi$ and $2 \pi$ cancel out
216 = r³
Take cube root to find the radius
$\sqrt[3]{216}$ = $\sqrt[3]{r^3}$
6 = r
Radius is 6 units

The formula of the surface area of a hemisphere is:
S.A = 2 $\pi$ r² + $\pi$ r²
= $2\pi$ (6)² + $\pi$ (6)²
=2 $\pi$ × 36 + 36 $\pi$
= 72 $\pi$ + 36 $\pi$
= 108 $\pi$ units² (in terms of $\pi$ )
≈ 339.12 units²

Surface area = 108 $\pi$ units

8 0

3 years ago

Riangle XYZ was dilated by a scale factor of 2 to create triangle ACB and sin ∠X = 5 over 5 and 59 hundredths.

DochEvi [55]

Answer:

Step-by-step explanation:

1. Part A: We know parts of our triangle since the cosine of X is given. XY = 2.5 and XZ = 5.59 and since it is a scale factor of 2, ABC is most likely similar to XYZ by angle measures and the special relationship is, that they are all equal, because with a scale factor of two, all the ratios in triangle ABC will simplify to the ratios of triangle XYZ.

Part B: Because triangle XYZ was dilated with a scale factor of 2 to create triangle ABC, just multiply the sides by 2 to get the sides AC and CB, which is AB = 2 times XY and CB = 2 times XZ.

2. We can first find the hypothenuse by adding squaring 8 and 6 to have 100. Then square root it to have 10 as our hypothenuse

Now we can use sin x = 6/10 and cos y = 6/10

3. Since this is using the angle of elevation, we can say that the length of side AB is perpendicular from the perspective of angle of elevation, and the hypotenuse's length is known, so in this case, we can use a sine or cosecant ratio.

Sin(40 Degrees) = AB/100

AB = 100 x sin(40 Degrees) ft

AB ~ 64.28 ft which can be rounded to 64 ft

The triangle I drew was a right triangle with points A, B, and C. 40 is on point C while 100 ft was on the hypotenuse. The kite was near A and the ground was between segment B and C.

4. Since the angle and Adjacent line is given and it is asking us to find H which is the opposite, we well try and be using Tangent = opposite/adjacent

500 ft Multiply by tan39 = 405 (Estimated after rounding to nearest hundreth 404.892).

To be honest, I didn't know so much about these questions but this might give a better understanding and if I'm wrong then I apologize.

7 0

2 years ago

Does anyone have the answers for all?

Shkiper50 [21]

Answer and Step-by-step explanation:

1-6

a.

What you can do is plug in 6 and start by doing the first machine first, then the second. If this doesn't work, do the second machine, then the first machine.

The order that works is second machine, then first machine.

Second Machine:

y = $(6)^{2} -6$ = 36 - 6 = 30

Plug into first machine now.

First Machine:

y = $\sqrt{(30) - 5} = \sqrt{25} = 5$

We see that the result is 5.

b. If we were to do the order of second machine, then first machine, we will never get a negative result (or -5 for that matter), due to the fact that you can't algebraically square root a negative number.

However, if we were to do the order of first machine, second machine, we can get a negative number. To get -5, we plug in 6 for x in the first machine, getting an answer of 1. We plug this into the second machine, getting 1^2 - 6, which results in -5.

1-7. The absolute value of a value is the positive version of that value.

a. |54| = 54

b. $-|-7\frac{3}{5}|$ = $-7\frac{3}{5}$

c. |3| - |-1| = 3 - 1 = 2

d. |2.2 - 5.13| = |-2.93| = 2.93

1-8.

a.

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(5 boxes on each side)

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(6 boxes on each side)

b. The amount of squares on each side of the figure increases by 1.

c. There would be 1 square, because we know that the pattern is there is 2 squares added to the next figure, 1 at each end. If we go back a figure, we take away 2 squares.

1-9.

a. -42 - 17 = -59

b. 8 - (-9) = 8 + 9 = 17

c. 8(-9) = -72

d. -42 ÷ (-7) = 6

e. -2(-3)(-4) = 6(-4) = 24

f. -18 - 7 = -25

g. $(-5)^{2}$ = 25