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3 years ago

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Mathematics

1 answer:

Tema [17]3 years ago

3 0

Answer:

Step-by-step explanation:

$\boxed{area \: of \: sector = \frac{1}{2} {r}^{2} θ }$

Radius= diameter ÷2

r= 32 ÷2

r= 16

$\frac{1}{2} {r}^{2} θ = \frac{512\pi}{3}$

Substitute r= 16,

$\frac{1}{2} ( {16}^{2} )(θ) = \frac{512\pi}{3}$

$128 \: θ = \frac{512\pi}{3} \\ θ = \frac{512\pi}{3} \div 128 \\ θ = \frac{512\pi}{384}$

Divide the denominator and numerator by 128:

$θ = \frac{4\pi}{3}$

Thus, the answer is B.

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Just help please need to pass

Anni [7]

Answer: $\frac{1}{10}$

Step-by-step explanation:

First, we need to find the common denominator

The easiest way to do this is by multiplying the two given denominators, which are 2 and 5.

2 × 5 = 10

So, our common denominator is 10. Then, multiply the numerators of the two fractions by 2 and 5. Here's why:

$\frac{3*2}{5*2}$ = $\frac{6}{10}$ We multiplied the top and bottom by 2 to make sure our new fraction stays equivalent to the original fraction.

Do the same thing for the other one:

$\frac{1*5}{2*5}$ = $\frac{5}{10}$

Finally, subtract the two fractions to find the difference between the two times:

$\frac{6}{10} -\frac{5}{10}$ = $\frac{1}{10}$

The reason we used the common denominator is because we can only add or subtract fractions if they have the same denominator.

7 0

3 years ago

Read 2 more answers

$49 jeans are 20% off, what is the sale price

madam [21]

Answer:

$39.2

Step-by-step explanation:

The sale price will be 20% of $49 subtracted from $49

That’s

20% /100% x $49

0.2 x $49

$9.8

Sale price = $49 - $9.8

= $39.2

The sale price is $39.2

8 0

4 years ago

Read 2 more answers

Louie is trying to find a rectangular canvas for his art project. Its height

Maru [420]

The length of the diagonal of the canvas is approximately 27 degrees.

The height of the rectangular canvas must reach 18 inches. It must form a 48 degrees angle with the diagonal at the top of the canvas.

<h3>Length of the diagonal Canvas</h3>

Therefore, the length of the diagonal can be found as follows:

Using trigonometric ratio,

cos ∅ = adjacent / hypotenuse

where

∅ = 48°

adjacent side = Height of the rectangle = 18 inches

hypotenuse = Length of the diagonal

Therefore,

cos 48° = 18 / h

cross multiply

h = 18 / cos 48°

h = 18 / 0.66913060635

h = 26.9005778976

length of the diagonal ≈ 27 inches

learn more on rectangle here: brainly.com/question/26099609?referrer=searchResults

8 0

3 years ago

¿give me the answer please?

nevsk [136]

Answer:

the volume is 60 cm cubed

Step-by-step explanation:

(5 x 8) / 2 x 3

5 x 8 = 40

40 / 2 = 20

20 x 3 = 60

6 0

3 years ago

Read 2 more answers

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