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3 years ago

Find the exact area of the shaded region

Mathematics

1 answer:

GREYUIT [131]3 years ago

8 0

Answer:

B: 192pi - 144

Step-by-step explanation:

Area of the sector = (120/360) * pi * r^2

Area of the sector = 1/3 * pi * 24 * 24

Area of the sector = 192 * pi

Now to find the area of the triangle.

The triangle is an isosceles triangle That means two of its sides are equal. They are equal to the radius of the circle, which is 24.

the small angles are equal to

2x + 120 = 180 Subtract 120 from both sides

2x = 60 Divide by 2

x = 60/2

x = 30

The height of the triangle is derived from sin(30) = opposite / hypotenuse

sin(30) = 1/2

hypotenuse = 24

1/2 = opposite / hypotenuse

1/2 = opposite / 24 Multiply both sides by 24

1/2 * 24 = opposite

opposite = 12

The height = 12

r = 24

Area of the triangle = 1/2 * 12 * 24

Area of the triangle = 144

So the area of the shaded area = 192*pi - 144 which looks like B

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Find the standard form of the equation of the parabola with a vertex at the origin and a focus at (0, -7).

creativ13 [48]

So hmm check the picture below

we know the vertex is at the origin, and the focus point is below it, that means two things, the parabola is vertical and it's opening downwards

notice the distance "p", from the vertex to the focus point, is just 7 units, however, since the parabola is opening downwards, the "p" value will be negative, so p = -7

$\bf \textit{parabola vertex form with focus point distance}\\\\
\begin{array}{llll}
(y-{{ k}})^2=4{{ p}}(x-{{ h}}) \\\\
\boxed{4{{ p}}(y-{{ k}})=(x-{{ h}})^2 }\\
\end{array}
\qquad 
\begin{array}{llll}
vertex\ ({{ h}},{{ k}})\\\\
{{ p}}=\textit{distance from vertex to }\\
\qquad \textit{ focus or directrix}
\end{array}\\\\
-------------------------------\\\\
4{{ p}}(y-{{ k}})=(x-{{ h}})^2\quad 
\begin{cases}
h=0\\
k=0\\
p=-7
\end{cases}\implies 4(-7)(y-0)=(x-0)^2
\\\\\\
-28y=x^2\implies y=-\cfrac{1}{28}x^2$

8 0

3 years ago

Johan and his friends go apple picking Jonah fills 5 baskets each basket holds15 apples. If 4 of Jonah’s friends pick the same a

11Alexandr11 [23.1K]

Answer:

the answer is 75

Step-by-step explanation:in total there are 5 full baskets and each holds 15 apples so 15 x 5 =75 and that is your answer.

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3 years ago

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Archy [21]

17 books in total, and 8 new. To find the number of used books, we subtract 8 from 17.

17-8= 9 used books

Now we have 8 new books and 9 used books.

All books: 17
Used books: 9
New books: 8

(a) all books: used books
17: 9

(b) new books: used books
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2 years ago

Read 2 more answers

36, 27, <br> 81<br> 4<br> Find the 10th term.

zaharov [31]

a_{10} = \frac{177147}{65536} is solution of arithmetic progression (AP).

What is arithmetic progression (AP) in math?

The difference between any two consecutive numbers in an arithmetic progression (AP) is always a fixed amount.
The AP cost per invoice is calculated by dividing the total number of invoices paid over a certain time period by all the expenditures incurred to pay those invoices over that same time period.
An accurate assessment of a company's AP efficiency can be made using this metric in conjunction with other accounts payable measures.

Write the general term through the pattern $a_{n} = 36( \frac{3}{4} )^{n-1}$

Substitute and calculate $a_{10} = \frac{177147}{65536}$

Learn more about arithmetic progression (AP)

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1 year ago

20 POINTS

Brut [27]

Answer:

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Step-by-step explanation:

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3 years ago