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dlinn [17]
3 years ago
10

A basketball team wants to paint half of a free-throw circle grey. If the circumference of the free-throw circle is 30.77 feet,

what is the area that will be painted grey? Use 3.14 for π, and round to the nearest square foot. Enter your answer in the box.
Mathematics
1 answer:
Anton [14]3 years ago
3 0

Answer:

37.69    (≈ 38 ft²)

Step-by-step explanation:

2πr = 30.77

r = 30.77 / (2 * 3.14) = 4.9

half of free-throw circle area: πr² / 2 = (3.14 * 4.9²) / 2 = 37.69    (≈ 38 ft²)

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BabaBlast [244]

\underline{\bf{Given \:equation:-}}

\\ \sf{:}\dashrightarrow ax^2+by+c=0

\sf Let\:roots\;of\:the\: equation\:be\:\alpha\:and\beta.

\sf We\:know,

\boxed{\sf sum\:of\:roots=\alpha+\beta=\dfrac{-b}{a}}

\boxed{\sf Product\:of\:roots=\alpha\beta=\dfrac{c}{a}}

\underline{\large{\bf Identities\:used:-}}

\boxed{\sf (a+b)^2=a^2+2ab+b^2}

\boxed{\sf (√a)^2=a}

\boxed{\sf \sqrt{a}\sqrt{b}=\sqrt{ab}}

\boxed{\sf \sqrt{\sqrt{a}}=a}

\underline{\bf Final\: Solution:-}

\\ \sf{:}\dashrightarrow \sqrt{\alpha}+\sqrt{\beta}

\bull\sf Apply\: Squares

\\ \sf{:}\dashrightarrow (\sqrt{\alpha}+\sqrt{\beta})^2= (\sqrt{\alpha})^2+2\sqrt{\alpha}\sqrt{\beta}+(\sqrt{\beta})^2

\\ \sf{:}\dashrightarrow (\sqrt{\alpha}+\sqrt{\beta})^2 \alpha+\beta+2\sqrt{\alpha\beta}

\bull\sf Put\:values

\\ \sf{:}\dashrightarrow (\sqrt{\alpha}+\sqrt{\beta})^2=\dfrac{-b}{a}+2\sqrt{\dfrac{c}{a}}

\\ \sf{:}\dashrightarrow \sqrt{\alpha}+\sqrt{\beta}=\sqrt{\dfrac{-b}{a}+2\sqrt{\dfrac{c}{a}}}

\bull\sf Simplify

\\ \sf{:}\dashrightarrow \underline{\boxed{\bf {\sqrt{\boldsymbol{\alpha}}+\sqrt{\boldsymbol{\beta}}=\sqrt{\dfrac{-b}{a}}+\sqrt{2}\dfrac{c}{a}}}}

\underline{\bf More\: simplification:-}

\\ \sf{:}\dashrightarrow \sqrt{\alpha}+\sqrt{\beta}=\dfrac{\sqrt{-b}}{\sqrt{a}}+\dfrac{c\sqrt{2}}{a}

\\ \sf{:}\dashrightarrow \sqrt{\alpha}+\sqrt{\beta}=\dfrac{\sqrt{a}\sqrt{-b}+c\sqrt{2}}{a}

\underline{\Large{\bf Simplified\: Answer:-}}

\\ \sf{:}\dashrightarrow\underline{\boxed{\bf{ \sqrt{\boldsymbol{\alpha}}+\sqrt{\boldsymbol{\beta}}=\dfrac{\sqrt{-ab}+c\sqrt{2}}{a}}}}

5 0
2 years ago
Read 2 more answers
A total of $12,000 is invested in two corporate bonds that pay 7.5% and 9% simple interest. The invest wants an annual interest
nlexa [21]

Answer:

$13,200

Step-by-step explanation:

You need to use the simple interest formula

I = P * r * t

I = Interest accrued

P = Principal amount invested

r = Interest rate          you need to divide by 100 to get it in decimal form

t = time, in years        if you are given a partial year, divide the months by 12

P = $12,000                                    

r = 7.5% = .075                                    

t = 1                                                  

But, because we want I to equal $990 then I is

I = $990

So we ignore our P and instead solve for the P that will give us the desired result.

I = P * r * t

$990 = P * .075 * 1

$990 = P.075        Divide each side by .075

$990/.075 = P.075/.075

$990/.075 = P

$13,200 = P

So, to earn an annual interest income of $990, $13,200 will have to be invested in the 7.5% bond.

6 0
3 years ago
If y = kx, what is the value of k if y = 20 and x = 0.4?
True [87]
Set up an equation 20=k(0.4)....to find k divide 20 by 0.4
8 0
3 years ago
What is the surface area of the cylinder d = 10 h = 7
Anna11 [10]
The answer is 120\pi. Hope I helped!
3 0
3 years ago
The vertices of a triangle are p(3,7) Q(7,-6) R(-8,7). Name the vertices of the image reflected across the x axis
pantera1 [17]

Answer:

<em>P'(3,-7) Q'(7,6) R'(-8,-7).</em>

Step-by-step explanation:

<u>Reflection across the x-axis</u>

Given a point P(x,y), its reflection across the x-axis will map to point P'(x,-y), i.e., the y-coordinate gets inverted.

We are given the vertices of a triangle P(3,7) Q(7,-6) R(-8,7). The vertices of the image reflected across the x-axis are:

P'(3,-7) Q'(7,6) R'(-8,-7).

The new triangle has vertices P'Q'R'.

6 0
2 years ago
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