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Dafna11 [192]
3 years ago
12

A circular pool of radius r m has a path 2 m wide around its perimeter. If the area of the pool is four-fifths of the total area

, prove that r²-16r-16=0. Hence calculate the radius of the pool in metres.
Mathematics
1 answer:
Rainbow [258]3 years ago
4 0

9514 1404 393

Answer:

  pool radius is 8+4√5 ≈ 16.94 meters

Step-by-step explanation:

Let r represent the radius of the pool. Then r+2 is the radius to the outside of the walkway. The ratio of areas is given as 4/5, so we have ...

  πr²/(π(r+2)²) = 4/5

  5r² = 4(r² +4r +4) . . . . cross-multiply

  r² -16r -16 = 0 . . . . . . . subtract the right-side expression from both sides

__

  r² -16r +64 = 80 . . . . . add 80 to complete the square

  (r -8)² = 80

  r -8 = √80 = 4√5 . . . . square root; use only the positive root

  r = 8 +4√5 ≈ 16.94 . . . meters

The radius of the pool is 8+4√5 ≈ 16.94 meters.

_____

The area of a circle of radius r is given by the formula ...

  A = πr²

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Answer: Each triangle:40 cm²

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Step-by-step explanation:

The area of a triangle is

1/2bh

The height of the triangle is

h=1/2(10)=5cm

and the base is 16 cm.

The area of each triangle is

= 1/2(16)(5)=40cm^2

2. The total area of the kite is 2 times the area of one triangle.

= 2*40=80cm^2

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4 years ago
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4 0
3 years ago
Please help will mark brainly!
Marina86 [1]
Hey man I got u. The answer for this question is B. Peace
3 0
3 years ago
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According to a marketing research study, American teenagers watched 14.8 hours of social media posts per month last year, on ave
ki77a [65]

Answer:

The value of test statistics is 1.06.

Step-by-step explanation:

We are given that according to a marketing research study, American teenagers watched 14.8 hours of social media posts per month last year, on average. A random sample of 11 American teenagers was surveyed and the mean amount of time per month each teenager watched social media posts was 15.6. This data has a sample standard deviation of 2.5.

We have to test if the mean amount of time American teenagers watch social media posts per month is greater than the mean amount of time last year or not.

Let, NULL HYPOTHESIS, H_0 : \mu = 14.8 hours  {means that the mean amount of time American teenagers watch social media posts per month is same as the mean amount of time last year}

ALTERNATE HYPOTHESIS, H_1 : \mu > 14.8 hours  {means that the mean amount of time American teenagers watch social media posts per month is greater than the mean amount of time last year}

The test statistics that will be used here is One-sample t-test;

             T.S. = \frac{\bar X - \mu}{\frac{s}{\sqrt{n} } } ~ t_n_-_1

where, \bar X = sample mean amount of time per month each teenager watched social media posts = 15.6 hours

             s = sample standard deviation = 2.5 hours

             n = sample of teenagers = 11

So, <u>test statistics</u> =  \frac{15.6 - 14.8}{\frac{2.5}{\sqrt{11} } } ~ t_1_0

                            = 1.06

Hence, the value of test statistics is 1.06.

5 0
3 years ago
Is this right? IDK I need help!!!
True [87]

Answer:

um... you are wrong

Step-by-step explanation:

its the the last one

you can't add when its division

you can change exponents from 1/x^-2

to   x^2

<h2><em><u>I nweed brainliest</u></em></h2>
5 0
3 years ago
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