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BabaBlast [244]
3 years ago
12

The image shows the dimensions of a pool.

Mathematics
1 answer:
Juliette [100K]3 years ago
8 0
<h3>Answer:  D) 198 square meters</h3>

======================================================

Explanation:

Extend the side that's 9.5 meters long out to the left so that you form a trapezoid on top and a rectangle underneath. The side we extended is now 5+9.5 = 14.5 meters long.

Let

  • A = area of the trapezoid up top
  • B = area of the rectangle underneath

The goal is to find A+B

The trapezoid has the parallel sides of 14.5 and 10 meters. The height of the trapezoid is 28-20 = 8 meters. So we can say

Area of trapezoid = height*(base1+base2)/2

A = h*(b1+b2)/2

A = 8*(14.5+10)/2

A = 98

The rectangle has area of B = length*width = 5*20 = 100 square meters

Therefore,

total area = A+B = 98+100 = 198 square meters.

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You can use trigonometric ratios to find the legs of this triangle, which are the x and y coordinates of the point.

\cos=\frac{adj}{hyp} \\\\ \cos(\frac{\pi}6)=\frac{x}5 \\\\ \frac{\sqrt{3}}2=\frac{x}5 \\\\ \frac{5\sqrt{3}}2=x

As for y...

\sin=\frac{opp}{hyp}\\\\\sin(\frac{\pi}6) = \frac{y}5 \\\\ \frac{1}2=\frac{y}5 \\\\ \frac{5}2=y

\boxed{(\frac{5\sqrt{3}}2,\ \frac{5}2)}

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3 years ago
A soap factory randomly inspects 100 bars of soap to better identify problems that occur during the manufacturing process. The t
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Answer:

They would expect 150 bars to be broken.

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Prove that if a and b are positive integers,then there exists a unique integers q and r such that a=bq+r where 0≤r&lt;b​
Vilka [71]

Step-by-step explanation:

Correct option is

C

0≤r<b

If r must satisfy0≤r<b

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..,a−3b,a−2b,a−b,a,a+b,a+2b,a+3b,..

clearly it is an arithmetic progression with common difference b and it extends infinitely in both directions.

Let r be the smallest non-negative term of this arithmetic progression.Then,there exists a non-negative integer q such that,

a−bq=r

=>a=bq+r

As,r is the smallest non-negative integer satisfying the result.Therefore, 0≤r≤b

Thus, we have

a=bq1+r1,   0≤r1≤b

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103,776 ways

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After 3 days a sample of radon-222 has decayed to 58% of its original amount.(
iren2701 [21]
Half-life = [elapsed time * log (2)] / [log (begng amt / endg amt)]
half-life =  (3 days * 0.30102999566) / log (1 / .58)
<span>half-life =  0.903089987 / log </span> (<span> <span> <span> 1.724137931)
</span></span></span>half-life =  <span>0.903089987 / 0.23657200643</span>
half-life =  <span> <span> <span> 3.8174 days

Source:
http://www.1728.org/halflife.htm

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