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siniylev [52]
1 year ago
7

The perimeter of a rectangle swimming pool Is 84 meters. The width of the pool is 3/4 the length. What are the length and width

of the pool?
Mathematics
1 answer:
soldier1979 [14.2K]1 year ago
8 0

Given:

Perimeter of rectangular swimming pool = 84 meters

Width of pool = 3/4 of the length

Let's find the length and width of the pool.

Since the swinning pool has the shape of a rectangle and we have the perimeter, to find the length and width, apply the perimeter of a rectangle formula:

\text{Perimeter = 2(L + W)}

Where:

L is the length

W is the width.

Given:

W = ¾L

Substitute 84 for perimeter and ¾L for W.

Hence, we have:

\begin{gathered} P=2(L+W) \\  \\ 84=2(L+\frac{3}{4}L) \end{gathered}

Let's evealuate the equation and solve for L.

We have:

\begin{gathered} 84=2(L+0.75L) \\  \\ 84=2(1.75L) \\  \\ 84=3.5L \end{gathered}

Divide both sides by 3.5:

\begin{gathered} \frac{84}{3.5}=\frac{3.5L}{3.5} \\  \\ 24=L \\  \\ L=24\text{ meters} \end{gathered}

To solve for the width W, substitute 24 for L in (W=¾L)

\begin{gathered} W=\frac{3}{4}\times L \\  \\ W=\frac{3}{4}\times24 \\  \\ W=\frac{3\times24}{4} \\  \\ W=\frac{72}{4} \\  \\ W=18\text{ meters} \end{gathered}

Therefore, the length of the swimming pool is 24 meters, while the width is 18 meters.

ANSWER:

Length = 24 meters

Width = 18 meters

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Answer:

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Variables = m, r

Coefficients = 7, 6 and -3

constant= -8

Step-by-step explanation:

We are given the expression 7m^3 + 6r^2 - 3r - 8

We need to give variable, coefficients and constant.

Variable: The value of variable may change. It can be represented by x, y or any other letter

Coefficients: A numerical or constant quality that is placed with the variable. For example in 4x, 4 is coefficient

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So, in the given expression 7m^3 + 6r^2 - 3r - 8

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A rock was thrown from the top of a cliff such that its distance above sea level was given by s(t)= at² + bt + c, where t is the
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Answer:

<h2>a) a = -3, b = 18, c = 48; </h2><h2>s(t) = -3t²+18t+48</h2><h2>b) 48m</h2><h2>c) 8secs</h2>

Step-by-step explanation:

The question is incomplete. Here is the complete question.

'A rock was thrown from the top of a cliff such that its distance above sea level was given by s(t)=at²+bt+c, where t is the time in seconds after the rock was released. After 1 second the rock was 63 m above sea level, after 2 seconds 72 m, and after 7 seconds 27 m. a. Find a, b and c and hence an expression for s(t). b. Find the height of the cliff. c. Find the time taken for the rock to reach sea level.'

Given the equation of the distance modelled as s(t)=at²+bt+c

If after 1 second the rock was 63 m, then 63 = a+b+c

If after 2 seconds, the distance was 72 m then 72 = 4a+2b+c

Also if after 7 seconds, the distance is 27 m, then 27 = 49a+7b+c

i) Solving the 3 equations simultaneously to get a, b and c we have;

a+b+c = 63 ... 1

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Subtracting 2 from 1 and 3 from 2 we will generate 2 new equations as shown;

eqn 2- eqn1: 3a + b = 9...4

eqn 3- eqn 2: 45a + 5b = -45

eqn 3- eqn 2: 9a+b = -9 ... 5

solving 4 and 5 simultaneously

3a + b = 9 ...4

9a+b = -9 ... 5  

Taking the difference of 4 and 5 we have

6a - -9-9

6a = -18

a = -3

substituting a = -3 into equation 4 to get b we have;

3(-3)+b = 9

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b = 9+9

b = 18

substituting a = -3 and b = 18 into equation 1 to get c we have;

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a = -3, b= 18 and c = 48

The distance function will be s(t) = -3t²+18t+48

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The height of the cliff is at when t = 0

s(0) = -3(0)²+18(0)+48

s(0) = 48m

The height of the cliff is 48m

iii) At the sea level, the height of the rock will be 0m, substituting this into the modeled equation for the height to get the time we have;

s(t)=at²+bt+c

0 = -3t²+18t+48

3t²-18t-48 = 0

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t² - 8t+2t - 16 = 0

t(t-8)+2(t-8) = 0

(t+2)(t-8) = 0

t = -2 or 8

Taking the positive value of the time, t = 8secs

Time taken for the rock to reach sea level is 8secs

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