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levacccp [35]
3 years ago
8

The volume of water and a rectangle swimming pool can be modeled by the function v(x)=x^3+13x-210. If the depth of the pool is g

iven by the expression x-3, what are the expressions that represent the width and length of the pool?
Mathematics
1 answer:
S_A_V [24]3 years ago
5 0

Answer:

Required,

L=\frac{3+\sqrt{37}}{2}-\frac{144}{x-3}

W=\frac{3-\sqrt{37}}{2}-\frac{144}{x-3}

Step-by-step explanation:

Given volume and depth respectively,

V(x)=x^3+13x-210 and x-3

To find length and width of the rectanglular swiming pool we know,

Volume=length\timesheight\timesdepth.

Let depth=D=x-3, length=L, width=W, then

V=DLW

x^3+13x-210= LW(x-3)

LW=\frac{x^3+13x-210}{x-3}

After divide we will get x^2-3x-22 with remainder -144.

Thus,

x^3+13x-210=(x^2-3x-22)(x-3)-144=(x-3)LW

Now to find root of,

x^2-3x-144=\frac{3\pm\sqrt{9+88}}{2}=\frac{3\pm \sqrt{37}}{2}

Thus,

L=\frac{3+\sqrt{37}}{2}-\frac{144}{x-3}

W=\frac{3-\sqrt{37}}{2}-\frac{144}{x-3}

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In the rolling of two fair dice calculate the following: P(Sum of the two dice is 7) = ______
vesna_86 [32]

Answer:

P(Sum of the two dice is 7) = 6/36

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

In this problem, we have that:

A fair dice can have any value between 1 and 6 with equal probability. There are two fair dices, so we have the following possible outcomes.

Possible outcomes

(first rolling, second rolling)

(1,1), (2,1), (3,1), (4,1), (5,1), (6,1)

(1,2), (2,2), (3,2), (4,2), (5,2), (6,2)

(1,3), (2,3), (3,3), (4,3), (5,3), (6,3)

(1,4), (2,4), (3,4), (4,4), (5,4), (6,4)

(1,5), (2,5), (3,5), (4,5), (5,5), (6,5)

(1,6), (2,6), (3,6), (4,6), (5,6), (6,6)

There are 36 possible outcomes.

Desired outcomes

Sum is 7, so

(1,6), (6,1), (5,2), (2,5), (3,4), (4,3).

There are 6 desired outcomes, that is, the number of outcomes in which the sum of the two dice is 7.

Answer

P(Sum of the two dice is 7) = 6/36

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Genrish500 [490]

Answer:

x = 33

Step-by-step explanation:

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  2x + 24 = 90      {Subtract 24 from both sides}

          2x  = 90 - 24

         2x   = 66

          x   = 66/2

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garik1379 [7]

Answer:

35\% represents the sample proportion of the population

Step-by-step explanation:

From the question we are told that

   The sample size is  n  = 947

   The proportion of the population that believes that the Yankees will miss the playoffs this year is    k = 35\% = 0.35

From the question we are told the confidence level is  97%

   The lower limit of the confidence level is a = 28%

    The upper limit of the  b = 42%

Generally the sample proportion of this population is mathematically represented as

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=>      \^ p = \frac{28 + 42 }{2}

=>      \^ p = 35\%

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