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umka2103 [35]
3 years ago
15

Find a formula for the described function. A rectangle has perimeter 16 m. Express the area A of the rectangle as a function of

the length, L, of one of its sides. A = 8L−L2 Correct: Your answer is correct. m2 State the domain of A. (Assume the length of the rectangle is longer than its width. Enter your answer in interval notation.) How do i get the domain
Mathematics
1 answer:
Alex17521 [72]3 years ago
3 0
Part A:

Let the length of one of the sides of the rectangle be L, then the length of the other side is obtained as follow.

Let the length of the other side be x, then

2(L+x)=16 \\  \\ \Rightarrow L+x=8 \\  \\ \Rightarrow x=8-L

Thus, if the length of one of the side is x, the length of the other side is 8 - L.

Hence, the area of the rectangle in terms of L is given by

L(8 - L) = 8L-L^2



Part B:

To find the domain of A

Recall that the domain of a function is the set of values which can be assumed by the independent variable. In this case, the domain is the set of values that L can take.

Notice that the length of a side of a rectangle cannot be negative or 0, thus L cannot be 8 as 8 - 8 = 0 or any number greater than 8.

Hence the domain of the area are the set of values between 0 and 8 not inclusive.

Therefore,

dom(Area)=0\ \textless \ L\ \textless \ 8 \ or \ (0, 8)
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melamori03 [73]

Answer:

a) 0.8413

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c) P_{95} = 189.675

Step-by-step explanation:

We are given the following information in the question:

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Standard Deviation, σ = 15

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Formula:

z_{score} = \displaystyle\frac{x-\mu}{\sigma}

a) P(IQ scores at most 180)

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P( x < 180) = P( z < \displaystyle\frac{180 - 165}{15}) = P(z < 1)

Calculation the value from standard normal z table, we have,  

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b) Number of the members of the club have IQ scores at most 180

n = 500

\text{Members} = n\times \text{P(IQ scores at most 180)}\\= 500\times 0.8413\\=420.65 \approc 421

c) P(X< x) = 0.95

We have to find the value of x such that the probability is 0.95

P( X < x) = P( z < \displaystyle\frac{x - 165}{15})=0.95  

Calculation the value from standard normal z table, we have,  

P(z < 1.645) = 0.95

\displaystyle\frac{x - 165}{15} = 1.645\\\\x = 189.675  

P_{95} = 189.675

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