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Sever21 [200]
3 years ago
5

Find the dimensions of the shaded region so that its area is maximized. x= y=

Mathematics
1 answer:
musickatia [10]3 years ago
3 0
1.  Find the equation of the line AB.  For reference, the answer is y=(-2/3)x+2.
2.  Derive a formula for the area of the shaded rectange.  It is A=xy (where x is the length and y is the height).
3.  Replace "y" in A=xy with the formula for y:  y= (-2/3)x+2:
       
                 A=x[(-2/3)x+2]    This is a formula for Area A in terms of x only.
4.  Since we want to maximize the shaded area, we take the derivative with respect to x of    A=x[(-2/3)x+2] , or, equivalently, A=(-2/3)x^2 + 2x.
This results in   (dA/dx) = (-4/3)x + 2.
5.  Set this result = to 0 and solve for the critical value:  

(dA/dx) = (-4/3)x + 2=0, or (4/3)x=2   This results in x=(3/4)(2)=3/2

6.  Verify that this critical value x=3/2 does indeed maximize the area function.
7.  Determine the area of the shaded rectangle for x=3/2, using the previously-derived formula          A=(-2/3)x^2 + 2x.

The result is the max. area of the shaded rectangle.
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Answer:

Suppose that a couple invested $50,000 in an account when their child was born, to prepare for the child's college education. If the average interest rate is 4.4% compounded annually, ( A ) Give an exponential model for the situation, and ( B ) Will the money be doubled by the time the child turns 18 years old?

( A ) First picture signifies the growth of money per year.

( B ) Yes, the money will be doubled as it's maturity would be $108,537.29.

a = p(1 + \frac{r}{n} ) {}^{nt}a=p(1+

n

r

)

nt

a = 50.000.00(1 + \frac{0.044}{1} ) {}^{(1)(18)}a=50.000.00(1+

1

0.044

)

(1)(18)

a = 50.000.00(1 + 0.044) {}^{(1)(18)}a=50.000.00(1+0.044)

(1)(18)

a = 50.000.00(1.044) {}^{(18)}a=50.000.00(1.044)

(18)

50,000.00 ( 2.17074583287910578440507440 it did not round off as the exact decimal is needed.

a = 108.537.29a=108.537.29

Step-by-step explanation:

Hope This Help you!!

6 0
2 years ago
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A 95% confidence interval estimate for a population mean u is determined to be 75.38 to 86.52. If the confidence level is reduce
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Answer:

C. becomes narrower

Step-by-step explanation:

If the confidence level is reduced from 95% to 90%, then, the confidence interval for u becomes narrower, i.e., we are less sure that the true value of u is contained inside the new interval. With a 95% confidence interval there is a probability of 0.95 that the parameter u is inside the interval and with a 90% confidence interval there is a probability of 0.90 that the parameter u is inside the interval.

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ruslelena [56]

Answer:

Therefore last week Yvette used 72 grams of tea leaves to make 288 ounces of tea.

Step-by-step explanation:

i) 6 grams of tea leaves are used to make 24 ounces of tea.

ii) 1 gram of tea leaves can be used to make  = \frac{24}{6} = 4\hspace{0.1cm}ounces\hspace{0.1cm}of\hspace{0.1cm}tea

iii)  number of grams of tea leaves to make 288 ounces of tea

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The answer is 72 grams of tea leaves are required to make 288 ounces of tea.

Therefore last week Yvette used 72 grams of tea leaves to make 288 ounces of tea.

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