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Radda [10]
3 years ago
5

The elevation of city A is 60 feet above sea level; the elevation of city C is 12 feet above sea level. The elevation of city D

is 1 over 2 of the elevation of city C. Part A: Write an expression to represent the elevation, in feet, of city D. (5 points) Part B: Solve the expression and explain why the answer is negative or positive. (5 points)
Mathematics
2 answers:
Likurg_2 [28]3 years ago
3 0

A) 1/2*12 = 6 ft above sea level

B) Because City D is 1/2 of 6, it cannot be negative because we are not multiplying anything by a negative number.

beks73 [17]3 years ago
3 0

Answer:

Part A: \dfrac{1}{2}\times 12\text{ feet}

Part B: 6 feet above sea level and positive

Step-by-step explanation:

The elevation of city A is 60 feet above sea level.

The elevation of city C is 12 feet above sea level.

The elevation of city D is \dfrac{1}{2} of the elevation of city C.

Part A: Expression which shows Elevation of city D in feet above sea level.

\text{Elevation of city D}=\dfrac{1}{2}\times \text{Elevation of city C}

\text{Elevation of city D}=\dfrac{1}{2}\times 12

Part B: Simplify the expression of part A

\text{Elevation of city D}=\dfrac{1}{2}\times 12=6\text{ feet}

The elevation of city D is 6 feet above sea level.

It would be positive because above sea level height is positive and below sea level takes negative.

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C(x)=\dfrac{20x^3+1715000}{x}\\$Minimum cost, C(35)=\$29,400

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Step-by-step explanation:

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Surface Area of the Sides=4xh

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= 20x^2+\dfrac{1715000}{x}\\C(x)=\dfrac{20x^3+1715000}{x}

To find the minimum total cost, we solve for the critical points of C(x). This is obtained by equating its derivative to zero and solving for x.

C'(x)=\dfrac{40x^3-1715000}{x^2}\\\dfrac{40x^3-1715000}{x^2}=0\\40x^3-1715000=0\\40x^3=1715000\\x^3=1715000\div 40\\x^3=42875\\x=\sqrt[3]{42875}=35

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h=\dfrac{171500}{x^2}\\Therefore:\\h=\dfrac{171500}{35^2}=140cm

The dimensions that will lead to minimum costs are base length of 35cm and height of 140cm.

Therefore, the minimum total cost, at x=35cm

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