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xeze [42]
3 years ago
7

E varies directly with The square root of C. If E=40 When C=25 find: E when C = 49 ( Please help ASAP I need to hand this in tom

orrow ! )
Mathematics
1 answer:
DiKsa [7]3 years ago
7 0

Answer:

E = 56

Step-by-step explanation:

Given that E varies directly with \sqrt{C} then the equation relating them is

E = k\sqrt{C} ← k is the constant of variation

To find k use the condition E = 40 when C = 25

k = \frac{E}{\sqrt{C} } = \frac{40}{\sqrt{25} } = \frac{40}{5} = 8, thus

E = 8\sqrt{C} ← equation of variation

When C = 49, then

E = 8 × \sqrt{49} = 8 × 7 = 56

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A company’s profit in dollars is modeled by the equation p(x) = –0.5x2 + 100x, where x represents the number of units sold.
serg [7]

Answers:

a. The company needs to sell 100 units to reach the maxmum profit.

b. The company's maximum profit is $5,000.

Solution:

a. How many unit does the company need to sell to reach the maximum profit?

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This is a quadratic equation, and its graph is a parabola vertical (because the veriable "x" is square). Comparing with the general form:

p(x)=ax^2+bx+c; a=-0.5, b=100, c=0

a=-0.5<0 (negative), then the parabola opens downward, and it has a maximimun value (maximum profit) at its vertex.

We can find the abscissa of the vertex (units that the company needs to sell to reach the maximum profit using the following formula:

x=-b/(2a)

Replacing b by 100 and a by -0.5 in the formula above:

x=-100/[2(-0.5)]

x=-100/(-1)

x=100

The company needs to sell 100 units to reach the maximum profit.


b. What's the company's maximum profit?  

To determine the maximum profit we substitute the value of "x" obrained in part "a" in the quadratic equation:

x=100→p(100)=-0.5(100)^2+100(100)

p(100)=-0.5(10,000)+10,000

p(100)=-5,000+10,000

p(100)=5,000

The company's maximum profit is $5,000.

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3 years ago
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Answer:

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Step-by-step explanation:

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