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Gekata [30.6K]
3 years ago
7

A box is to be made where the material for the sides and the lid cost​ $0.20 per square foot and the cost for the bottom is ​$0.

05per square foot. Find the dimensions of a box with volume 15cubic feet that has minimum cost.
Mathematics
1 answer:
luda_lava [24]3 years ago
4 0

Answer:

Let the width of the base be x and the height of the box be y. The base is a square so its area is x2. Then the volume of the box is "base area times height", so the volume is V=x2y=40ft3.

The area of the base is x2, so the cost of the base is 0.31x2.

The area of each side is xy, so the cost of each side is 0.05xy, so the cost of all four sides is 4×0.05xy=0.2xy.

The area of the top is x2, so the cost of the top is 0.19x2.

So the total cost is C=0.31x2+0.19x2+0.2xy=0.5x2+0.2xy.

Since x2y=40, we have y=40/x2, so C=0.5x2+0.2x×40x2=0.5x2+8x. This we can optimise using derivatives.

Step-by-step explanation:

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Answer:

Look below.

Step-by-step explanation:

FYI: Im a bit confused on what this question is asking but I am responding based on what I believe the question is asking.

The point 100 spaces to the left of -1 would be (-101,0) and the point 100 spaces to the left of -1 would be (100,0).

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The table shows how much money Edguardo earns as a golf coach. He charges a flat fee of $38, plus $22 per hour. Complete the tab
Vesnalui [34]
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Every hour that goes by, he earns $22 each hour.
Now that we've broken this down, we can make an equation.
Let's do 1 hour.
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olga2289 [7]

Answer:

(x - 5)(x + 3)

Step-by-step explanation:

Given

x² - 2x - 15

Consider the factors of the constant term (- 15) which sum to give the coefficient of the x- term (- 2)

The factors are - 5 and + 3, since

- 5 × 3 = - 15 and - 5 + 3 = - 2, thus

(x - 5)(x + 3) ← in factored form

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3 years ago
Solve this equation for x: 2x^2 + 12x - 7 = 0
zhannawk [14.2K]

Answer:

x=0.5355 or x=-6.5355

First step is to: Isolate the constant term by adding 7 to both sides

Step-by-step explanation:

We want to solve this equation: 2x^2 + 12x - 7 = 0

On observation, the trinomial is not factorizable so we use the Completing the square method.

Step 1: Isolate the constant term by adding 7 to both sides

2x^2 + 12x - 7+7 = 0+7\\2x^2 + 12x=7

Step 2: Divide the equation all through by the coefficient of x^2 which is 2.

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Step 3: Divide the coefficient of x by 2, square it and add it to both sides.

Coefficient of x=6

Divided by 2=3

Square of 3=3^2

Therefore, we have:

x^2 + 6x+3^2=\frac{7}{2}+3^2

Step 4: Write the Left Hand side in the form (x+k)^2

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Step 5: Take the square root of both sides and solve for x

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