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3 years ago

1)

Mathematics

1 answer:

Mars2501 [29]3 years ago

8 0

Answer:

$186.86

Step-by-step explanation:

4 eggs cost:

1 dollar per dozen (12 eggs), so by unitary method (ratios), we can find cost of 4 eggs. Shown below:

$\frac{1}{12}=\frac{x}{4}\\12x=4\\x=0.33$

So, 4 eggs cost $0.33 approx

12 lb. flour cost:

2.50 dollar per pound, so 12 pounds would simply cost:

2.5 * 12 = $30

14 lb of sugar cost:

4.50 dollar per pound means 14 pounds would cost:

4.5 * 14 = $63

2 ready-made edible flowers cost:

5 cents for each flower means 2 flowers would cost:

5 cent = 0.05 dollars

0.05 * 2 = $0.10

We add all up to find cost of 1 cake. Shown below:

Cost of 1 cake = $0.33 + $30 + $63 + $0.10 = $93.43

Cost of 2 cakes = $93.43 * 2 = $186.86

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Distance of Ben from the base of the pole = 8 feet

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A rectangular solid has width w, a length of 7 more than the width, and a height that is equivalent to 15 decreased by 3 times t

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Answer:

For a rectangular solid with:

width = w

length = l

height = h

The volume is equal to:

V = w*l*h

in this case we know that:

width = w.

"length of 7 more than the width"

l = w + 7.

"a height that is equivalent to 15 decreased by 3 times the width."

h = 15 - 3*w

Then the volume will be:

V = w*l*h = w*(w + 7)*(15 - 3w) = (w^2 + 7*w)*(15 - 3*w)

V = ( -3*w^3 + 15*w^2 + 105*w - 21*w^2)

V = (-3*w^3 - 6*w^2 + 105*w)

Now, the maximum volume will be for the value of w such that:

V'(w) = 0.

and:

V''(W) < 0

Where:

dV/dw = V'(w).

dV'/dw = V''(w)

Then first we need to differentiate the equation for the volume.

V'(w) = dV/dw = ( 3*(-3*w^2) + 2*(-6*w) + 105)

V'(w) = -9*w^2 - 12*w + 105.

Then we need to find the solution for:

-9*w^2 - 12*w + 105 = 0.

We can use the Bhaskara formula, and we will get:

$w = \frac{+12 +-\sqrt{(-12)^2 - 4*(-9)*105} }{2*-9} = \frac{+12 +- 62.6}{-18}$

Then the two solutions are:

w₁ = (+12 - 62.6)/(-18) = 2.81

w₂ = (+12 + 62.6)/(-18) = -15.5

But we can not have a negative width, so we can just discard the second solution.

Now let's check the second condition for the maximum, we must have:

V''(2.81) < 0.

V'' = dV'/dw = 2*(-9*w) - 12 = -18*w - 12

V''(2.81) = -18*2.81 - 12 = -62.58 < 0 .

Then the volume is maximized when w = 2.81, and the maximum volume will be:

V(2.81) = (-3*(2.81)^3 - 6*(2.81)^2 + 105*2.81) = 180.1

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