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3 years ago

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1. Four boys decide to equally share some money they found on the ground. If each boys gets $5, how much money did the boys find

? Write an equation to determine to find out how money they found. __________________________ How much money did they find? __________________

1 answer:

Ivan3 years ago

5 0

So if 4 boys each got $5 then the equation would be
4 x 5
They found 20 dollars.

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Determine the value of r so that a line through the points (r,3) and (5,-4) has a slope of -1/2

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3 years ago

A Norman window has the shape of a rectangle surmounted by a semicircle. Suppose the outer perimeter of such a window must

Feliz [49]

The base length that will maximize the area for such a window is 168.03 cm. The exact largest value of x when this occurs is 233.39 cm

Suppose we make an assumption that:

(x) should be the width of the rectangle base;
(h) should be the height of the rectangle

Also, provided that the diameter of the semi-circle appears to be the base of the rectangle, then;

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and, the perimeter of the window can now be expressed as:

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Given that the perimeter = 600 cm

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$\mathbf{ h = 300 - \Big( \dfrac{1}{2} + \dfrac{\pi}{4}\Big) x}$

Since h > 0, then:

$\mathbf{ h = 300 - \Big( \dfrac{1}{2} + \dfrac{\pi}{4}\Big) x>0}$

By rearrangement and using the inverse rule:

$\mathbf{ x< \dfrac{ 300}{\Big( \dfrac{1}{2} + \dfrac{\pi}{4}\Big) } }$

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Thus, the largest length x = 233.39 cm

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$\mathbf{A = x \Big [ 300 - \Big ( \dfrac{1}{2}+\dfrac{1}{4} \Big) x \Big ] +\dfrac{1}{2}\pi \Big(\dfrac{x}{2} \Big )^2}$

$\mathbf{A (x) = 300x - \Big( \dfrac{1}{2} + \dfrac{\pi}{8}\Big) x^2 \ cm^2}$

Now, at maximum, when the area A = 0. Taking the differentiation, we have:

$\mathbf{\dfrac{d}{dx} 300x - \dfrac{d}{dx} \Big( \dfrac{1}{2} + \dfrac{\pi}{8}\Big) x^2 \ =0}$

$\mathbf{ 300 - 2x \Big( \dfrac{1}{2} + \dfrac{\pi}{8}\Big) \ =0}$

Making x the subject of the formula, we have:

$\mathbf{x = \dfrac{1200}{4 +\pi}}$

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Taking the second derivative:

$\mathbf{\dfrac{d}{dx} \Big [300 -2x \Big( \dfrac{1}{2} + \dfrac{\pi}{8}\Big) \Big]}$

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Therefore, we can conclude that the maximum area that exists for such a window is 168.03 cm

Learn more about derivative here:

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3 years ago

Solve the system of equations.

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Answer:

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Step-by-step explanation:

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3 years ago

Work out the area of this triangle.<br><br> I will mark you as brainliest, please help quick.

nataly862011 [7]

Answer:

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Step-by-step explanation:

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2 years ago

Explain it so I can better understand it

lorasvet [3.4K]

The question is essentially asking who's equation works better (Part A) and to explain why (Part B).
Marcella is suggesting the equation 6r + 12 = 683.88
Julia is suggesting the equation 6(r + 12) = 683.88

Six people are on the trip.
It is $12 PER person to rent a floatation device.
The total cost of the trip was $683.88.

Hope I've helped!

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3 years ago