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Vinil7 [7]
3 years ago
15

A rectangle is constructed with its base on theâ x-axis and two of its vertices on the parabola yequals=2525minusâxsquared2. wha

t are the dimensions of the rectangle with the maximumâ area? what is theâ area?
Mathematics
1 answer:
Nina [5.8K]3 years ago
6 0
You should have drawn1 - x-axis and y-axis in light pencil.2 - graphed a down-facing parabola with the top of the frown on the y-axis at y = 2.  It should be crossing the x-axis at ±√2.  This should be in dark pencil or another color.3 - In dark pencil or a completely new color, draw a rectangle with one of the horizontal sides sitting on top of the x-axis and the other horizontal side touching the parabola at each of the top corners of the rectangle. The rectangle will have half of its base in the positive x-axis and the other half on the negative x-axis.  It should be split right down the middle by the y-axis.  So each half of the base we will say is "x" units long.  So the whole base is 2x units long (the x units to the right of the y-axis, and the x units to the left of the y-axis)  I so wish I could draw you this picture...   In the vertical direction, both vertical edges are the same length and we will call that y.   The area that we want to maximize has a width 2x long, and a height of y tall. So A = 2xy     This is the equation we want to maximize (take derivative and set it = 0), we call it the "primary equation", but we need it in one variable. This is where the "secondary equation" comes in.  We need to find a way to change the area formula to all x's or all y's. Since it is constrained to having its height limited by the parabola, we could use the fact that y=2 - x2 to make the area formula in only x's.   Substitute in place of the "y", "2 - x2" into the area formula. A = 2xy = 2x(2 - x2)   then simplify A = 4x - 2x3     NOW you are ready to take the deriv and set it = 0 dA/dx = 4 - 6x2       0 = 4 - 6x2   6x2 = 4    x2 = 4/6 or 2/3 So x = ±√(2/3) Width remember was 2x.   So the width is 2[√(2/3)]Height is y which is 2 - x2 = 2 - 2/3  =4/3
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Answer:

$200,000

Step-by-step explanation:

6,000×100=600,000

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So $200,000

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A soccer league has 160 players. Of those players 40% are boys. How many boys are in the soccer league?
MatroZZZ [7]
The answer is 64 boys are in the soccer league.

X/160 = 40/100

X/160 * 100 = 40/100 * 100

5x/8 = 40

(8 * 5x)/8 = 40 * 8

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5x/5 = 320/5

x = 64
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1. D=5.9 ft.
Shtirlitz [24]

\qquad\qquad\huge\underline{{\sf Answer}}♨

Here's the solution ~

As we know, we can calculate the circumference of a circle in terms of its diameter as :

\qquad \sf  \dashrightarrow \:c =  \pi d

where, c = circumference and d = diameter

And also, circumference of circle is terms of radius (r) is :

\qquad \sf  \dashrightarrow \:c =  2\pi r

Now, let's move on to questions ~

<h3>First </h3>

\qquad \sf  \dashrightarrow \:3.14 \times 5.9

\qquad \sf  \dashrightarrow \: \approx18.53 \: ft

<h3 />

・ .━━━━━━━†━━━━━━━━━.・

<h3>Second</h3><h3 /><h3 /><h3 /><h3>\qquad \sf  \dashrightarrow \:3.14 \times 3.2</h3>

\qquad \sf  \dashrightarrow \: \approx10.048 \: ft

・ .━━━━━━━†━━━━━━━━━.・

<h3>Third</h3>

\qquad \sf  \dashrightarrow \:3.14 \times 6.1

\qquad \sf  \dashrightarrow \: \approx19.15 \: ft

・ .━━━━━━━†━━━━━━━━━.・

<h3>Fourth</h3>

\qquad \sf  \dashrightarrow \:2×3.14 \times  3.7

\qquad \sf  \dashrightarrow \: \approx2×11.62  \: m

\qquad \sf  \dashrightarrow \: \approx23.24  \: m

・ .━━━━━━━†━━━━━━━━━.・

<h3>Fifth </h3>

\qquad \sf  \dashrightarrow \:2×3.14 \times  6.2

\qquad \sf  \dashrightarrow \: \approx2× 19.47 \: units

\qquad \sf  \dashrightarrow \: \approx38.94  \: m

・ .━━━━━━━†━━━━━━━━━.・

<h3>Sixth</h3>

\qquad \sf  \dashrightarrow \:2×3.14 \times  5.1

\qquad \sf  \dashrightarrow \: \approx2×16.01 \: ft

\qquad \sf  \dashrightarrow \: \approx \: 32.02m

➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖

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Answer:

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