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devlian [24]
3 years ago
6

A normal window is constructed by adjoining a semicircle to the top of an ordinary rectangular window, (see figure ) The perimet

er of the window is 12 feet. what dimensions will produce a window of maximum area? (Round you answers to two decimal places ) what is the width x= what is the length y.?
(Question2) write the function in the form f(×) = ×^3- 6×^2- 15×+9, k = -2.
f (×)=?

Mathematics
1 answer:
Dima020 [189]3 years ago
3 0
Let's find the perimeter of the window.

The bottom side is x. The left and right sides make 2y.
The perimeter of a circle is 2\pi r, so the perimeter of a semicircle must be \pi r, The radius is \frac{1}2x, so that gives \frac{1}2\pi x for the curve. All of that is equal to 12.

x+2y+\frac{1}2\pi x=12

We only want to use one variable to create the area formula, so let's solve for y.

2y=12-x-\frac{1}2\pi x

y=6-\frac{1}2x-\frac{1}4\pi x

Now that we have a value for y in terms of x, we can find the area in terms of x.

The area of the rectangle is going to be xy, which then becomes

A_r=x(6-\frac{1}2x-\frac{1}4\pi x

A_r=6x-\frac{1}2x^2-\frac{1}4\pi x^2

The area of the semicircle is going to be \frac{1}2\pi r^2.

Since r=\frac{1}2x, A_{sc}=\frac{1}2\pi (\frac{1}2x)^2.

A_{sc}=\frac{1}2\pi \frac{1}4x^2

A_{sc}=\frac{1}8\pi x^2

Now let's add the areas of the rectangle and semicircle.

A=A_r+A_{sc}

A=6x-\frac{1}2x^2-\frac{1}4\pi x^2+\frac{1}8\pi x^2

A=6x-\frac{1}2x^2-\frac{1}8\pi x^2

If you wanted to factor out \frac{1}8 like you did, this would become

\boxed{A(x)=\frac{1}8(48x=4x^2-\pi x^2)}

Now what we want to do is find what x is when A is at its highest point, Once we have the value for x we can also find the value for y, of course.

Let's put our equation in the general form of a quadratic.

A(x)=(-\frac{1}2-\frac{1}8\pi )x^2+6x

Now we can use the vertex formula x=\frac{-b}{2a}.
(a and b refer to ax^2+bx+c.)

x=\frac{-6}{2(-\frac{1}2-\frac{1}8\pi)}

x=\frac{-6}{-\frac{1}4\pi -1}

x=\frac{-24}{-\pi -4}

\boxed{x=\frac{24}{\pi +4}}

Now let's plug that in for y=6-\frac{1}2x-\frac{1}4\pi x.

Since our final answers are in decimal form and not exact form, we can make our lives a little easier here and just use x\approx3.36059492.

y\approx6-\frac{1}2(3.36059492)-\frac{1}4\pi(3.36059492)

<span>y\approx6-(1.68029746+2.63940507809)

</span><span>\boxed{y\approx1.68029746191}

Let's take our answers for x and y and round to 2 decimal places.

\boxed{x\approx 3.36\ ft}

\boxed{y\approx 1.68\ ft}</span>
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3 décimas multiplicadas por 100 equivalen a 300 milésimas
larisa86 [58]

3/10 *1 = 3/10  so 3/10 * (100/100) = 300/1000 = 3/10

8 0
3 years ago
What is the slope of the line in the graph?
Triss [41]

Answer:

B

Step-by-step explanation:

The slope of a line is written as a fraction of the vertical distance to the horizontal distance. The line drops down from (0,1) to (4,-2). This is a vertical distance of -3 and a horizontal distance of 4. The slope if the fraction -3/4.

4 0
2 years ago
I need help on this question
anyanavicka [17]

Remark

There is a very quick way to do this. Scan the numbers. You want 75 to be the mean, so make it so. Then figure out how many up or down you go from 75. I'll make a list of the givens.

72 - 3 72 is three down from 75 so call it - 3

75 0 That is your desired average so it adds nothing to the score.

74 -1 It is one down from 75, so call it -1

76 +1 It is one up from 75

76 +1 it is one up from 75

75 adds 0.

-3 - 1 + 1 + 1 = - 2

That comes - 2/7 which means that you need a score just under 75. So 75 will give you the right average of 75

Answer B <<<<<

7 0
3 years ago
At the end of the day of teaching the skill of cutting and sewing to make capes, Ms. Ironperson and Mr. Thoro decided to go to t
olga_2 [115]

Answer:

The cost of a chicken shawarma wrap = $10.99

The cost of an order of spiced potatoes=$4.99

Equations needed

3x+2y =42.95

5x + 4y=74.91

Step-by-step explanation:

x = the cost of a chicken shawarma wrap

y = the cost of an order of spiced potatoes

Ms. Ironperson

3x+2y =42.95

Mr. Thoro

5x + 4y=74.91

3x+2y =42.95 (1)

5x + 4y=74.91 (2)

Multiply (1) by 2

6x + 4y=85.9 (3)

5x + 4y=74.91. (2)

Subtract (2) from (3)

6x - 5x= 85.9 - 74.91

x=$10.99

Substitute the value of x into (1)

3x+2y =42.95 (1)

3(10.99) + 2y =42.95

32.97 + 2y = 42.95

2y = 42.95 - 32.97

2y=9.98

Divide both sides by 2

y=9.98/2

=4.99

y=$4.99

Therefore,

The cost of a chicken shawarma wrap = $10.99

The cost of an order of spiced potatoes=$4.99

3 0
3 years ago
Can someone please help me?:\
katrin [286]

The circumference of the top of the cake is 9.5\pi\approx29.845 in.

It sounds like the baker is trying to line the circumference with cherriesto fit as many as possible along the border, like in the picture I've attached below.

This comes down to dividing the cake's circumference by the diameter of each cherry:

\dfrac{9.5\pi}{0.75}\approx39.79

or about 39 cherries, making the answer D.

7 0
3 years ago
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