All categories

3 years ago

HELP ASAP PLEASE ………………..

Mathematics

2 answers:

Natalka [10]3 years ago

4 0

Answer:

I think it's D

ivanzaharov [21]3 years ago

3 0

Answer:

its D

Step-by-step explanation:

You might be interested in

A norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular. Find the dimensions of a norman

Yanka [14]

Answer:

$W\approx 8.72$ and $L\approx 15.57$ .

Step-by-step explanation:

Please find the attachment.

We have been given that a norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular. The total perimeter is 38 feet.

The perimeter of the window will be equal to three sides of rectangle plus half the perimeter of circle. We can represent our given information in an equation as:

$2L+W+\frac{1}{2}(2\pi r)=38$

We can see that diameter of semicircle is W. We know that diameter is twice the radius, so we will get:

$2L+W+\frac{1}{2}(2r\pi)=38$

$2L+W+\frac{\pi}{2}W=38$

Let us find area of window equation as:

$\text{Area}=W\cdot L+\frac{1}{2}(\pi r^2)$

$\text{Area}=W\cdot L+\frac{1}{2}(\pi (\frac{W}{2})^2)$

$\text{Area}=W\cdot L+\frac{\pi}{2}(\frac{W}{2})^2)$

$\text{Area}=W\cdot L+\frac{\pi}{2}(\frac{W^2}{4})$

$\text{Area}=W\cdot L+\frac{\pi}{8}W^2$

Now, we will solve for L is terms W from perimeter equation as:

$L=38-(W+\frac{\pi }{2}W)$

Substitute this value in area equation:

$A=W\cdot (38-W-\frac{\pi }{2}W)+\frac{\pi}{8}W^2$

Since we need the area of window to maximize, so we need to optimize area equation.

$A=W\cdot (38-W-\frac{\pi }{2}W)+\frac{\pi}{8}W^2$

$A=38W-W^2-\frac{\pi }{2}W^2+\frac{\pi}{8}W^2$

Let us find derivative of area equation as:

$A'=38-2W-\frac{2\pi }{2}W+\frac{2\pi}{8}W$

$A'=38-2W-\pi W+\frac{\pi}{4}W$

$A'=38-2W-\frac{4\pi W}{4}+\frac{\pi}{4}W$

$A'=38-2W-\frac{3\pi W}{4}$

To find maxima, we will equate first derivative equal to 0 as:

$38-2W-\frac{3\pi W}{4}=0$

$-2W-\frac{3\pi W}{4}=-38$

$\frac{-8W-3\pi W}{4}=-38$

$\frac{-8W-3\pi W}{4}*4=-38*4$

$-8W-3\pi W=-152$

$8W+3\pi W=152$

$W(8+3\pi)=152$

$W=\frac{152}{8+3\pi}$

$W=8.723210$

$W\approx 8.72$

Upon substituting $W=8.723210$ in equation $L=38-(W+\frac{\pi }{2}W)$ , we will get:

$L=38-(8.723210+\frac{\pi }{2}8.723210)$

$L=38-(8.723210+\frac{8.723210\pi }{2})$

$L=38-(8.723210+\frac{27.40477245}{2})$

$L=38-(8.723210+13.70238622)$

$L=38-(22.42559622)$

$L=15.57440378$

$L\approx 15.57$

Therefore, the dimensions of the window that will maximize the area would be $W\approx 8.72$ and $L\approx 15.57$ .

8 0

3 years ago

I need help with 1-32 it’s a test help ASAP thanks

Illusion [34]

What’s in it for me will u give me vbucks

5 0

3 years ago

I need to convert x^2 +6x-16 to vertex form with steps listed please

Naddika [18.5K]

What steps are listed?

7 0

4 years ago

The function C = x - 2y is maximized at the vertex point of the feasible region at (8, 2). What is the maximum value?

lubasha [3.4K]

The required maximum value of the function C = x - 2y is 4.

Given that,
The function C = x - 2y is maximized at the vertex point of the feasible region at (8, 2). What is the maximum value is to be determined.

<h3>What is the equation?</h3>

The equation is the relationship between variables and represented as y =ax +m is an example of a polynomial equation.

Here,
Function C = x - 2y
At the vertex point of the feasible region at (8, 2)
C = 8 - 2 *2
C= 4

Thus, the required maximum value of the function C = x - 2y is 4.

Learn more about equation here:

brainly.com/question/10413253

#SPJ1

5 0

1 year ago

What formula do we use to find slope?

Kamila [148]

Answer:Remember, the formula for slope is (y2 - y1) / (x2 - x1).

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers