If the scale factor is 1, then the size of the image will___

earnstyle [38]

It si cool so basicly u take 5 divide bye 13 times 5

8 0

3 years ago

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

Consider the following function. F(x)=3/2+4 Using the given function, plot all the ordered pairs for the values in the domain be

Butoxors [25]

I can't edit pictures for you so as a result I can't answer it. But label those numbers on the x line and that will be your answer. And OMG your laptop is torn up I tell you TORN.

8 0

3 years ago

John's goal is to have more then -7 dollars in his bank account by the end of the month.The variable d is the number of dollars

Alona [7]

Answer:

i need more info

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

Solve for x; y=mx+b I can find x by_______________ on both sides of the equation PLZ Show your Work Thank You

amid [387]

Answer:

"subtracting b, then dividing by m"

Step-by-step explanation:

To solve for a particular variable, look a the operations that are being performed on that variable. Then "undo" those operations in reverse order.

Here, the operations done to x are ...

• multiply by m

• add b to the product

Using the above recipe, first we "undo" the additon of b. We accomplish that by subtracting b from both sides of the equation. This gives ...

y - b = mx + b - b

y - b = mx . . . . . . . . . simplify

Next, we "undo" the multiplicatin by m. We accomplish that by dividing both sides of the equation by m.

(y -b)/m = mx/m

(y -b)/m = x . . . . . . . . simplify

This is your solution for x:

x = (y - b)/m

We found it by subtracting b, then dividing by m on both sides of the equation.

6 0

3 years ago

If the scale factor is 1, then the size of the image will____?