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3 years ago

14

WITH EXPLANATION PLS HELP WILL MARK BRAINLIEST

1 answer:

jasenka [17]3 years ago

7 0

B. The banner is a rectangle because 120² + 22² = 122² ; therefore, the angles opposite the diagonal are not right angles.

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K is the midpoint of JL JK=3x-1 and KL=2x+8 find JL

Masteriza [31]

Answer:

JL = 52

Step-by-step explanation:

It is given in the question that K is the midpoint of JL.

So, JK = KL ......... (1)

Now, given that, JK =3x - 1 and KL = 2x + 8

Therefore, from equation (1), we can write

3x - 1 = 2x + 8

⇒ x = 9

So, JK = 3x - 1 = 3(9) -1 = 26 and KL = 2x + 8 = 2(9) + 8 = 26

Hence, JL = JK + KL = 26 + 26 = 52. (Answer)

3 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

kykrilka [37]

Answer:

Bc=20

Step-by-step explanation:

Sin61=BC/AC=BC/23

BC=23sin61=20

4 0

3 years ago

68.40 5% what is the original price

olga2289 [7]

The original price would be $72. Hope this is right, and helps you.

3 0

3 years ago

You and six friends play a game where each person writes down his or her name on a scrap of paper, and the names are randomly di

Vanyuwa [196]

It would be 1/7 chance cause there are 7 people total but you have the 1 chance that you are going to get your own name

7 0

4 years ago