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3 years ago

I will give brainliest for correct answer !

Mathematics

2 answers:

Vesna [10]3 years ago

7 0

Answer:

Hey! It's me again!

nikdorinn [45]3 years ago

6 0

Answer:

Step-by-step explanation:

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Henry wants to join a book of the month club. The first club costs $30 to join and $10 per

Lena [83]

Answer:

Step-by-step explanation:

7 0

3 years ago

the length of a rectangle is four times its width. the rectangle has an area of 1024cm^2 work out the width of the rectangle

olga2289 [7]

The width is 16 so the length is 64 (TO clarify W=16)

Hope this helps :)

7 0

4 years ago

Read 2 more answers

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

A star in the sky appears to move by 12 arcseconds over the course of 6 months. Convert this number into first areminutes then d

Bumek [7]

Answer:

Given :A star in the sky appears to move by 12 arc seconds over the course of 6 months.

To Find :Convert this number into first arc minutes then degrees.

Solution:

60 arc seconds = 1 arc minute

1 arc seconds = $\frac{1}{60}$ arc minute

12 arc seconds = $\frac{1}{60} \times 12$ arc minute

12 arc seconds = $\frac{1}{5}$ arc minute

So, 12 arc seconds = $\frac{1}{5}$ arc minute

Now convert it into degrees

60 arc minute = 1 degree

1 arc minute = $\frac{1}{60}$ degree

$\frac{1}{5}$ arc minute = $\frac{1}{60} \times \frac{1}{5}$ degree

$\frac{1}{5}$ arc minute = $\frac{1}{300}$ degrees

12 arc seconds = $\frac{1}{300}$ degrees

8 0

3 years ago

How to do -7x-3x+2=8x-8

zavuch27 [327]

If you would like to solve the equation - 7 * x - 3 * x + 2 = 8 * x - 8, you can calculate this using the following steps:

- 7 * x - 3 * x + 2 = 8 * x - 8
- 7 * x - 3 * x - 8 * x = - 8 - 2
- 18 * x = - 10 /(-18)
x = 10 / 18
x = 5/9

The correct result would be 5/9.

7 0

3 years ago

Read 2 more answers