Find the volume V of the cone. Round your answer to the nearest tenth.

g A window is being built and the bottom is a rectangle and the top is a semi-circle. If there is 12 meters of framing materials

photoshop1234 [79]

Answer:

Semicircle of radius of 1.6803 meters

Rectangle of dimensions 3.3606m x 1.6803m

Step-by-step explanation:

Let the radius of the semicircle on the top=r

Let the height of the rectangle =h

Since the semicircle is on top of the window, the width of the rectangular portion =Diameter of the Semicircle =2r

The Perimeter of the Window

=Length of the three sides on the rectangular portion + circumference of the semicircle

$=h+h+2r+\pi r=2h+2r+\pi r=12$

The area of the window is what we want to maximize.

Area of the Window=Area of Rectangle+Area of Semicircle

$=2hr+\frac{\pi r^2}{2}$

We are trying to Maximize A subject to $2h+2r+\pi r=12$

$2h+2r+\pi r=12\\h=6-r-\frac{\pi r}{2}$

The first and second derivatives are,

Area, A(r) $=2r(6-r-\frac{\pi r}{2})+\frac{\pi r^2}{2}}=12r-2r^2-\frac{\pi r^2}{2}$

Taking the first and second derivatives

$A'\left( r \right) = 12 - r\left( {4 + \pi } \right)\\A''\left( r \right) = - 4 - \pi$

From the two derivatives above, we see that the only critical point of r

$A'\left( r \right) = 12 - r\left( {4 + \pi } \right)=0$

$r = \frac{{12}}{{4 + \pi }} = 1.6803$

Since the second derivative is a negative constant, the maximum area must occur at this point.

$h=6-1.6803-\frac{\pi X1.6803}{2}=1.6803$

So, for the maximum area the semicircle on top must have a radius of 1.6803 meters and the rectangle must have the dimensions 3.3606m x 1.6803m ( Recall, The other dimension of the window = 2r)

5 0

3 years ago

Will mark branniest if gotten right

iris [78.8K]

Answer:

? = 30°

Step-by-step explanation:

All angles in a triangle add up to 180°

? + 130° + 20° = 180°

? = 180° - 130° - 20°

? = 30°

8 0

3 years ago

The expression to find the perimeter of a rectangle is 2(length + width). What is the perimeter, in units, of a rectangle of len

Allisa [31]

First you plug in the data to the formula. So it will be 2(1/3+1/2). You then want to add the fractions together but must first find the common denominator which will be 6. So it is 2(2/6+3/6). The fractions then add up to be 5/6. So all you have to do is multiply it by 2 to get 5/3 which simplifies to 1 2/3 so it is D.

4 0

3 years ago

Read 2 more answers

Brainiest fastest answer no link or bot or I report you I report you if you report me

Elodia [21]

38.79
3053.63
904.78
2544.69
226.19
402.12
1072.33
1526.81
28.73
113.1
3801.33
268.08
2094.4
75.4
94.25
37.7
1884.96
2065.24
19861.7
1385.44
287.98
4.19
3619.11
113.1
50.27

I did this really quick so I hope all the answers are right, and double check them if you have time just in case

4 0

3 years ago

EXTRA POINTS!

antiseptic1488 [7]

Answer:

y = 15

Step-by-step explanation:

angle poq + angle qor equals mpor (120)

4y + 3y + 15= 120

7y+15=120

subtract 15 from both sides

7y=150

divide both sides by 7

y=15

check:

4(15) + 3(15) + 15 equals 120

60 + 45 + 15 = 120

120 = 120

7 0

3 years ago