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3 years ago

Select the correct answer.

Mathematics

1 answer:

ohaa [14]3 years ago

8 0

Answer:

Set the compass to a convenient width, and draw an arc that is centered at the vertex of the original angle and intersects both legs of the original angle.

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Work out the volume of the shape

pashok25 [27]

Answer:

$\large\boxed{V=\dfrac{1,421\pi}{3}\ cm^3}$

Step-by-step explanation:

We have the cone and the half-sphere.

The formula of a volume of a cone:

$V_c=\dfrac{1}{3}\pi r^2H$

r - radius

H - height

We have r = 7cm and H = (22-7)cm=15cm. Substitute:

$V_c=\dfrac{1}{3}\pi(7^2)(15)=\dfrac{1}{3}\pi(49)(15)=\dfrac{735\pi}{3}\ cm^3$

The formula of a volume of a sphere:

$V_s=\dfrac{4}{3}\pi R^3$

R - radius

Therefore the formula of a volume of a half-sphere:

$V_{hs}=\dfrac{1}{2}\cdot\dfrac{4}{3}\pi R^3=\dfrac{2}{3}\pi R^3$

We have R = 7cm. Substitute:

$V_{hs}=\dfrac{2}{3}\pi(7^3)=\dfrac{2}{3}\pi(343)=\dfrac{686\pi}{3}\ cm^3$

The volume of the given shape:

$V=V_c+V_{hs}$

Substitute:

$V=\dfrac{735\pi}{3}+\dfrac{686\pi}{3}=\dfrac{1,421\pi}{3}\ cm^3$

7 0

3 years ago

An open box is to be made out of a 12-inch by 20-inch piece of cardboard by cutting out squares of equal size from the four corn

Natali5045456 [20]

Answer:

Length = 15.14, width = 7.14 and height = 2.43 inches.

( correct to the nearest hundredth).

Step-by-step explanation:

Let the lengths of the squares cut out be x inches.

Then the width of the box will be 12 - 2x and the length will be

20 - 2x inches.

The height of the box is x inches.

Volume V = x(20-2x)(12-2x)

To find the value of x when V is a maximum we find the derivative and equate it to zero.

V = x( 240 - 64x + 4x^2)

V = 4x^3 - 64x^2 + 240x

dV/dx = 12x^2 - 128x + 240 = 0

4(3x^2 - 32x + 60) = 0

This won't factor so we use the formula:

x = [-(-32) +/- √((-32)^2 - 4*3*60)] / 6

= 8.24, 2.43.

So one of these gives a maximum Volume.

The second derivative

d^2V/dx^2 = 24x - 128

When x = 8.24, this = 69.6 (positive) so this gives a minimum.

x = 2.43 gives a negative value ( -49.7) so this is the maximum

So the dimensions are:-

length = 20 - 2(2.43) = 15.14

width = 12 - 2(2.43) = 7.14

height = 2.43.

7 0

2 years ago

The pair of figures to the right are similar. what is the ratio of the perimeters and the ratio of the areas?

marissa [1.9K]

Answer:

the ratio of perimeters is 3/5

the ratio of areas is 9/25

Step-by-step explanation:

first we divide the given sides of both figures

perimeter=side 1/side 2

=15/25

p=3/5

to find the ratios of the area

=(side 1/side 2)^2

=(3/5)^2

=9/25

3 0

2 years ago

S = 2d over t, solve for d

marishachu [46]

Answer:

t=2d/s

Step-by-step explanation:

Combining Expressions and isolating the variable t

8 0

2 years ago

Solve the following automotive-services problems based on the examples shown previously. Voltage = 12 v Current = 48 amps Resist

yawa3891 [41]

For this case the first thing you should know is that we have the following definition:
V = I * R
Where,
V: voltage
I: current
R: resistance
Therefore, by clearing the Resistance we have:
R = V / I
Substituting the values:
R = 12/48
R = 1/4 ohms
Answer:
The value of the resistance is:
R = 1/4 ohms

4 0

3 years ago