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3 years ago

What is the volume of a sphere with a radius of 41 in, rounded to the nearest tenth of a cubic inch?

Mathematics

1 answer:

Lynna [10]3 years ago

8 0

<h2>Volume = 288695.6 in³</h2>

Step-by-step explanation:

Volume of a sphere is given by

$V = \frac{4}{3} \pi {r}^{3}$

Where r is the radius of the sphere

From the question

radius = 41 in

Substitute the value into the above formula

We have

$V = \frac{4}{3} \times {41}^{3} \pi$

$= \frac{275684}{3} \pi$

= 288695.6097

We have the final answer as

<h3>Volume = 288695.6 in³ to the nearest tenth</h3>

Hope this helps you

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An artificial lake is in the shape of a rectangle and has an area of 9/20 square mile. The width of the lake is 1/5 the length o

Zina [86]

X=width of the lake
y=length of the lake.
we set out this system of equiations
x*y=9/20
x=y/5
we solve by sustitution method
(y/5)*y=9/20
y²/5=9/20
y²=(5*9)/ 20
y²=2.25
y=√2.25=1.5

x=y/5
x=1.5/5=0.3

Solution:
width of the lake=0.3 miles
lenght of the lake=1.5 miles

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3 years ago

The length of a rectangle is 7 more than the width. The area is 744 sqaure yards, find the length and width of the rectangle

AVprozaik [17]

Answer:

Length of rectangle is 31 yards and Width is 24 yards.

Given:

The length of a rectangle is 7 more than the width.
The area is 744 sqaure yards

Solution:

Let's assume Width of rectangle be x and Length of rectangle be x + 7 respectively.

Using formula

$\\ \: \: \: \: \pink{ \dashrightarrow \: \: \: \: \sf { \underbrace{Area_{(Rectangle)} = Length × Width }}} \\ \\$

On Substituting the required values, we get;

$\\ \: \: \: \: \dashrightarrow \: \: \: \: \sf (x)(x + 7) = 744 \\ \\ \\ \: \: \: \: \dashrightarrow \: \: \: \: \sf {x}^{2} + 7x = 744 \\ \\ \\ \: \: \: \: \dashrightarrow \: \: \: \: \sf {x}^{2} + 7x - 744 = 0 \\ \\ \\ \: \: \: \: \dashrightarrow \: \: \: \: \sf {x}^{2} + 31x - 24x - 744 = 0 \\ \\ \\ \: \: \: \: \dashrightarrow \: \: \: \: \sf x(x + 31) - 24 (x + 31) = 0 \\ \\ \\ \: \: \: \: \dashrightarrow \: \: \: \: \sf (x + 31)(x - 24) = 0 \\ \\ \\ \: \: \: \: \dashrightarrow \: \: \: \: \sf x = 24 \: or \: - 31 \\ \\$

As we know that width of the rectangle can't be negative. So x = 24

<u>Hence</u>,

Width of rectangle = x = 24 yards
Length of the rectangle = x + 7 = 31 yards

$\therefore$ Length of rectangle is 31 yards<u> </u>and Width is 24 yards.

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2 years ago

Which graph has a rate of change equal to 1/3 in the interval between 0 and 3 on the x-axis?

attashe74 [19]

The answer to your question is C.

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3 years ago

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Drag each function to the correct location on the chart. Classify the functions as continuous and discontinuous functions. If a

Ilia_Sergeevich [38]

Answer:

Continuous: g(x) and j(x)

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Step-by-step explanation:

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3 years ago

Can someone help me

djverab [1.8K]

Step-by-step explanation:

10)

any triangle inscribed into a circle with the baseline being a diameter of the circle must be a right-angled triangle.

the arc angle of 84° means that also the angle at Q is 84°, because the arc angle is the same as the segment angle at the center of the circle (that is how arc sngles are defined).

that means the supplementary angle (together they have 180°) of Q at the inner top angle of the small left triangle is 180 - 84 = 96°.

as the legs of this small left triangle are both the radius of the circle, this triangle is an isoceles triangle (both legs are equally long, and both angles at its baseline are equally large).

remember, the sum of all angles in a triangle is always 180°.

so,

y = (180 - 96)/2 = 42°

x is a complimentary angle (together they are 90°, remember, the large triangle is inscribed and is right-angled) to the second 42° angle

x = 90 - 42 = 48°

11)

y is the supplementary angle to 126°

y = 180 - 126 = 54°

this inner segment angle is the mean value between the 2 outer angles.

54 = (57 + 2nd outer angle of y)/2

108 = 57 + 2nd outer angle of y

2nd outer angle of y = 108 - 57 = 51°

all arc angles around a circle must be 360°.

x = 360 - 57 - 104 - 51 = 148°

12)

again, all arc angles together must be 360°.

y = 360 - 148 = 212°

x is the same angle as the top angle of a triangle inscribed to the right of the chord.

and that angle is half of the opposing arc angle (148°).

it is therefore 148/2 = 74°

and so,

x = 74°

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2 years ago