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2 years ago

7 copper spheres with radii of 4

Mathematics

1 answer:

Anit [1.1K]2 years ago

6 0

We will see that the cube must be 10.23 inches tall.

The volume of the cube must be equal to the volume of the 4 spheres. Remember that the volume of a sphere of radius R is:

V = (4/3)*3.14*R^3

In this case, the radius is 4 inches, so we can write:

V = (4/3)*3.14*(4 in)^3 = 267.95 in^3

Then the volume of the 4 spheres is:

4*267.95 in^3 = 1,071.79 in^3

The volume of a cube of side length S is given by:

V = S^3

Then we must have:

S^3 = 1,071.79 in^3

S = ∛(1,071.79 in^3) = 10.23 in

We conclude that the cube is 10.23 inches tall.

If you want to learn more about spheres, you can read:

brainly.com/question/10171109

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Can someone help me with this question???

Lorico [155]

Pretty sure the answer is k

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3 years ago

Find the angle that the line through the given pair of points makes with the positive direction of the x-axis

alexdok [17]

Answer:

Therefore the angle that the line through the given pair of points makes with the positive direction of the x-axis is 45°.

Step-by-step explanation:

Given:

Let

A(x₁ , y₁) = (1 , 4) and

B( x₂ , y₂ ) = (-1 , 2)

To Find:

θ = ?

Solution:

Slope of a line when two points are given is given bt

$Slope(AB)=\dfrac{y_{2}-y_{1} }{x_{2}-x_{1} }$

Substituting the values we get

$Slope(AB)=\dfrac{2-4}{-1-1}=\dfrac{-2}{-2}=1\\\\Slope=1$

Also Slope of line when angle ' θ ' is given as

$Slope=\tan \theta$

Substituting Slope = 1 we get

$1=\tan \theta$

$\tan \theta=1\\\theta=\tan^{-1}(1)$

We Know That for angle 45°,

tan 45 = 1

Therefore

$\theta=45\°$

Therefore the angle that the line through the given pair of points makes with the positive direction of the x-axis is 45°.

5 0

3 years ago

Which situation represents a proportional relationship?

Natalka [10]

Answer:

B) Jack biked 5 miles in 25 minutes and 8 miles in 40 minutes.

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form $y=kx$

The ratio between the two variables is a constant called constant of proportionality k

$k=y/x$

<u><em>Verify each case</em></u>

A) Julie sold 4 necklaces for $12 and 9 necklaces for $25.

$\frac{4}{12}=\frac{9}{25}$

Multiply in cross

$4(25)=9(12)\\100\neq108$

Is not true

therefore

The situation not represent a proportional relationship

B) Jack biked 5 miles in 25 minutes and 8 miles in 40 minutes.

$\frac{5}{25}=\frac{8}{40}$

Multiply in cross

$5(40)=8(25)\\200=200$

Is true

therefore

The situation represent a proportional relationship

C) Larry packed 24 apples in 6 boxes and 46 apples in 9 boxes

$\frac{24}{6}=\frac{46}{9}$

Multiply in cross

$24(9)=46(6)\\216\neq276$

Is not true

therefore

The situation not represent a proportional relationship

D) Allie put 14 pieces of candy in 2 bags and 30 pieces of candy in 4 bags

$\frac{14}{2}=\frac{30}{4}$

Multiply in cross

$14(4)=30(2)\\56\neq60$

Is not true

therefore

The situation not represent a proportional relationship

7 0

3 years ago

How can we solve this?

Delvig [45]

Both angles will equal 180, as there is a line bisecting line AB to create the two angles.

Set up the following equation to have both angles equal 180:

$(x + 35) + (x - 23) = 180$

$x + 35 + x - 23 = 180$

Combine like terms:

$x + x = 2x$
$35 - 23 = 12$

$2x + 12 = 180$

Subtract 12 from both sides:

$2x = 168$

Divide both sides by 2:

$x = 84$

We now know the value of x, so plug it into the equation we set up:

$(84 + 35) + (84 - 23) = 180$

$119 + 61 = 180$

An obtuse angle will have a measure above 90 degrees. The number on the left side that is above 90 degrees is 119. This would be the measure for the obtuse angle.

The obtuse angle is 119 degrees wide.

8 0

3 years ago

a golf practice range has 245 balls. the owner bought a carton of golf ball. how many golf balls does the owner have after buyin

konstantin123 [22]

Uh i dont know are you supposed to add or substract multiply or divid use nixed numbers on no mixed numbers

5 0

4 years ago

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