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Verdich [7]
3 years ago
7

The volume of two spheres is shown:

Mathematics
2 answers:
sp2606 [1]3 years ago
6 0

Answer:

0.6 in

Step-by-step explanation:

  • <em>Volume of the sphere formula: V = 4/3πr³, where r is the radius</em>

<u>Given:</u>

  • Volume of Sphere A = 30 cubic inches
  • Volume of Sphere B = 10 cubic inches

<u>Let R be the radius of sphere A and r be the radius of sphere B</u>

  • 30 = 4/3*3.14R³
  • R³ = 30*3/(4*3.14) ≈ 7.2
  • R = ∛7.2 ≈ 1.9 in

<u>And, similarly,</u>

  • r³ = 10*3/(4*3.14) ≈ 2.4
  • r = ∛2.4 ≈ 1.3 in

<u>The difference:</u>

  • R - r = 1.9 - 1.3 = 0.6 in

Sliva [168]3 years ago
3 0

Answer: 20.0 inches

Step-by-step explanation:

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You are riding the swings at a fair. What are the coordinates of your location after a rotation of 180°?
nekit [7.7K]

Answer:

(6, -3)

Step-by-step explanation:

The actual coordinates are x = -6 and y = 3

If we rotate 180 degrees and the center of rotation is at (0,0), all we need to do is invert the signal of each axis, that is, we invert the sign of the original x-coordinate and invert the signal of the original y-coordinate.

So the final x-coordinate is - (-6) = 6

And the final y-coordinate is - (3) = -3

So the coordinates will be (6, -3).

5 0
3 years ago
On Monday Ravi drives for 4 hours.
tensa zangetsu [6.8K]

Answer:

Step-by-step explanation:

On Monday Ravi drives for 4 hours.

His average speed is 30 mph.

How far does Ravi drive on Monday?

4 0
3 years ago
Read 2 more answers
How many times does the graph of 4x = 32 - x2 cross the x-axis?
garik1379 [7]

Answer:

The graph crosses the x-axis 2 times

The solutions are  x = -8  &  x = 4

Step-by-step explanation:

Qaudratics are in the form ax^2 + bx+ c

Where a, b, c are constants

Now, let's arrange this equation in this form:

4x=32-x^2\\x^2+4x-32=0

Where

a = 1

b = 4

c = -32

We need to know the discriminant to know nature of roots. The discriminant is:

D=b^2-4ac

If

  • D = 0 , we have 2 similar root and there is 2 solutions and that touches the x-axis
  • D > 0,  we have 2 distinct roots/solutions and both cut the x-axis
  • D < 0,  we have imaginary roots and it never cuts the x-axis

Let's find value of Discriminant:

D=b^2-4ac\\D=(4)^2 -4(1)(-32)\\D=144

Certainly D > 0, so there are 2 distinct roots and cuts the x-axis twice.

We get the roots/solutions by factoring:

x^2+4x-32=0\\(x+8)(x-4)=0\\x=4,-8

Thus,

The graph crosses the x-axis 2 times

The solutions are  x = -8  &  x = 4

6 0
3 years ago
Read 2 more answers
The graph shows a reflection in the x-axis. The matrix M such that, for any point (x, y), M(x, y) = (x', y') is
Rashid [163]

Answer:

This is a reflection about the x-axis.


Step-by-step explanation:

A reflection about the x-axis has the rule

[x,y]-> [x,-y].

Therefore

M[x,y] = [x,-y}

Let M=

|a  b|

|c  d|

Then the matrix multiplication gives

ax+by=x.............(1)

cx+dy=-y............(2)

Solving the previous equations (1) and (2) gives

a=1, b=0

c=0, d=-1

giving M as

|1  0|

|0 -1|


4 0
3 years ago
Evaluate cube root of 5 multiplied by square root of 5 over cube root of 5 to the power of 5.
Andre45 [30]

Answer:

Option d)  5 to the power of negative 5 over 6 is correct.

\dfrac{\sqrt[3]{\bf 5} \times \sqrt{\bf 5}}{\sqrt[3]{\bf 5^{\bf 5}}}= 5^{\frac{\bf -5}{\bf 6}}

Above equation can be written as 5 to the power of negative 5 over 6.

ie, 5^\frac{\bf -5}{\bf 6}

Step-by-step explanation:

Given that cube root of 5 multiplied by square root of 5 over cube root of 5 to the power of 5.

It can be written as below

\dfrac{\sqrt[3]{5} \times \sqrt{5}}{\sqrt[3]{5^5}}

\dfrac{\sqrt[3]{5} \times \sqrt{5}}{\sqrt[3]{5^5}}= \dfrac{5^{\frac{1}{3}} \times 5^{\frac{1}{2}}}{5^{\frac{5}{3}}}

\dfrac{\sqrt[3]{5} \times \sqrt{5}}{\sqrt[3]{5^5}}= \dfrac{5^{\frac{1}{3}+\frac{1}{2}}}{5^{\frac{5}{3}}}

\dfrac{\sqrt[3]{5} \times \sqrt{5}}{\sqrt[3]{5^5}}= \dfrac{5^{\frac{2+3}{6}}}{5^{\frac{5}{3}}}

\dfrac{\sqrt[3]{5} \times \sqrt{5}}{\sqrt[3]{5^5}}= 5^{\frac{5}{6}} \times 5^{\frac{-5}{3}}

\dfrac{\sqrt[3]{5} \times \sqrt{5}}{\sqrt[3]{5^5}}= 5^{\frac{5-10}{6}}

\dfrac{\sqrt[3]{5} \times \sqrt{5}}{5^5}= 5^{\frac{-5}{6}}

Above equation can be written as 5 to the power of negative 5 over 6.

7 0
3 years ago
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