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wariber [46]
3 years ago
9

These two right circular cylinders have the same height, 45 centimeters. The radius of the smaller cylinder is 22 centimeters an

d the radius of the larger cylinder is 6 times greater than that of the smaller cylinder. What is the ratio of the volume of the larger cylinder to the volume of the smaller cylinder?
Mathematics
1 answer:
Andrei [34K]3 years ago
6 0
22x6=132

V=(3.14)r^2h
V=(3.14)(132)^2(45)
V=(3.14)(17424)(45)
V=2462001.2cm^3

H A P P Y ?
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The company sells the toys for $12 each. Write an expression for the amount of
Nady [450]

Answer: I(x)=12x

Step-by-step explanation:

Let I represent the total money earned

Let x represent the number of toys sold

Since each toy is 12 dollars, then the company will earn 12 dollars for each toy that is sold.

Therefore,  the equation is,

I(x)=12x  

5 0
3 years ago
What is the solution to this system of equations? 2t + w = 10 4t = 20 − 2w A. It has no solution. B. It has infinite solutions.
joja [24]

Answer:

<h3>B. It has infinite solutions</h3>

Step-by-step explanation:

Given the system of equations:

2t + w = 10 ..... 1

4t = 20 − 2w ... 2

From 1:

w = 10-2t ...3

Substitute 3 into 2 to have;

4t = 20 - 2(10-2t)

4t = 20-20+4t

4t = 4t

Let t = k

Substitute t = k into 1 and get w;

From 1: 2t + w = 10

2k + w =10

w = 10 - 2k

<em>k can take any integers. This shows that the solution to the equation is infinite</em>

<em></em>

7 0
3 years ago
Please answer this to the best of your ability
Lilit [14]

Answer:

For this exercise we need to solve the next equation:

3 +6x = 2x + 27

We can start substracting 3 at both sides:

3 + 6x - 2 = 2x + 27 - 3

6x = 2x + 25

And then, we can substract 2x::

6x - 2x = 2x + 24 - 2x

4x = 25

Then, we divide by 4:

4x/4 = 24/4

x = 24/4 = 6

Now, we can see if we have done it correctly:

3 + 6*6 = 39

2 * 6 + 27 = 39

And we have seen our result is correct

7 0
3 years ago
In a right triangle ABC, CD is an altitude, such that AD=BC. Find AC, if AB=3 cm, and CD= 2 cm.
konstantin123 [22]

Consider right triangle ΔABC with legs AC and BC and hypotenuse AB. Draw the altitude CD.

1. Theorem: The length of each leg of a right triangle is the geometric mean of the length of the hypotenuse and the length of the segment of the hypotenuse adjacent to that leg.

According to this theorem,

BC^2=BD\cdot AB.

Let BC=x cm, then AD=BC=x cm and BD=AB-AD=3-x cm. Then

x^2=(3-x)\cdot 3,\\ \\x^2=9-3x,\\ \\x^2+3x-9=0,\\ \\D=3^2-4\cdot (-9)=9+36=45,\\ \\\sqrt{D}=\sqrt{45}=3\sqrt{5},\\ \\x_1=\dfrac{-3-3\sqrt{5} }{2}0.

Take positive value x. You get

AD=BC=\dfrac{-3+3\sqrt{5} }{2}\ cm.

2. According to the previous theorem,

AC^2=AD\cdot AB.

Then

AC^2=\dfrac{-3+3\sqrt{5} }{2}\cdot 3=\dfrac{-9+9\sqrt{5} }{2},\\ \\AC=\sqrt{\dfrac{-9+9\sqrt{5} }{2}}\ cm.

Answer: AC=\sqrt{\dfrac{-9+9\sqrt{5} }{2}}\ cm.

This solution doesn't need CD=2 cm. Note that if AB=3cm and CD=2cm, then

CD^2=AD\cdot DB,\\ \\2^2=AD\cdot (3-AD),\\ \\AD^2-3AD+4=0,\\ \\D

This means that you cannot find solutions of this equation. Then CD≠2 cm.

8 0
3 years ago
Read 2 more answers
10 1/2 * 10 1/2 simplify
Marta_Voda [28]

\frac{441}{4}

change the mixed numbers to improper fractions and multiply the numerators / denominators

10 \frac{1}{2} = \frac{21}{2}

\frac{21}{2} × \frac{21}{2} = \frac{441}{4} = 1110 \frac{1}{4}

4 0
3 years ago
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