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kolbaska11 [484]

3 years ago

9

The difference between two numbers is 12. The LCM of the two numbers is 133. Find the two numbers.

1 answer:

nikitadnepr [17]3 years ago

5 0

If the difference between two numbers is 12, those two numbers may be:

13...1
14...2
15...3
16...4
etc...

We can ignore numbers which can be divided by themselves (like 2...14 or 4...16), so we have:

13...1
17...5
19...7
20...8
21...9
22...10

Let's stop here and find LCMs of given numbers:

13...1 = 13
17...5 = 85
19...7 = 133
20...8 = 40
21...9 = 63
22...10 = 110

So as we can see the numbers we're looking for are 19 and 7.

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3 years ago

what is the ratio for the volumes of two similar spheres given that the ratio of their radii is 4:7 A.)343:64 B.)49:16 C.)16:49

quester [9]

Answer:

Volume of the similar sphere be 64 :343 .

Option (D) is correct.

Step-by-step explanation:

Formula

$Volume\ of\ a sphere = \frac{4}{3}\pi r^{3}$

As given

The volumes of two similar spheres given that the ratio of their radii is 4:7 .

Let us assume that the x be the scalar multiple of the radi .

Radius of first sphere = 4x

Radius of second sphere = 7x

Putting the values in the formula

$Volume\ of\ first\ sphere = \frac{4}{3}\pi\times 4x\times 4x\times 4x$

$Volume\ of\ first\ sphere = \frac{4}{3}\pi\times 64x^{3}$

$Volume\ of\ second\ sphere = \frac{4}{3}\pi\times 7x\times 7x\times 7x$

$Volume\ of\ second\ sphere = \frac{4}{3}\pi\times 343x^{3}$

Thus

$\frac{Volume\ of\ first\ sphere}{Volume\ of\ second\ sphere} = \frac{\frac{4\pi\times 64x^{3}}{3}}{\frac{4\pi\times 343x^{3}}{3}}$

$\frac{Volume\ of\ first\ sphere}{Volume\ of\ second\ sphere} = \frac{64}{343}$

Therefore the ratio of the volume of the similar sphere be 64 :343 .

Option (D) is correct .

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