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2 years ago

Choose all the numbers that are common multiples of 3 and 12.

Mathematics

1 answer:

spayn [35]2 years ago

6 0

<h3>Answers: 48 and 72</h3>

=========================================================

Explanation:

The number 12 is a multiple of 3 because 3*4 = 12.

So when looking for common multiples of 3 and 12, we simply need to look at multiples of 12.

The multiples of 12 are:

12, 24, 36, 48, 60, 72, 84, 96, 120, ...

We see that 48 and 72 are on the list. The values 21, 27, 63, 81 are not on the list, so cross them out.

Now we could keep that list of multiples going to see if 844 is on there or not. A better method is to divide 844 over 12. If we get a whole number, then it's a multiple of 12.

844/12 = 70.333 approximately.

This shows that 844 is <u>not</u> a multiple of 12. So we cross 844 from the list.

Only 48 and 72 are multiples of 12 (and also multiples of 3).

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2 years ago

Find, correct to four decimal places, the length of the curve of intersection of the cylinder 4x2 1 y2 − 4 and the plane x 1 y 1

charle [14.2K]

<u>Answer-</u> Length of the curve of intersection is 13.5191 sq.units

<u>Solution-</u>

As the equation of the cylinder is in rectangular for, so we have to convert it into parametric form with

x = cos t, y = 2 sin t (∵ 4x² + y² = 4 ⇒ 4cos²t + 4sin²t = 4, then it will satisfy the equation)

Then, substituting these values in the plane equation to get the z parameter,

cos t + 2sin t + z = 2

⇒ z = 2 - cos t - 2sin t

∴ $\frac{dx}{dt} = -\sin t$

$\frac{dy}{dt} = 2 \cos t$

$\frac{dz}{dt} = \sin t-2cos t$

As it is a full revolution around the original cylinder is from 0 to 2π, so we have to integrate from 0 to 2π

∴ Arc length

$= \int_{0}^{2\pi}\sqrt{(\frac{dx}{dt})^{2}+(\frac{dy}{dt})^{2}+(\frac{dz}{dt})^{2}$

$=\int_{0}^{2\pi}\sqrt{(-\sin t)^{2}+(2\cos t)^{2}+(\sin t-2\cos t)^{2}$

$=\int_{0}^{2\pi}\sqrt{(2\sin t)^{2}+(8\cos t)^{2}-(4\sin t\cos t)$

Now evaluating the integral using calculator,

$=\int_{0}^{2\pi}\sqrt{(2\sin t)^{2}+(8\cos t)^{2}-(4\sin t\cos t)$ $= 13.5191$

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3 years ago

What is the length of the hypotenuse of the triangle when x=15?

Luden [163]

Answer:

114.24°

Step-by-step explanation:

7(15)+6= 105

3(15)= 45, now we plug it in the formula, $a^{2}+b^{2}=c^{2}$

$105^{2}+45^{2} = 13050$

so now we square root it

$\sqrt{13050}$ = 114.24

6 0

3 years ago

Read 2 more answers

Yony wants to buy a scooter that is $129. This is $24 more than 3 time sthan what he saved last month. How much did he save last

9966 [12]

44.33 is the right answer

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3 years ago

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Bas_tet [7]

Answer:

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Step-by-step explanation:

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2 years ago