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Montano1993 [528]
2 years ago
14

Proof true or false: For all integers a,b,and c,if ab|c then a|c and b|c

Mathematics
1 answer:
olya-2409 [2.1K]2 years ago
4 0

Answer with explanation:

It is given that for three integers , a, b and c, if

              \frac{ab}{c}\rightarrow then, \frac{a}{c} \text{or} \frac{b}{c}

Since , a b is divisible by c , following are the possibilities

1.→ a and b are prime integers .Then , c will be prime number either equal to a or b.

2.→a and b are not prime integers ,then any of the factors of a or b will be equal to c.For example:

 ⇒a=m × n

 b=p × q× c

or,

⇒a=u×v×c

b=s×t

So, whatever the integral values taken by a, and b, if \frac{ab}{c} then either of  \frac{a}{c} \text{or} \frac{b}{c} is true.

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Step2247 [10]

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A = 297\pi

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To solve this problem we need to be familiar with the formula for the surface area of a cone:

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We are given the length of a side and the diameter, to calculate the radius divide the diameter in half:

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We can treat the side length as the hypotenuse C, the radius as the base A, and solve for height B. Set the expression up like this:

C^2 = A^2 + B^2\\24^2 = 9^2 + B^2\\B^2 = 24^2 - 9^2\\B = \sqrt{24^2 - 9^2}\\B = \sqrt{576 - 81}\\B = \sqrt{495}\\B \approx 22.25

Now we can plug into our original formula:

A = \pi r(r + \sqrt{h^2+r^2})\\A = \pi 9(9+\sqrt{\sqrt{495}^2+9^2}\\A = \pi 9(9+\sqrt{495 + 81}\\A = \pi 9(9+\sqrt{576})\\A = \pi 9(9 + 24)\\A = \pi 9(33)\\A = 297\pi

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2 years ago
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If you simplify this, you get:
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