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aivan3 [116]
3 years ago
11

I thought of the smallest counting number that is divisible by 10, 14, and 35...what is my number?

Mathematics
1 answer:
Inessa [10]3 years ago
3 0

Answer:

70

Step-by-step explanation:

break down each of the three numbers into primes

10 = 2 x 5

14 = 2 x 7

35 = 5 x 7

multiply 2 x 5 x 7 = 70

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I think I know this much so far for A (but I could be wrong):
Eduardwww [97]
Part A. You have the correct first and second derivative.

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Part B. You'll need to be more specific. What I would do is show how the quantity (-2x+1)^4 is always nonnegative. This is because x^4 = (x^2)^2 is always nonnegative. So (-2x+1)^4 >= 0. The coefficient -10a is either positive or negative depending on the value of 'a'. If a > 0, then -10a is negative. Making h ' (x) negative. So in this case, h(x) is monotonically decreasing always. On the flip side, if a < 0, then h ' (x) is monotonically increasing as h ' (x) is positive.

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Part C. What this is saying is basically "if we change 'a' and/or 'b', then the extrema will NOT change". So is that the case? Let's find out

To find the relative extrema, aka local extrema, we plug in h ' (x) = 0
h  ' (x) = -10a(-2x+1)^4
0 = -10a(-2x+1)^4
so either
-10a = 0 or (-2x+1)^4 = 0
The first part is all we care about. Solving for 'a' gets us a = 0. 
But there's a problem. It's clearly stated that 'a' is nonzero. So in any other case, the value of 'a' doesn't lead to altering the path in terms of finding the extrema. We'll focus on solving (-2x+1)^4 = 0 for x. Also, the parameter b is nowhere to be found in h ' (x) so that's out as well. 
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Step-by-step explanation:

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Answer:

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2. (p^2-6)[1-q(p^2-6)]

Step-by-step explanation:

1. The first thing to do to factor the expression is to take the expression (a + 3) as a common factor with its lowest exponent.

Then the expression. 5(a + 3)^2- (a + 3) remains as:

(a + 3)(5 (a + 3) -1)\\\\(a + 3)(5a +15 -1)\\\\(a + 3)(5a-14)

2. The first thing to do to factor the expression is to take the expression  p^2 -6 as its common factor with its lowest exponent.

Then the expression p^2- 6 - q(p^2- 6)^2 remains as:

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Answer:

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Step-by-step explanation:

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