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3 years ago

7

Looking at the two, 7

ula1" title="a^{4} b^{2} c^{2} and14abc^{6}" alt="a^{4} b^{2} c^{2} and14abc^{6}" align="absmiddle" class="latex-formula">

what is the GCF of these

1 answer:

AlexFokin [52]3 years ago

5 0

Answer:

$7abc^{2}$

Step-by-step explanation:

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The machinist's goal was to increase his production by at least 10% each day. Assume he achieved his goal. If he was able to mac

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3 years ago

A cone with radius 5 units is shown below. Its volume is 105 cubic units. Find the height of the cone.

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Answer:

height of the cone = 4.01273885 units

Step-by-step explanation:

Volume of a cone(V) is given by:

$V = \frac{1}{3} \pi r^2h$ ....[1]

where,

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4 years ago

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3 years ago

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Step-by-step explanation:

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We know that the summation between k = 0, and k = N - 1 for:

∑ r^k = (1 - r^N)/(1 - r)

if we have the summation between k = 0 and k = ∞ - 1 = ∞

(here we used that ∞ is really big, then ∞ - 1 = ∞)

In the numerator we will have the term r^∞, if 0 < r < 1, then r^∞ = 0.

Then if we assume that 0 < r < 1 we can write:

∑ r^k = 1/(1 - r)

In our case, we can rewrite our summation as:

3*∑ (1/2)^n

for n = 0 to n = ∞

You can see that i changed the limits for n, this does not really matter because we are summing between a number and infinity, the only thing you need to take care is that now the power is n, instead of (n - 1)

Then we have r = (1/2) which is clearly smaller than 1.

then (1/2)

Then this summation is equal to:

3*∑ (1/2)^n = 3*( 1/(1 - 1/2)) = 3*( 1/( 2/2 - 1/2)) = 3*( 1/(1/2)) = 3*2 = 6

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3 years ago