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3 years ago

-3√-20 written as a complex number

Mathematics

1 answer:

galben [10]3 years ago

3 0

Answer: 3√-20 = 3√20√-1 = (3√20)i

Step-by-step explanation:

√-20 can be written √20√-1 since

(√20√-1)^2 is indeed -20.

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Use induction to show that 12 + 22 + 32 + ... + n2 = n(n+1)(2n+1)/6, for all n > 1.

dlinn [17]

Answer with Step-by-step explanation:

Let $P(n)=1^2+2^2+3^2+.....+n^2=\frac{n(n+1)(2n+1)}{6}$

Substitute n=2

Then $P(2)=1+2^2=5$

$P(2)=\frac{2(2+1)(4+1)}{6}=5$

Hence, P(n) is true for n=2

Suppose that P(n) is true for n=k >1

$P(k)=1^2+2^2+3^2+...+k^2=\frac{k(k+1)(2k+1)}{6}$

Now, we shall prove that p(n) is true for n=k+1

$P(k+1)=1^2+2^2+3^2+...+k^2+(k+1)^2=\frac{(k+1)(k+2)(2k+3)}{6}$

LHS

$P(k+1)=1^2+2^2+3^2+.....+k^2+(k+1)^2$

Substitute the value of P(k)

$P(k+)=\frac{k(k+1)(2k+1)}{6}+(k+1)^2$

$P(k+1)=(k+1)(\frac{k(2k+1}{6})+k+1)$

$P(k+1)=(k+1)(\frac{2k^2+k+6k+6}{6})$

$P(k+1)=(k+1)(\frac{2k^2+7k+6}{6})$

$P(k+1)=(k+1)(\frac{2k^2+4k+3k+6}{6})$

$P(k+1)=\frac{(k+1)(k+2)(2k+3)}{6}$

LHS=RHS

Hence, P(n) is true for all n >1.

Hence, proved

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3 years ago

To determine the number of trout in a lake, a conservationist catches 94 trout, tags them and throws them back into the lake.

densk [106]

Tagged? 84 if the 10 weren’t thrown back in general? 94+20=114 I’m not sure if this answers your question, sorry if it doesn’t, your question wasn’t very specific.

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3 years ago

A rectangular chair cushion

vodka [1.7K]

Answer:

144 square inches.

Step-by-step explanation:

4*12*3=144

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3 years ago

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Marco mark changes $3.98 for a pound of lean ground beef.how much a customer pay for 2.6 pound of lean ground beef?

melamori03 [73]

Answer:

$10.348

Step-by-step explanation:

(3.98)(2.6)= 10.348

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3 years ago

3) (Infer) What would happen if two kinds of animals living in the same habitat had the same niche?

Vedmedyk [2.9K]

1) if they had the same niche they either live in different areas of the niche due to adaptation or one of them will die due to competition with the other animal.
2) they might need to move to a different habitat due to lack of resources and the competition was better adapted to the circumstances.
hope this helps

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3 years ago