Use the Pythagorean Equation to find the distance between points x and y

Mathematics

1 answer:

snow_tiger [21]3 years ago

6 0

Start at point x and count down until you are in line with point y. (This will be five units). From the point you just ended at, count across until you get to point y. (This will be 9 units). Five units and nine units are the lengths of your two legs. The Pythagorean theorem is a^2+b^2=c^2. So you then take 5^2+9^2=c^2, or 25+81=c^2, or 106=c^2. Then square root each side, and get 10.2956=c. Therefore the distance between points x and y is 10.2956, or 10.3 if you choose to round.

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What is the term of a 7-term geometric series if the first term is -11 the last term is -45,056 and the common ratio is -4

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I assume you mean to ask how to find the sum of the seven terms?

You have

$a_2=ra_1$
$a_3=ra_2=r^2a_1$
$a_4=ra_3=r^3a_1$
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$a_7=ra_6=r^6a_1$

So the sum is

$a_1+ra_1+r^2a_1+\cdots+r^6a_1=a_1(1+r+r^2+\cdots+r^6)=a_1\times\dfrac{1-r^7}{1-r}$

You know that $a_1=-11$ and $r=-4$ , so the sum is equal to

$-4\times\dfrac{1-(-4)^7}{1-(-4)}=-13108$