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3 years ago

If the perimeter of an isosceles triangle with integral sides is 2017, how many different lengths are possible for the legs

1 answer:

7 0

Because the perimeter is 2017, the side lengths must add to 2017;
a+b+c=2017
An isosceles triangle has two sides of the same length, so b=a. These two sides of the same length are the "legs".
a+a+c=2017
2a+c=2017
Integral means integer (assuming this is not a calculus problem). So, the smallest possible length for side c is 1.
2a+1=2017
2a=2016
a=1008
The legs can be up to 1008 units long apiece. Because the legs must be integer values, 1008 different lengths are possible for the legs.

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Answer:

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Step-by-step explanation:

Let the number of years passed since 2010 to reach population more than 7000000 be 'x'.

Given:

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A population growth is an exponential growth and is modeled by the following function:

$P=P_0(1+r)^x$

Taking log on both sides, we get:

$\log(P)=\log(P_0(1+r)^x)\\\log P=\log P_0+x\log (1+r)\\x\log (1+r)=\log P-\log P_0\\x\log(1+r)=\log(\frac{P}{P_0})\\x=\frac{\log(\frac{P}{P_0})}{\log(1+r)}$

Plug in all the given values and solve for 'x'.

$x=\frac{\log(\frac{700,000}{450,000})}{\log(1+0.05)}\\x=\frac{0.192}{0.021}=9.13\approx 10$

So, for $x > 9.13$ , the population is over 700,000. Therefore, from the tenth year after 2010, the population will be over 700,000.

Therefore, the tenth year after 2010 is 2020.

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Step-by-step explanation:

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Step-by-step explanation:

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