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aleksandrvk [35]
3 years ago
15

A certain gecko measured 3.5 inches as a hatchling, and then grows at a steady rate of 1.2 inches per month for the first 12 mon

ths. After that, the gecko grows at 0.4 inches per month for the next 16 months. How many inches long will the gecko be 20 months after hatching? please I need help and no link
Mathematics
1 answer:
gregori [183]3 years ago
6 0

Answer:

21.1 inches

Step-by-step explanation:

The gecko is 3.5 inches to start with.

If it grows at a rate of 1.2 inches per month for the first 12 months, after 12 months the gecko will be 14.4 inches larger. (Because 12 times 1.2 is 14.4)

So, after 12 months the gecko will be 17.9 inches.

Since the gecko grows at 0.4 inches per month for the next 16 months, and the gecko has grown for 20 months, all we need to do is subtract 12 from 20 (since we already calculated how long it will be after 12 months) and multiply that by 0.4.

Since 20 - 12 is 8, we just multiply 8 by 0.4 to get 3.2. We now add 3.2 to 17.9 to get 21.1 inches.

Hope this helps!

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Notice that

(n+1)^4-n^4=4n^3+6n^2+4n+1

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\displaystyle\sum_{i=1}^n((n+1)^4-n^4)=\sum_{i=1}^n(4i^3+6i^2+4i+1)

We have

\displaystyle\sum_{i=1}^n((i+1)^4-i^4)=(2^4-1^4)+(3^4-2^4)+(4^4-3^4)+\cdots+((n+1)^4-n^4)

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\displaystyle(n+1)^4-1=\sum_{i=1}^n(4i^3+6i^2+4i+1)

You might already know that

\displaystyle\sum_{i=1}^n1=n

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\displaystyle\sum_{i=1}^ni^2=\frac{n(n+1)(2n+1)}6

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\displaystyle(n+1)^4-1=4\sum_{i=1}^ni^3+n(n+1)(2n+1)+2n(n+1)+n

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If you don't know the formulas mentioned above:

  • The first one should be obvious; if you add n copies of 1 together, you end up with n.
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  • The third can be derived using a similar strategy to the one used here. Consider the expression (n+1)^3-n^3=3n^2+3n+1, and so on.
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