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lord [1]
3 years ago
10

How would you do this problem? :

Mathematics
1 answer:
Nat2105 [25]3 years ago
5 0
L = 3 + w

2(L+w) < 52.  Substitute the first equation into inequality

2(3 + w +w) < 52
2(3+2w) < 52      Divide both sides by 2
3 + 2w  < 26
2w < 26-3
2w < 23
w < 23/2
w < 11.5

Recall, L = 3+w.
w < 11.5  Add 3 to both sides.
w+3 < 11.5 +3
L < 14.5.

The width is less than 11.5, and the length is less than 14.5.
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the Following table shows alexandra's investment options over the course of three years. Her initial investment was $1,000 . wri
Y_Kistochka [10]

The pattern in the given series of amount in the account are in the form of

arithmetic and geometric progression.

  • The function for Option 1 is;  \underline{ f(n) = 1,100 + (n - 1) \cdot 100}
  • The function for Option 2 is; \underline{f(n) = 1,100 \times  1.1^{(n - 1)}}

Reasons:

The given table of values is presented as follows;

\begin{tabular}{c|c|c|c|}Number of years&1&2&3\\Option 1 (Amount in dollars)&1,100&1,200&1,300\\Option 2 (Amount in dollars)&1,100&1,210&1,331\end{array}\right]

In Option 1, the amount in dollars for each year has a common difference of d = 100

The first term, a = 1,100

Therefore;

The Option 1 can be represented as an arithmetic progression , A.P. in the

form, tₙ = a + (n - 1)·d as follows;

For the Option 1, we have;

  • The amount in dollars after <em>n</em> years, \underline{ f(n) = 1,100 + (n - 1) \cdot 100}

For Option 2, it is possible to find;

1,331 ÷ 1,210 = 1,210 ÷ 1,100 = 1.1

Therefore;

The terms in the Option 2 have a common ratio of r = 1.1

The Option 2 is a geometric progression, G.P.

The first term in Option 2 is a = 1,100

Which gives, the nth term, tₙ = a·r⁽ⁿ ⁻ ¹⁾

Therefor;

  • The function for the Option 2 is; \underline{f(n) = 1,100 \times  1.1^{(n - 1)}}

Learn more about arithmetic and geometric progression here:

brainly.com/question/8932895

brainly.com/question/22977503

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2 years ago
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Step-by-step explanation:

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nexus9112 [7]

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Potential  \:  \: Energy =(mass) \times (gravity \: acceleration) \times (height) \\

_________________________________

If gravity acceleration is 10 :

PE = 25 \times 10 \times 10

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_________________________________

If gravity acceleration is 9.8 :

PE = 25 \times 9.8 \times 10

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Step-by-step explanation:

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