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Viktor [21]
3 years ago
7

Maria rented a coat at $285 for 3 days. If she rents the same coat for 6 days, she has to pay a total rent of $510.

Mathematics
1 answer:
Dmitry_Shevchenko [17]3 years ago
6 0
The situation above is an arithmetic sequence with the third term (a3) equal to $285 and sixth term (a6) equal to $510. To determine the nth term of the arithmetic sequence, use the equation,
                                     an = a1 + (n - 1)d
where a1 is the first term and d is the common difference. To solve for these, use the given values,
                                 285 = a1 + (3-1)(d)
                                 510 = a1 + (5 -1)(d)
Solving for the unknowns gives an answer of a1 = 60 and d = 112.5.Thus, the equation is,
                                 y = 60 + 112.5x 
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The perimeter of a square with side a = 7.2 cm is 28.8 cm. Yes there exists a direct proportional relationship between Side length and Perimeter of square

<h3><u>Solution:</u></h3>

Given that side of square "a" = 7.2 cm

We have to find the perimeter of square

<em><u>The perimeter of square is given as:</u></em>

Perimeter of square = 4a

Where "a" represents the length of side of square

Substituting the given value a = 7.2 cm in above formula, we get perimeter of square

Perimeter of square = 4(7.2) = 28.8 cm

<em><u>Are the perimeter of the square and the length of its side directly proportional quantities?</u></em>

\begin{array}{l}{\text { perimeter of square }=4 a=4 \times \text { length of side }} \\\\ {\frac{\text { perimeter of square }}{\text { length of side }}=4}\end{array}

The Perimeter is equal to a constant times the Side length, or the Perimeter divided by the Side length is equal to four. So this is definitely a proportional relationship between Side length and Perimeter.

Two values are said to be in direct proportion when an increase in one results in an increase in the other.

So when length of sides increases, perimeter also increases

Hence perimeter and length of side of square are directly propotional quantities

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