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allsm [11]
2 years ago
5

What is the sum of all of the perfect squares between

Mathematics
1 answer:
Nonamiya [84]2 years ago
7 0

Answer:

(-138) is the answer.

Step-by-step explanation:

Perfect square numbers between 15 and 25 inclusive are 16 and 25.

Sum of perfect square numbers 16 and 25 = 16 + 25 = 41

Sum of the remaining numbers between 15 and 25 inclusive means sum of the numbers from 17 to 24 plus 15.

Since sum of an arithmetic progression is defined by the expression

S_{n}=\frac{n}{2}[2a+(n-1)d]

Where n = number of terms

a = first term of the sequence

d = common difference

S_{8}=\frac{8}{2} [2\times 17+(8-1)\times 1]

   = 4(34 + 7)

   = 164

Sum of 15 + S_{8} = 15 + 164 = 179

Now the difference between 41 and sum of perfect squares between 15 and 25 inclusive = 41-179

= -138

Therefore, answer is (-138).

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The area of a rectangle is 30 square meters. Find the length and width if the length is 1.45 times the width.
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Answer:

<u>The length of the rectangle is 14.5√6/29 or 6.6 meters and the width is 10√6/29 or 4.55 meters.</u>

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Area of a rectangle = 30 square meters

2. Find the length and width if the length is 1.45 times the width.

Width of the rectangle = x

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Now substituting in the formula of the area of a rectangle, this way:

30 = x * 1.45x

30 = 1.45x²

x² = 30/1.45

x = √30/1.45

x = 10 √6/29 or 4.55 (Rounding to two decimal places)

1.45 x = 14.5 √6/29 or 6.6

<u>The length of the rectangle is 14.5√6/29 or 6.6 meters and the width is 10√6/29 or 4.55 meters.</u>

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Step-by-step explanation:

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Answer:

Step-by-step explanation:

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