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torisob [31]
3 years ago
7

Use mathematical induction to prove that the statement is true for every positive integer n. 8 + 16 + 24 + . . . + 8n = 4n(n + 1

)
Mathematics
1 answer:
mezya [45]3 years ago
3 0
First show the statement holds for n=1. The left hand side is just 8, and the right hand side is 4(1)(1+1)=8, so it's true.

Assume the statement holds for n=k, i.e.

8+16+\cdots+8(k-1)+8k=4k(k+1)

and use this to show it holds for n=k+1, i.e.

8+16+\cdots+8(k-1)+8k+8(k+1)=4(k+1)(k+2)

By the assumption above, you have

\underbrace{8+16+\cdots+8(k-1)+8k}_{n=k}+8(k+1)=4k(k+1)+8(k+1)=4(k+1)(k+2)

so the statement is true for all n\ge1.
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The least common multiple of two numbers is 60, and one of the numbers is 7 less than the other number. What are the numbers? Co
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Explanation: As the least common multiple of two numbers is 60 , the two numbers are factors of 60 . Among {1,2,3,4,5,6,10,12,15,20,30,60} ,5 & 12 is the only two pair of numbers whose difference is 7 .

Answer: 5 & 12
8 0
3 years ago
5,398.461538461538 round to one more decimal
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Answer:

5,398.5

Step-by-step explanation:

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4 0
3 years ago
Two square sheets of cardboard used for making book covers differ in area by 64 square inches. An edge of the larger square is 2
photoshop1234 [79]

Answer:

15 inches

Step-by-step explanation:

We assume that the edge of the small square is x (inches).

As the edge of the larger square is 2 inches greater than that of the smaller one, so that the edge of the larger square = edge of the small square  + 2 = x + 2 (inches)

The equation to calculate the are of a square is: <em>Area = Edge^2 </em>

So that:

+) The area of the larger square is: <em>Area large square = </em>(x+2)^{2}<em> (square inches)</em>

+) The area of the smaller square is: <em>Area small square = </em>x^{2}<em>(square inches)</em>

<em />

As difference in area of both squares are 64 square inches, so that we have:

<em>Area large square - Area small square  = 64 (square inches)</em>

<em>=> </em>(x+2)^{2} -x^{2} =64<em />

<em>=>  </em>x^{2}+4x+4  -x^{2} =64<em />

<em>=> 4x + 4 = 64</em>

<em>=> 4x = 64 - 4 = 60 </em>

<em>=> x = 60/4 = 15 (inches)</em>

So the length of an edge of the smaller square is 15 inches

3 0
3 years ago
Why is there a 1/2 in this formula for the area of a trapezoid?
aleksandrvk [35]

A simple answer is that any given trapezoid with height h and length of the parallel lines a and b, is half of a parallelogram with an area of (a+b) x h. Since the trapezoid is half of this, it is h(a+b)/2

7 0
2 years ago
What is the solution to the inequality x - 2 &lt; -2?
7nadin3 [17]
Well the solution to this problem is x < -4
3 0
3 years ago
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