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Svetlanka [38]
3 years ago
9

Jean has a loan of $2,000 the rate of simple interest in 8% a year he has paid $640 interest how many years has he had the loan

(with working out please)
Mathematics
1 answer:
Andreas93 [3]3 years ago
8 0
Simple interest means the interest at the end of each year will always be 8% of 2000 (assuming he doesnt pay some of it off), and will not be compounded with the existing interest.

To get a percentage, multiply by the percentage/100, in this case i.e. multiply by 0.08.
2000*0.08 = $160.
Therefore he has $160 of interest each year to pay.
Now we just need to work out how many lots of 160 go into 640, i.e. divide through.
640/160 = 4 - therefore he has had the loan for 4 years.
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The face of the triangular concrete panel shown has an area of 22 square meters, and its base is 3 meters longer than twice its
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Answer:

The length of the base is 11 meters.

Step-by-step explanation:

The diagram of the triangle is not shown; However, the given details are enough to solve this question.

Given

<em>Shape: Triangle</em>

<em>Represent the height with h and the base with b</em>

b = 3 + 2h

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Required

Find the length of the base

The area of a triangle is calculated as thus;

Area = \frac{1}{2} * b * h

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The formula becomes

22 = \frac{1}{2} * (3 + 2h) * h

Multiply both sides by 2

2 * 22 = 2 * \frac{1}{2} * (3 + 2h) * h

44 = (3 + 2h) * h

Open the bracket

44 = 3 * h + 2h * h

44 = 3h + 2h^2

Subtract 44 from both sides

44 - 44 = 3h + 2h^2 - 44

0 = 3h + 2h^2 - 44

Rearrange

0 = 2h^2 +3h - 44

2h^2 +3h - 44 = 0

At this point, we have a quadratic equation; which is solved as follows:

2h^2 +3h - 44 = 0

2h^2 + 11h - 8h - 44 = 0

h(2h + 11) - 4(2h + 11) = 0

(h - 4)(2h + 11) = 0

Split the above

(h - 4) = 0\ or\ (2h + 11) = 0

h - 4 = 0\ or\ 2h + 11 = 0

Solve the above linear equations separately

h - 4 = 0

Add 4 to both sides

h - 4 + 4 = 0 + 4

h = 0 + 4

h = 4 ---- <em>First value of h</em>

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Subtract 11 from both sides

2h + 11 - 11 = 0 - 11

2h  = 0 - 11

2h = -11

Divide both sides by 2

\frac{2h}{2} = -\frac{11}{2}

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Since height can be negative, we'll discard h = -\frac{11}{2}

Hence, the usable value of height is h = 4

Recall that b = 3 + 2h

Substitute 4 for h

b = 3 + 2(4)

b = 3 + 8

b = 11

Hence, the length of the base is 11 meters

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