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Setler [38]
3 years ago
13

Two sides of a parallelogram are 65 feet and 87 feet. The measure of the angle between these sides is 52°. Find the area of the

parallelogram to the nearest square foot.
Mathematics
1 answer:
telo118 [61]3 years ago
3 0

Answer:

Area of the parallelogram is approximately 4,456.2 square feet

Step-by-step explanation:

The lengths of the sides of the parallelogram are 65 feet and 87 feet

The measure of the angle between the sides, Y = 52°

The formula for finding the area of a parallelogram is given as follows;

Area of a parallelogram = A·B·sin(Y)

Where;

'A' and 'B' are the length of the parallel sides and 'Y' is the measure of the angle between them

Let 'A' and 'B' represent the 65 feet and the 87 feet respectively, we get;

Area of the parallelogram = 65 ft. × 87 ft. × sin(52°) ≈ 4,456.2 ft.²

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Step-by-step explanation:

I'm not quite sure if I'm doing this right myself but I'll give it a shot.

We use this formula to find half-life but we can just plug in the numbers we know to find <em>t</em>.

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We know half-life is 5730 years and that the parchment has retained 74% of its Carbon-14. For A_{0 let's just assume that there are 100 original  atoms of Carbon-14 and for A(t) let's assume there are 74 Carbon-14 atoms AFTER the amount of time has passed. That way, 74% of the C-14 still remains as 74/100 is 74%. Not quite sure how to explain it but I hope you get it. <em>h</em> is the last variable we need to know and it's just the half-life, which has been given to us already, 5730 years, so now we have this.

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Now, solve. First, divide by 100.

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Take the log of everything

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Divide the entire equation by log (0.5) and multiply the entire equation by 5730 to isolate the <em>t</em> and get

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