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9 days ago

How many pairs of whole numbers have a sum of 99

Mathematics

2 answers:

babunello [11.3K]9 days ago

8 0

I believe the answer is 99, as pairs can be formed by using numbers from 0 through 99.

Leona [12.1K]9 days ago

4 0

There are 50 pairs of whole numbers that can add up to 99. To clarify, consider the combinations: 0 + 99, 1 + 98, 2 + 97, and so on, up to 49 + 50. This observation indicates that counting all combinations would result in 50 pairs of distinct whole numbers that sum to 99. I hope this response assists you!

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21 day ago

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The blimp's altitude is 1635.363039 feet above the ground.

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Archie and Veronica stand one mile (5280 ft) apart on the ground, leading to AV = 5280 feet.

Let's denote the blimp's height above ground as XB = h feet.

Archie records the angle of elevation from the ground to the blimp as 53 degrees, signifying angle ∠BAX = 53°.

Veronica, meanwhile, measures the angle of elevation to the blimp at 22 degrees, indicating angle ∠BVX = 22°.

In Right triangle ΔAXB, we utilize cot(A) = AX / XB.

Thus, AX can be expressed as AX = XB*cot(A) = h*cot(53°) = 0.75355405*h.

In Right triangle ΔVXB, cot(B) is similar: cot(B) = VX / XB.

Consequently, VX is VX = XB*cot(B) = h*cot(22°) = 2.475086853*h.

We know AV = 5280, meaning AX + VX = AV.

Therefore, AX + VX equals 5280.

From here, we can write: 0.75355405*h + 2.475086853*h = 5280.

This simplifies to: 3.228640904*h = 5280.

Thus, h is calculated as 5280 / 3.228640904 = 1635.363039 feet.

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