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Oliga [24]
2 years ago
7

In right triangle $ABC,$ $\angle C = 90^\circ.$ Median $\overline{AM}$ has a length of $19,$ and median $\overline{BN}$ has a le

ngth of $13.$ What is the length of the hypotenuse of the triangle?
Mathematics
1 answer:
Kryger [21]2 years ago
8 0

Answer:

  AB = 2√106 ≈ 20.591

Step-by-step explanation:

The Pythagorean theorem says the square of the hypotenuse is equal to the sum of the squares of the legs.

For median AM, we have ...

  AM² = CM² +AC² = (BC/2)² +AC²

For median BN, we have ...

  BN² = CN² +BC² = (AC/2)² +BC²

The sum of these two equations is ...

  AM² +BN² = BC²/4 +AC² +AC²/4 +BC² = (5/4)(AC² +BC²)

  AM² +BN² = (5/4)(AB²)

The hypotenuse of triangle ABC is then ...

  AB = √(4/5(AM² +BN²))

  AB = 2√((19² +13²)/5)

  AB = 2√106 ≈ 20.591

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This question is incomplete. Below is the complete question:

A bank account earned 3.5% continuously compounded annual interest. After the initial deposit, no deposits or withdrawals were made. At the end of an 8 year period, the balance in the account was $13231.30. what is the amount of the initial deposit?

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Step-by-step explanation:

To solve this we need to utilize the continuous compounding interest formula:-

Fv = Pv × e^(i × t)

Where, Fv = the future value

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