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2 years ago

12 and 35 Pythagorean theorem

Mathematics

1 answer:

Natali [406]2 years ago

5 0

Answer:

Hypotenuse = 37

Step-by-step explanation:

Let the base is 12 and height is 35.

We can use Pythagorean theorem to find the third side (hypotenuse or the longest side). The Pythagoras theorem can be given by :

$H^2=b^2+h^2\\\\H^2=12^2+35^2\\\\H^2=1369\\\\H=\sqrt{1369} \\\\H=37$

Hence, the hypotenuse is 37 units.

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Pachacha [2.7K]

The capital formation of the investment function over a given period is the

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$I(t) = 100 \cdot e^{0.1 \cdot t}$

(a) The capital formation is given as follows;

$\displaystyle Capital = \int\limits {100 \cdot e^{0.1 \cdot t}} \, dt =1000 \cdot e^{0.1 \cdot t}} + C$

From the end of the second year to the end of the fifth year, we have;

The end of the second year can be taken as the beginning of the third year.

Therefore, for the three years; Year 3, year 4, and year 5, we have;

$\displaystyle Capital = \int\limits^5_3 {100 \cdot e^{0.1 \cdot t}} \, dt \approx 298.87$

The capital formation from the end of the second year to the end of the fifth year, C ≈ 298.87

(b) When the capital stock exceeds $100,000, we have;

$\displaystyle \mathbf{\left[1000 \cdot e^{0.1 \cdot t}} + C \right]^t_0} = 100,000$

Which gives;

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The number of years before the capital stock exceeds $100,000 ≈ 46.15 years.

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