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Karo-lina-s [1.5K]
3 years ago
14

Find the sum of the angle measures in a regular polygon.

Mathematics
2 answers:
Oksana_A [137]3 years ago
6 0

Answer:

D) 1260°

Step-by-step explanation:

In an n-sided polygon, the sum of all angles is equal to (n-2)*180°.

Look at it this way - let's add a point in the middle and connect it to each vertex. Then we've got n triangles for a total of n*180°, but all of the angles at the middle point aren't "part" of the polygon, so a full 360° angle should be subtracted, giving us n*180°-360° = (n-2)*180°

You can easily confirm that it works for triangles and quadrangles ;)

The figure in the picture has 9 sides, so the sum of angles is (9-2)*180° = 7*180° = 1260°

Stells [14]3 years ago
5 0

1260°

hope this helps ^-^

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Pachacha [2.7K]

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

accumulated  capital for the period.

  • (a) The capital formation from the end of the second year to the end of the fifth year is approximately <u>298.87</u>.

  • (b) The number of years before the capital stock exceeds $100,000 is approximately <u>46.15 years</u>.

Reasons:

(a) The given investment function is presented as follows;

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;

\displaystyle 1000 \cdot  e^{0.1 \cdot t}} - 1000 = 100,000

\displaystyle \mathbf{1000 \cdot  e^{0.1 \cdot t}}} = 100,000 + 1000 = 101,000

\displaystyle e^{0.1 \cdot t}} = 101

\displaystyle t = \frac{ln(101)}{0.1} \approx 46.15

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

Learn more investment function here:

brainly.com/question/25300925

6 0
2 years ago
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Alexxx [7]

9514 1404 393

Answer:

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Step-by-step explanation:

To find c using the Law of Sines, you must know angle C. That is found from ...

  C = 180° -A -B = 180° -150° -12° = 18°

Then the law of sines tells you ...

  c/sin(C) = b/sin(B)

  c = b·sin(C)/sin(B) = (10 cm)·sin(18°)/sin(12°)

  c ≈ 14.9 cm

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2 years ago
(3/7 * (- 5/8)) + (1/3 * 5/6) + |- 1/2 - 1/5|
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Answer:

Exact Form:

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Decimal Form:

0.70992063

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