3 years ago

If four angles of a convex pentagon measure 120°, 93°, 108°, and 101°, find the measure of the fifth angle

Mathematics

1 answer:

Art [367]3 years ago

6 0

Answer:

Step-by-step explanation:

For a polygon of N sides, the sum is

N*(180-360/N) = N*180 - 360 degrees

Subtract (120 +93 +108 +101) from 540 for your answer

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Plutonium-240 decays according to the function L where o

PIT_PIT [208]

Answer:

$\boxed{\textbf{1700 yr}}$

Step-by-step explanation:

$-\dfrac{\text{d}L}{\text{d}t} = kL\\\\\dfrac{dL}{L}=-kdt\\\\\ln L = -kt + C\\\text{At t = 0, L = L$_{0}$, so C = $\ln L_{0}$}\\\ln L = -kt + \ln L_{0}\\\ln L_{0} - \ln L = kt\\\\\ln \dfrac{L_{0}}{L} =kt$

Data:

L₀ = 24 g

L = 20 g

k = 0.000 11 yr⁻¹

Calculation:

$\ln \dfrac{24}{20} =0.000 11t\\\\\ln 1.2 = 0.000 11t\\\\0.1823 = 0.000 11t\\\\t = \dfrac{0.1823}{0.000 11} = \textbf{1700 yr}\\\\\text{It will take } \boxed{\textbf{1700 yr}}\text{ for the polonium to decay to 20 g}$