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a 500 mg known substance in fossils decays at a rate of 10% per year. scientists find a fossil with 295.25 mg of the known substance. how old is the fossil?

x ≈ 5 years

Step-by-step explanation:

Given amount = A = 500 mg

Decay rate = r = 10% per year

Remaining amount = L = 295.25 mg

The formula to calculate remaining amount after x years decay =

L = A((100-r)/100)^x

By putting values in this formula, we get

295.25 = 500 ((100-10)/10)^x

295.25 = 500 (0.90)^x    

295.25/500 = 0.90^x

0.5905 = 0.90^x

0.90^x =0.5905

taking log on both sides

ln(0.90^x) =ln(0.5905)

x*ln(0.90) =ln(0.5905)  using property of log

x = ln(0.5905)/ln(0.90)

x = 4.9984

x ≈ 5 years

step-by-step explanation:

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°