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valina [46]
3 years ago
14

If AB = 10, AD = 8, and AE = 12, what is the length of EC?

Mathematics
1 answer:
Karolina [17]3 years ago
6 0

Answer:

AB is 16 units.

Step-by-step explanation:

Given:

AE = EC

BF = FC

EF = 8 and DF = 10

To Find:

AB = ?

Solution:

Mid Point Theorem:

The Midpoint Theorem states that "the segment joining two sides of a triangle at the midpoints of those sides is parallel to the third side and is half the length of the third side".

AE = EC .....Given

Therefore E is the Mid Point of AC.

BF = FC .....Given

Therefore F is the Mid Point of BC.

Therefore,

EF || AB            ........................Mid Point Theorem.

         ..............Mid Point Theorem.

Substituting the values we get

Therefore AB is 16 units.

Step-by-step explanation:

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The half life of silicone-32 is 710 years. If 30 grams is present now, how much will be present in 300 years?
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Answer:

22.38 g of silicone-32 will be present in 300 years.

Step-by-step explanation:

A radioactive half-life refers to the amount of time it takes for half of the original isotope to decay and its given by

                                           N(t)=N_0(\frac{1}{2})^{\frac{t}{t_{1/2}}

where,

N(t) = quantity of the substance remaining

N_0 = initial quantity of the substance

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From the information given we know:

  • The initial quantity of silicone-32 is 30 g.
  • The time elapsed is 300 years.
  • The half life of silicone-32 is 710 years.

So, to find the quantity of silicone-32 remaining we apply the above equation

N(t)=30\left(\frac{1}{2}\right)^{\frac{300}{710}}=30\left(\frac{1}{2}\right)^{\frac{30}{71}}\approx22.38 \:g

22.38 g of silicone-32 will be present in 300 years.

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There is a blizzard, and Matt notices that the snow is falling at a constant rate. Two hours after the beginning of the snowstor
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In 2000, the population of Massachusetts
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Answer:

The population reaches 7 million people in the year 2032.

Step-by-step explanation:

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Using this model, find the year when the population reaches 7 million people.

This is x years after 2000, in which x is found when f(x) = 7. So

f(x) = 6.3*(1.0032)^{x}

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We have to following logarithm rule

\log{a^{x}} = x\log{a}

So we apply log to both sides of the equality

\log{(1.0032)^{x}} = \log{1.11}

x\log{1.0032} = \log{1.11}

x = \frac{\log{1.11}}{\log{1.0032}}

x = 32.66

2000 + 32.66 = 2032

The population reaches 7 million people in the year 2032.

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