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3 years ago

In the diagram, DEC is a

Mathematics

1 answer:

Leya [2.2K]3 years ago

7 0

Step-by-step explanation:

This is a reflection. A reflection is a transformation involving two shapes looking the same by "bouncing it off a line without coming back.( meaning a reflection goes some where else not to it original poistion.)

Others reason why Why?

Line m is perpendicular to Line c.

B and E are equidistant from c that BC=CE.

Why the others are wrong.

While you could rotate this triangle 180 degrees, the transformation occurs about a line not a point. So using a rotation is wrong.

A translation doesnt occur about a line.

A guide reflection doesnt work since the transformations are already mapped correctly if you do the reflection. It doesnt need a translation.

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Step-by-step explanation:

At a constant decay rate, the half-life of a radioactive substance is the time taken for the substance to decay to half of its original mass. The formula for radioactive exponential decay is given by:

$A(t) = A_0 e^{(kt)}\\where:\\A(t) = Amount\ left\ at\ time\ (t) = 75\ grams\\A_0 = initial\ amount = 1000\ grams\\k = decay\ constant\\t = time\ of\ decay = 2500\ years$

First, let us calculate the decay constant (k)

$75 = 1000 e^{(k2500)}\\dividing\ both\ sides\ by\ 1000\\0.075 = e^{(2500k)}\\taking\ natural\ logarithm\ of\ both\ sides\\In 0.075 = In (e^{2500k})\\In 0.075 = 2500k\\k = \frac{In0.075}{2500}\\ k = \frac{-2.5903}{2500} \\k = - 0.001036$

Next, let us calculate the half-life as follows:

$\frac{1}{2} A_0 = A_0 e^{(-0.001036t)}\\Dividing\ both\ sides\ by\ A_0\\ \frac{1}{2} = e^{-0.001036t}\\taking\ natural\ logarithm\ of\ both\ sides\\In(0.5) = In (e^{-0.001036t})\\-0.6931 = -0.001036t\\t = \frac{-0.6931}{-0.001036} \\t = 669.02 years\\\therefore t\frac{1}{2} \approx 669\ years$

Therefore the half-life is between 600 and 700 years

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