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drek231 [11]
3 years ago
14

Find the slope of the line that passes through (10,8) and (1,9).

Mathematics
2 answers:
alexandr1967 [171]3 years ago
5 0

Answer:

-1/9

Step-by-step explanation:

plug in the slope formula:

y-y

-----

x-x

=9-8

-------

1-10

=-1/9

lesya [120]3 years ago
3 0

Answer:

-\frac{1}{9}

Step-by-step explanation:

between (1, 9) and (10, 8), the x moves by 9 and y moves by -1

The slope is equal to: \frac{\Delta y}{\Delta x} = \frac{-1}{9} = -\frac{1}{9}

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A student in Greece discovers a pottery bowl that contains 28% of its original amount of C-14 find the age of the pottery bowl t
Andreyy89

Answer:

The age of the pottery bowl is 10523 years.

Step-by-step explanation:

Amount of substance:

The amount of a substance after t years is given by the following equation:

A(t) = A(0)(1-r)^t

In which A(0) is the initial amount and r is the decay rate.

Half-life of C14.

Researching, the half-life of c-14 is 5730 years.

This means that:

A(5730) = 0.5A(0)

We use this to find r. So

A(t) = A(0)(1-r)^t

0.5A(0) = A(0)(1-r)^{5730}

(1-r)^{5730} = 0.5

\sqrt[5730]{(1-r)^{5730}} = \sqrt[5730]{0.5}

1 - r = 0.5^{\frac{1}{5730}}

1 - r = 0.99987903922

So

A(t) = A(0)(0.99987903922)^t

Age of the pottery bowl:

We have that:

A(t) = 0.28A(0)

We have to find t. So

A(t) = A(0)(0.99987903922)^t

0.28A(0) = A(0)(0.99987903922)^t

(0.99987903922)^t = 0.28

\log{(0.99987903922)^t} = \log{0.28}

t\log{0.99987903922} = \log{0.28}

t = \frac{\log{0.28}}{\log{0.99987903922}}

t = 10523.1

So

The age of the pottery bowl is 10523 years.

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Answer:

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