What does the slope signify in this equation and why?

Mathematics

1 answer:

Vadim26 [7]3 years ago

6 0

Answer:

The slope and y-intercept values indicate characteristics of the relationship between the two variables x and y. The slope indicates the rate of change in y per unit change in x.

Step-by-step explanation:

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Divide 8/12 to find an equivalent fraction

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3 years ago

The isotope samarium-151 decays into europium-151, with a half-life of around 96.6 years. A rock contains 5 grams of samarium-15

Olegator [25]

Part A:

The amount of substance left of a radioactive substance with a half life $t_{ \frac{1}{2} }$ and amount of initial substance $N_0$ is given by

$N(t)=N_0\left( \frac{1}{2} \right)^{ \frac{t}{t_{ \frac{1}{2} }} }$

Given that the isotope samarium-151 has a half-life of around 96.6 years and the rock contains 5 grams of samarium-151 when it reaches its closure temperature, and it contains 0.625 grams when it is discovered.

The time since the rock reached its closure temperature is obtained as follows:

$0.625=5\left( \frac{1}{2} \right)^{ \frac{t}{96.6} } \\ \\ \Rightarrow\left( \frac{1}{2} \right)^{ \frac{t}{96.6} }= \frac{0.625}{5} =0.125 \\ \\ \Rightarrow\frac{t}{96.6}\log{ \frac{1}{2} }=\log0.125 \\ \\ \Rightarrow\frac{t}{96.6}= \frac{\log0.125}{\log{ \frac{1}{2} }} =3 \\ \\ \Rightarrow t=3(96.6)=289.8$

Therefore, the time since the rock reached its closure temperature is 289.8 years.

Part B:

Given that the rock contains 5 grams of samarium-151 when it reaches its closure temperature, and it contains 0.625 grams when it is discovered. The number of grams of europium-151 when the rock was discovered is 5 - 0.625 = 4.375

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4 years ago

How many diagonals does a cube have

Aleksandr-060686 [28]

A cube has 4 "space" diagonals or diagonals within the cube's interior.

On its surface, a cube has 12 "face" diagonals, 2 per each of its six congruent square faces.

So the total number of diagonals is 4 + 12 = 16

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3 years ago

What does the slope signify in this equation and why?​

What does the slope signify in this equation and why?