What is 1.0833333333 in a fraction

The half-life of a radioactive substance is the time it takes for a quantity of the substance to decay to half of the initial am

posledela

Step-by-step walkthrough:

a.

Well a standard half-life equation looks like this.

$N = N_0 * (\frac{1}{2})^{t/p$

$N_0$ is the starting amount of parent element.

$N$ is the end amount of parent element

$t$ is the time elapsed

$p$ is a half-life decay period

We know that the starting amount is 74g, and the period for a half-life is 2.8 days.

Therefore you can create a function based off of the original equation, just sub in the values you already know.

$N(t) = 74g * (\frac{1}{2})^{t/2.8days$

b.

This is easy now that we have already made the function. Here we just reuse it, but plug in 2.8 days.

$N(t) = 74g * (\frac{1}{2})^{t/2.8days} = N(2.8days) = 74g * (\frac{1}{2})^{2.8days/2.8days}\\= 74g * \frac{1}{2} = 37g$

c.

Now we just gotta do some algebra. Use the original function but this time, replace $N(t)$ with 10g and solve algebraically.

$10g = 74g * (\frac{1}{2})^{t/2.8days}\\\\\frac{10g}{74g} = (\frac{1}{2})^{t/2.8days}$

Take the log of both sides.

$log(\frac{5}{37}) = log((\frac{1}{2})^{t/2.8days})$

Use the exponent rule for log laws that, $log(b^x) = x*log(b)$

$log(\frac{5}{37}) = \frac{t}{2.8days} * log(\frac{1}{2})$

$\frac{log(\frac{5}{37})}{log(\frac{1}{2})} = \frac{t}{2.8days}$

$2.8 * \frac{log(\frac{5}{37})}{log(\frac{1}{2})} = t$

slap that in your calculator and you get

$t = 8.1 days$

7 0

2 years ago

Ben is 12 years older than Ishaan. Ben and Ishaan first met two years ago. Three years ago, Ben was 4 times as old as Ishaan?

Marina86 [1]

The first statement means:

b=i+12,

The third statement means:

b-3=4(i-3),

b-3=4i-12

b=4i-9

Using the value for b from the first statement in the third statement gives you:

i+12=4i-9

-3i=-21

i=7: and since b=i+12

b=19

So Ben is 19 and Ishaan is 7.

6 0

3 years ago

Is 6.6 a rational number

Crank

it is a rational number because it can be written as the ratio of two integers

3 0

3 years ago

Read 2 more answers

I have no idea what im doing, can someone please help me? ASAP!!!! Use the pythagorean theorem to find the missing slide.

Solnce55 [7]

Answer:

1. b=√56

Step-by-step explanation:

1. Pythagorean therom states a²+b²=c² and in number 1 we are given the c or the hypotenuse so plugging in the values we know 13²+b²=15²

which equals 169+b²=225 subtract 169 from both sides and we get b²=56

square root both sides and we get b=√56

7 0

3 years ago

I really need help with number 12

Usimov [2.4K]

Answer:

7.8125 gallons

Step-by-step explanation:

Because 5 gallons would cover 1600 square-foot wall so 1 gallon would cover:

1600 / 5 = 320 square-foot wall.

So to cover 2500 square foot-wall, we need in total of:

2500 / 320 = 7.8125 gallons of paint

Hope this can help you :3

5 0

3 years ago