Factor -8m^3n^3+2m^5+2m^3

The half-life of a newly discovered radioactive element is 30 seconds. To the nearest tenth of a second, how long will it take f

Alexeev081 [22]

Answer:

It will take about 109.3 seconds for nine grams of the element to decay to 0.72 grams.

Step-by-step explanation:

We can write a half-life function to model our function.

A half-life function has the form:

$\displaystyle A=A_0\left(\frac{1}{2}\right)^{t/d}$

Where A₀ is the initial amount, t is the time that has passes (in this case seconds), d is the half-life, and A is the amount after t seconds.

Since the half-life of the element is 30 seconds, d = 30. Our initial sample has nine grams, so A₀ is 9. Substitute:

$\displaystyle A=9\left(\frac{1}{2}\right)^{t/30}$

We want to find the time it will take for the element to decay to 0.72 grams. So, we can let A = 0.72 and solve for t:

$\displaystyle 0.72=9\left(\frac{1}{2}\right)^{t/30}$

Divide both sides by 9:

$\displaystyle 0.08=\left(\frac{1}{2}\right)^{t/30}$

We can take the natural log of both sides:

$\displaystyle \ln(0.08)=\ln\left(\left(\frac{1}{2}\right)^{t/30}\right)$

By logarithm properties:

$\displaystyle \ln(0.08)=\frac{t}{30}\ln(0.5)$

Solve for t:

$\displaystyle t=\frac{30\ln(0.08)}{\ln(0.5)}\approx109.3\text{ seconds}$

So, it will take about 109.3 seconds for nine grams of the element to decay to 0.72 grams.

5 0

3 years ago

Level 1-2 1. Sally picked 5 apples, but she needs 12 to bake 3 apple pies. How many more apples does Sally need? (To access the

Mnenie [13.5K]

Step-by-step explanation:

sally needs 7 more Apples, but if Sally is doubling the recipe she will need 14 more Apples

7 0

3 years ago

Read 2 more answers

The Sugar Sweet Company will choose from two companies to transport its sugar to market. The first company charges $7500 to rent

Oduvanchick [21]

This seems to be an incomplete question. I think you want to know the amount of sugar at which both company will charge the same. Based on this idea, i am answering the question.
Let us assume the quantity of sugar = x
Then
For company A, charge = 7500 + 125.25x
For company B, charge = 5995 + 200.50x
Now
7500 + 125.25x = 5995 + 200.50x
7500 - 5995 = 200.50x - 125.25x
1505 = 75.25x
x = 20
From the above deduction it can be concluded that the quantity of sugar at which the prices of both the companies will be the same is 20 ton.

8 0

3 years ago

If f(x)=2x+3÷2,find f-1(x).

BartSMP [9]

The required inverse function $f^{-1}(x)$ = (2x - 3 ) / 4.

Given that,
f(x) = (2x+3) / 2

To find $f^{-1}(x)$

<h3>What are functions?</h3>

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Let f(x) = y
y = (2x + 3) / 2
y * 2 = 2x + 3
2y - 3 = 2x
x = (2y - 3) / 2
Now replace y = x and x = $f^{-1}(x)$
$f^{-1}(x)$ = (2x - 3 ) / 4

Thus, the required inverse function $f^{-1}(x)$ = (2x - 3 ) / 4.

Learn more about function here:

brainly.com/question/21145944

#SPJ1

3 0

2 years ago

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Question 10 of 10

Zina [86]

Step-by-step explanation:

D.the set of all possible output values.