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2 years ago

Y

Mathematics

1 answer:

aev [14]2 years ago

7 0

Answer:

See attachment.

a) y = -x + 2

b) (2,1)

Step-by-step explanation:

Explained in the attachment.

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Situation:A researcher in North America discoversa fossile that contains 65% of its originalamount of C-14..-ktN=NoeNo inital am

zheka24 [161]

SOLUTION

We have been given the equation of the decay as

$\begin{gathered} N=N_0e^{-kt} \\ where\text{ } \\ N_0=initial\text{ amount of C-14 at time t} \\ N=amount\text{ of C-14 at time t = 65\% of N}_0=0.65N_0 \\ k=0.0001 \\ t=time\text{ in years = ?} \end{gathered}$

So we are looking for the time

Plugging the values into the equation, we have

$\begin{gathered} N=N_0e^{-kt} \\ 0.65N_0=N_0e^{-0.0001t} \\ e^{-0.0001t}=\frac{0.65N_0}{N_0} \\ e^{-0.0001t}=0.65 \end{gathered}$

Taking Ln of both sides, we have

$\begin{gathered} ln(e^{-0.000t})=ln(0.65) \\ -0.0001t=ln(0.65) \\ t=\frac{ln(0.65)}{-0.0001} \\ t=4307.82916 \end{gathered}$

Hence the answer is 4308 to the nearest year

8 0

9 months ago

Find the slope<br><br><br> Don’t mind my answer! I clicked a random on accident

Triss [41]

Answer:

The Answer is A, 1/2

8 0

3 years ago

Read 2 more answers

Each bag of pattern blocks contains 50 blocks. To make a class pattern, the teacher combines 4 bags of blocks. How many pattern

iVinArrow [24]

Each bag contains 50 pattern blocks so 4 bags is

50 x 4 = 200 pattern blocks

hope this helps

4 0

2 years ago

A family spent $186 per week for food. This was 20% of its weekly income. What was the weekly income?

geniusboy [140]

It was $930.

To over check, multiply it by 20% , you will get $186.

Hope this helps !

5 0

3 years ago

Read 2 more answers

Simplify completely. (w^15/w^5)^4 <br> HELP PLEASE

Umnica [9.8K]

Answer:

$w^{40}$

Step-by-step explanation:

To simplify recall exponent rules:

1. An exponent is only a short cut for multiplication. It simplifies how we write the expression.

2. When we multiply terms with the same bases, we add exponents.

3. When we divide terms with the same bases, we subtract exponents.

4. When we have a base to the exponent of 0, it is 1.

5. A negative exponent creates a fraction.

6. When we raise an exponent to an exponent, we multiply exponents.

7. When we have exponents with parenthesis, we apply it to everything in the parenthesis.

We will use these rules to simplify.

Use rule #3 to simplify inside the parenthesis first.

$\frac{w^{15}}{w^5} = w^{10}$

Now simplify the exponent of 4 using rule 6.

$(w^{10})^4 = w^{40}$

8 0

3 years ago