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KIM [24]
4 years ago
6

PLEASE HELP ASAP WILL GIVE BRAINLIYS

Mathematics
1 answer:
lubasha [3.4K]4 years ago
4 0

Answer:

$ x = 1$ or $ x = 2 $

Step-by-step explanation:

Given:

$ f(x) = 2x \hspace{5mm} \& \hspace{5mm} g(x) = 2^x $

We are to find the values of $ x $ such that these two functions are equal.

Substitute $ x = 1 $.

We get $ f(x) = 2(1) = 2 \hspace{5mm} \& \hspace{5mm} g(x) = 2^{(1)} = 2$

Hence for $ x = 1 $ we have the functions to be equal.

Now for $ x =  2 $

$ f(2) = 2(2) = 4 \hspace{5mm} \& \hspace{5mm} g(2) = 2^{(2)} = 4 $

We see the functions are once again equal.

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A small town has 2000 inhabitants. At 8 AM, 160 people have heard a rumor. By noon half the town has heard it. At what time will
QveST [7]

Answer:

3:36 PM

Step-by-step explanation:

Let fraction (y) of the people that heard the rumor , the differential equation that is satisfied by the by y is,

                            \frac{dy}{dt} = ky(1-y)

Solving the differential equation,

                          y(t) = \frac{y_{o}}{[y_{o} + (1 + y_{o})e^{-kt}]}

The total number of inhabitants of the town = 2000

The number of people that  heard the rumor = 160

At 8 AM, let t = 0,

               y(0) = \frac{160}{2000}

                       = 0.08

By noon, half of the town as heard the rumor.

Then,    

                y(4) = \frac{1}{2}

Therefore,

              \frac{1}{2} = \frac{0.08}{[0.08 + (1 - 0.08)e^{-4k}]}

              \frac{0.08}{[0.08 + 0.92e^{-4k}]} = \frac{1}{2}

              0.08 + 0.92e^{-4k} = 0.16  

              0.92e^{-4k} = 0.16 - 0.08

              0.92e^{-4k} = 0.08

              e^{-4k} = \frac {0.08}{0.92}

              k = - \frac{1}{4} In(\frac {0.08}{0.92})

              k ≈ 0.06106

Calculating time, t when y(t) = 90%

        ⇒ y(t) = 0.9

              \frac{0.08}{[0.08 + 0.92e^{-0.06106t}]} =0.9

              0.08 + 0.92e^{-0.06106t} = \frac {0.9}{0.08}

              0.08 + 0.92e^{-0.06106t} = 0.089

              0.92e^{-0.06106t} = 0.089 - 0.08

              0.92e^{-0.06106t} = 0.0089

              t = - \frac{1}{0.06106}In (\frac{0.0089}{0.92})

              t = 7.59 hours

              ⇒ 7 hours 36 minutes

From 8 A.M. plus 7 hours 36 minutes = 3:36 PM

At 3:36 PM will 90% of the population have heard the rumor

             

             

             

7 0
3 years ago
What equation has the solution x=8?
Anton [14]

Answer:

X/4 = 2


X=8

8 divided by 4 is 2 and 4x2 is 8


6 0
2 years ago
The total amount of deductions for an employee's gross pay is $83.20. If the gross pay is $378.18, what percent of their gross p
fredd [130]

Answer:

22%

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
Please can you help me with this problem? Thanks.
777dan777 [17]
-2.5(1-2n)-1.5n
=-2.5+5n-1.5n
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Answer: B.  -2.5+3.5n

8 0
4 years ago
Read 2 more answers
the cost of tickets is 72 dollars for six pets and 96 for eight pets what is the independent variable
murzikaleks [220]

Answer:

Amount of pets

Step-by-step explanation:

The price of a ticket doesn't necesarilly effect the amount of pets but the amount of pets effects the ticket price. Therefore, the ticket price needs the pets which means that is the independent variable and the number of pets is the independent.

7 0
3 years ago
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