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2 years ago

Please help me thank you

Mathematics

1 answer:

Olenka [21]2 years ago

4 0

Step-by-step explanation:

$6 \sqrt{2}$

this is the answer

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An advertising company designs a campaign to introduce a new product to a metropolitan area of population 3 Million people. Let

Advocard [28]

Answer:

$P(t)=3,000,000-3,000,000e^{0.0138t}$

Step-by-step explanation:

Since P(t) increases at a rate proportional to the number of people still unaware of the product, we have

$P'(t)=K(3,000,000-P(t))$

Since no one was aware of the product at the beginning of the campaign and 50% of the people were aware of the product after 50 days of advertising

We have and ordinary differential equation of first order that we can write

$P'(t)+KP(t)= 3,000,000K$

The <em>integrating factor </em>is

$e^{Kt}$

Multiplying both sides of the equation by the integrating factor

$e^{Kt}P'(t)+e^{Kt}KP(t)= e^{Kt}3,000,000*K$

Hence

$(e^{Kt}P(t))'=3,000,000Ke^{Kt}$

Integrating both sides

$e^{Kt}P(t)=3,000,000K \int e^{Kt}dt +C$

$e^{Kt}P(t)=3,000,000K(\frac{e^{Kt}}{K})+C$

$P(t)=3,000,000+Ce^{-Kt}$

But P(0) = 0, so C = -3,000,000

and P(50) = 1,500,000

$e^{-50K}=\frac{1}{2}\Rightarrow K=-\frac{log(0.5)}{50}=0.0138$

And the equation that models the number of people (in millions) who become aware of the product by time t is

$P(t)=3,000,000-3,000,000e^{0.0138t}$

5 0

3 years ago

What is 7 4/10 -1 1/3

Goryan [66]

The answer is 6 and 1/15.

7 0

2 years ago

Read 2 more answers

What is the inverse of f(x) = sqft x+ 3

grin007 [14]

Answer:

$f^{-1} (x)=x^{2} -3$

Step-by-step explanation:

Given the function

$f\left(x\right)=\sqrt{x+3}$

We can find the inverse function by exchanging x and y, and then solve for y.

$y=\sqrt{x+3}$

Replace x with y.

$x=\sqrt{y+3}$

square both sides

$x^2=y+3$

$y=x^2-3$

Hence,

$f^{-1} (x)=x^{2} -3$

8 0

2 years ago

Jason bought 3 dozen eggs from the grocery store to bake some cakes how many eggs did Jason buy?

Snowcat [4.5K]

Answer:

He bought 36 eggs

Step-by-step explanation:

3x12=36

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2 years ago

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On a blueprint of a house, 48 millimeters represents 7 meters. The length of the living room is 60 millimeters on the blueprint.

Pani-rosa [81]

Here is the equation 48/7=60/x, 48÷7=6.8571428571. Now we know that every one meter in real life is equal to 6.8571428571 millimeters so, 60÷6.8571428571= 8.75 meters. The living room is 8.75 meters

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3 years ago