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3 years ago

Where is this graph decreasing

Mathematics

1 answer:

coldgirl [10]3 years ago

8 0

Answer:

Show me the graph, and I will answer the question

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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

4 years ago

Write this ratio 1:3.5 in the form p:q where p and q are whole numbers

Orlov [11]

We have to express the ratio 1 : 3.5 in the form p:q where p and q are whole numbers.

Consider the ratio of 1 and 3.5,

1 : 3.5 = $\frac{1}{3.5}$

= $\frac{10}{35}$

Reducing the above fraction to its lowest form.

So, we get $\frac{10}{35}=\frac{2}{7}$

Therefore, the ratio 1 : 3.5 is expressed as $\frac{2}{7}$

where 2 and 7 are the whole numbers.

4 0

3 years ago

5/12 hour = how many minutes. And 2/3 yard = how many inches

Brums [2.3K]

There are 60 minutes in one hour. So 5/12 of 60 minutes (1 hr) is 25 minutes.
There are 36 inches in one yard. So 2/3 of 36 inches (1 yard) is 24 inches.
Hope this helps.

3 0

4 years ago

Prove that \displaystyle \frac{\cos \theta}{1 + \sin \theta} = \frac{1 - \sin \theta}{\cos \theta}

Bogdan [553]

Answer:

sin^2(θ)+cos^2(θ)=1

Step-by-step explanation:

We know that the statement above is true because of the Pythagorean identity theorem, which states the aforementioned equation. If you solve the equation for 1 you get the same equation.

To do this first multiply both sides by cos(θ), this gives you (cos^2θ)/1+sinθ = 1-sinθ

Then, multiply both sides by sinθ. This equals cos^θ=1-sin^2θ.

Finally, add sin^2θ to both sides. This equals the final answer of cos^2θ+sin^2θ=1. Which is true.

7 0

3 years ago

Audrey has $120 to spend on a tennis racket and lessons the racket cost $45 and the lessons cost $15 per hour to find the variab

Leni [432]

Answer:

120 = 15x + 45 5 hours of lessons

Step-by-step explanation:

120 is total money so that goes on one side.

45 is a one-time cost so it is on its own.

15 per hour is another cost but this one depends on a variable so it has an x.

X represents the number of hours.

You put this together to from the equation: 120 = 15x + 45.

Subtract 45 from both sides: 75 = 15x

Divide 15 from both sides: 5 = x.

X = hours so 5 hours

7 0

3 years ago

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Where is this graph decreasing ​

Where is this graph decreasing