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3 years ago

The area is ___ square units

Mathematics

1 answer:

suter [353]3 years ago

5 0

Answer:

392 square units

Step-by-step explanation:

We can make 2 right trapezoids out of this shape.

The area of a trapezoid would be 1/2×(b1+b2)×h or (b1+b2)×h ÷ 2.

If we do 1 half it would be 1/2×(14+14)×14 = 196

Now if we multiply by 2 (because we have 2 trapezoids) it would be 392.

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Divide the following polynomials and then and then complete the quotient

Ludmilka [50]

The answer is
2x4 + 4x2 -3

Two raised to four plus
Four raised to two minus
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3 years ago

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

P(0) = 0 and P(50) = 1,500,000

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

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

The integrating factor 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

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

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4 years ago

Among all rectangles that have a perimeter of 134, find the dimensions of the one whose area is largest. write your answers as f

mestny [16]

The answer to this question would be: L= 33.5, W=33.5

In this question, the rectangle has a perimeter of 134. From this number, you can get this equation:

perimeter=134
2(L+W)= 134
L+W=67
L= 67-W

Using the formula for dimension you can get this equation:
dimension= L * W
dimension= (67-W)W= 67W- W^2

The maximum dimension should be differentiation of the equation which will look like:
67 -2w= 0
2w= 67
w= 33.5

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