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4 years ago

Calculate area of tetrahedron given 4 vertices

Mathematics

1 answer:

Nostrana [21]4 years ago

3 0

Area = root 3 * a^2 ,
a is number of edges

so, area = 1.732 * 16 = 27.712 sq unit

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Coffee sells for $5 per pound. If a farmer sells 12,000,000 pounds of coffee, how much money will the farmer make?

lana [24]

Answer:

8939459577232

Step-by-step explanation:

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3 years ago

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Write 3/60 as a fraction in its simplest form

mart [117]

Answer:

$\frac{1}{20}$

Step-by-step explanation:

$\frac{3}{60}=\frac{1}{20}$

To get $\frac{1}{20}$ you needed to divide the numerator and denominator by 3.

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4 years ago

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) Use the Laplace transform to solve the following initial value problem: y′′−6y′+9y=0y(0)=4,y′(0)=2 Using Y for the Laplace tra

artcher [175]

Answer:

$y(t)=2e^{3t}(2-5t)$

Step-by-step explanation:

Let Y(s) be the Laplace transform Y=L{y(t)} of y(t)

Applying the Laplace transform to both sides of the differential equation and using the linearity of the transform, we get

L{y'' - 6y' + 9y} = L{0} = 0

(*) L{y''} - 6L{y'} + 9L{y} = 0 ; y(0)=4, y′(0)=2

Using the theorem of the Laplace transform for derivatives, we know that:

$\large\bf L\left\{y''\right\}=s^2Y(s)-sy(0)-y'(0)\\\\L\left\{y'\right\}=sY(s)-y(0)$

Replacing the initial values y(0)=4, y′(0)=2 we obtain

$\large\bf L\left\{y''\right\}=s^2Y(s)-4s-2\\\\L\left\{y'\right\}=sY(s)-4$

and our differential equation (*) gets transformed in the algebraic equation

$\large\bf s^2Y(s)-4s-2-6(sY(s)-4)+9Y(s)=0$

Solving for Y(s) we get

$\large\bf s^2Y(s)-4s-2-6(sY(s)-4)+9Y(s)=0\Rightarrow (s^2-6s+9)Y(s)-4s+22=0\Rightarrow\\\\\Rightarrow Y(s)=\frac{4s-22}{s^2-6s+9}$

Now, we brake down the rational expression of Y(s) into partial fractions

$\large\bf \frac{4s-22}{s^2-6s+9}=\frac{4s-22}{(s-3)^2}=\frac{A}{s-3}+\frac{B}{(s-3)^2}$

The numerator of the addition at the right must be equal to 4s-22, so

A(s - 3) + B = 4s - 22

As - 3A + B = 4s - 22

we deduct from here

A = 4 and -3A + B = -22, so

A = 4 and B = -22 + 12 = -10

It means that

$\large\bf \frac{4s-22}{s^2-6s+9}=\frac{4}{s-3}-\frac{10}{(s-3)^2}$

and

$\large\bf Y(s)=\frac{4}{s-3}-\frac{10}{(s-3)^2}$

By taking the inverse Laplace transform on both sides and using the linearity of the inverse:

$\large\bf y(t)=L^{-1}\left\{Y(s)\right\}=4L^{-1}\left\{\frac{1}{s-3}\right\}-10L^{-1}\left\{\frac{1}{(s-3)^2}\right\}$

we know that

$\large\bf L^{-1}\left\{\frac{1}{s-3}\right\}=e^{3t}$

and for the first translation property of the inverse Laplace transform

$\large\bf L^{-1}\left\{\frac{1}{(s-3)^2}\right\}=e^{3t}L^{-1}\left\{\frac{1}{s^2}\right\}=e^{3t}t=te^{3t}$

and the solution of our differential equation is

$\large\bf y(t)=L^{-1}\left\{Y(s)\right\}=4L^{-1}\left\{\frac{1}{s-3}\right\}-10L^{-1}\left\{\frac{1}{(s-3)^2}\right\}=\\\\4e^{3t}-10te^{3t}=2e^{3t}(2-5t)\\\\\boxed{y(t)=2e^{3t}(2-5t)}$

5 0

3 years ago

This recipe makes 24 cupcakes.

Hatshy [7]

8 ounces butter
4sugar
6flour
2 eggs

3 0

3 years ago

The surface area, A, of a cylinder is given by the formula A = 2 Trh + 2nr, where ris the radius and h is the height

lord [1]

Answer:

Area = 87.9646 sq. units from A = 28*π sq. units.

However I cannot see this in your answer list, since the numbers look all jumbled. Choice A. looks close to it, since there is a 28...

Step-by-step explanation:

We have a cylinder with height h = 5

radius = 2

We want the surface area of this cylinder.

A = (circumference)*h + 2*(pi)*r^2

A = ( 4*π)*5 + 2*π*(2^2)

A = 20π + 8π = 28 π square units

A = 87.9646 sq.. units

7 0

3 years ago