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3 years ago

(Prove that):2 sin 70. cos 20 = sin 90 + sin 50

Mathematics

1 answer:

Sphinxa [80]3 years ago

5 0

Answer:

see explanation

Step-by-step explanation:

Using the trigonometric identity

2sinxcosy = sin(x + y) + sin(x - y) , then

with x = 70 and y = 20

2sin70cos20

= sin(70 + 20) + sin(70 - 20)

= sin90 + sin50

= right side , thus proven

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givi [52]

Use the divergence theorem. Let $R$ be the cylindrical region, then

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(where $\mathbf n$ denotes the unit normal vector to $\partial R$ , but we don't need to worry about it now)

We have

$\mathrm{div }\mathbf F=(\nabla\cdot\mathbf F)(x,y,z)=\dfrac{\partial\mathbf F}{\partial x}+\dfrac{\partial\mathbf F}{\partial y}+\dfrac{\partial\mathbf F}{\partial z}$
$\nabla\cdot\mathbf F=3x^2+3y^2+3z^2$

For the solid $R$ with boundary $\partial R$ , we can set up the following volume integral in cylindrical coordinates for ease:

$\displaystyle3\iiint_R(x^2+y^2+z^2)\,\mathrm dV=3\int_{z=0}^{z=4}\int_{\theta=0}^{\theta=2\pi}\int_{r=0}^{r=2}(r^2+z^2)r\,\mathrm dr\,\mathrm d\theta\,\mathrm dz$
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3 years ago

Graph y= x−2. PLZZ HELP

nataly862011 [7]

Explanation: To graph the equation y = x - 2, the idea is simple.

We pick three values for x, plug them into the

equation, and find the corresponding values for y.

In order to do this in an organized way, we set up a chart.

Down the left side we make a column for our x's, down the right side we make a column for our y's, and in the middle we make a column for the side of the equation that contains the x, in this case, x - 2.

So reading the chart from left to right, we have our x or what we plug into the equation, then we have the x - 2 or what happens to the x when we plug it into the equation, and finally we have our y or what we end up with after plugging x into the equation.

So our first step in filling out the chart is choosing

the x's that we want to plug into the equation.

When graphing lines, I always choose three x's,

a positive number, zero, and a negative number.

The easiest numbers to pick are usually 1, 0, and -1.

So for 1, we plug a 1 into the equation for x

and we have y = (1) - 2 or -1

For 0 we plug a 0 into the equation for x

and we have y = (0) - 2 or -2.

For -1 we plug a -1 into the equation for x

and we have y = (-1) - 2 or -3.

So our points are (1, -1), (0, -2), and (-1, -3).

I looked at the x and y column to find those points.

Since our domain is all real numbers, we can connect these points based on the pattern that they are forming on the graph which is a line.

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3 years ago

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3 years ago

What are the coordinates of point B on AC such that the rario of AB to BC is 2:3

pishuonlain [190]

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Step-by-step explanation:

im not too sure buy i have the exact questions

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3 years ago

Find the circumference use 3.14 for the value of

Reil [10]

Answer:

the answer is 69.3

Step-by-step explanation:

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3 years ago

(Prove that):2 sin 70. cos 20 = sin 90 + sin 50​

(Prove that):2 sin 70. cos 20 = sin 90 + sin 50