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2 years ago

Find the coordinates of point E if C is the midpoint of AE A has the coordinates of (-3,1) C has the coordinates of (-2,-1)

1 answer:

7 0

$coordinates\ of\ E(x,y)\\\\ 
midpoint:\ C(-2,-1)\\
endpoint:\ A(-3,1) \\\\ 
B(-2,-1)=(\frac{-3+x}{2}\ ;\ \frac{1+y}{2})\\\\
-2=\frac{-3+x}{2}\ \ | multiply\ by\ 2\\
-4=-3+x\ \ | add\ 3\\
-1=x\\\\
-1=\frac{1+y}{2}\ \ | multiply\ by\ 2\\
-2=1+y\ \ \ | subtract\ 1\\
-3=y\\\\Coordinate\ of\ C=(-1,-3)$

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3 years ago

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2 years ago

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3 years ago

Read 2 more answers

Evaluate the following integral using trigonometric substitution

serg [7]

Answer:

The result of the integral is:

$\arcsin{(\frac{x}{3})} + C$

Step-by-step explanation:

We are given the following integral:

$\int \frac{dx}{\sqrt{9-x^2}}$

Trigonometric substitution:

We have the term in the following format: $a^2 - x^2$ , in which a = 3.

In this case, the substitution is given by:

$x = a\sin{\theta}$

$dx = a\cos{\theta}d\theta$

In this question:

$a = 3$

$x = 3\sin{\theta}$

$dx = 3\cos{\theta}d\theta$

$\int \frac{3\cos{\theta}d\theta}{\sqrt{9-(3\sin{\theta})^2}} = \int \frac{3\cos{\theta}d\theta}{\sqrt{9 - 9\sin^{2}{\theta}}} = \int \frac{3\cos{\theta}d\theta}{\sqrt{9(1 - \sin^{\theta})}}$

We have the following trigonometric identity:

$\sin^{2}{\theta} + \cos^{2}{\theta} = 1$

$1 - \sin^{2}{\theta} = \cos^{2}{\theta}$

Replacing into the integral:

$\int \frac{3\cos{\theta}d\theta}{\sqrt{9(1 - \sin^{2}{\theta})}} = \int{\frac{3\cos{\theta}d\theta}{\sqrt{9\cos^{2}{\theta}}} = \int \frac{3\cos{\theta}d\theta}{3\cos{\theta}} = \int d\theta = \theta + C$

Coming back to x:

We have that:

$x = 3\sin{\theta}$

$\sin{\theta} = \frac{x}{3}$

Applying the arcsine(inverse sine) function to both sides, we get that:

$\theta = \arcsin{(\frac{x}{3})}$

The result of the integral is:

$\arcsin{(\frac{x}{3})} + C$

8 0

2 years ago

Substitute x = 5 into the expression (-2)x + 6. Do you get -4? Substitute x = -1 into the expression (-2)x + 6. Do you get - 4 W

8090 [49]

Answer:The first method, by substituting 5 into the expression (-2)x + 6 gives the coreect answer of -4

Step-by-step explanation:

Ist method

Substituting x = 5 into the expression (-2)x + 6, we have

(-2) 5 + 6,

=-10 + 6

=-4

2nd method

Substitute x = -1 into the expression (-2)x + 6,we have

(-2)(-1) + 6

2 +6=10

The first method, by substituting 5 into the expression (-2)x + 6 gives the coreect answer of -4

7 0

2 years ago