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EastWind [94]
3 years ago
11

What is the equation (simplified) the inverse of y=2x^2?

Mathematics
1 answer:
Yuki888 [10]3 years ago
3 0
2x^2=y\ \ \ |divide\ both\ sides\ by\ 2\\\\x^2=\dfrac{y}{2}\\\\\boxed{x=\sqrt{\frac{y}{2}}}\\\\x=\dfrac{\sqrt{y}}{\sqrt2}=\dfrac{\sqrt{y}\cdot\sqrt2}{\sqrt2\cdot\sqrt2}\to\boxed{x=\dfrac{\sqrt{2y}}{2}}\\\\\\\boxed{f(x)=2x^2\to f^{-1}(x)=\dfrac{\sqrt{2y}}{2}}
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raph the equation with a diameter that has endpoints at (-3, 4) and (5, -2). Label the center and at least four points on the ci
andreyandreev [35.5K]

Answer:

Equation:

{x}^{2}   +  {y}^{2} +  2x  - 2y   -  35= 0

The point (0,-5), (0,7), (5,0) and (-7,0)also lie on this circle.

Step-by-step explanation:

We want to find the equation of a circle with a diamterhat hs endpoints at (-3, 4) and (5, -2).

The center of this circle is the midpoint of (-3, 4) and (5, -2).

We use the midpoint formula:

( \frac{x_1+x_2}{2}, \frac{y_1+y_2,}{2} )

Plug in the points to get:

( \frac{ - 3+5}{2}, \frac{ - 2+4}{2} )

( \frac{ -2}{2}, \frac{ 2}{2} )

(  - 1, 1)

We find the radius of the circle using the center (-1,1) and the point (5,-2) on the circle using the distance formula:

r =  \sqrt{ {(x_2-x_1)}^{2} + {(y_2-y_1)}^{2} }

r =  \sqrt{ {(5 -  - 1)}^{2} + {( - 2- - 1)}^{2} }

r =  \sqrt{ {(6)}^{2} + {( - 1)}^{2} }

r =  \sqrt{ 36+ 1 }  =  \sqrt{37}

The equation of the circle is given by:

(x-h)^2 + (y-k)^2 =  {r}^{2}

Where (h,k)=(-1,1) and r=√37 is the radius

We plug in the values to get:

(x- - 1)^2 + (y-1)^2 =  {( \sqrt{37}) }^{2}

(x + 1)^2 + (y - 1)^2 = 37

We expand to get:

{x}^{2}  + 2x  + 1 +  {y}^{2}  - 2y + 1 = 37

{x}^{2}   +  {y}^{2} +  2x  - 2y +2 - 37= 0

{x}^{2}   +  {y}^{2} +  2x  - 2y   -  35= 0

We want to find at least four points on this circle.

We can choose any point for x and solve for y or vice-versa

When y=0,

{x}^{2}   +  {0}^{2} +  2x  - 2(0)  -   35= 0

{x}^{2}   +2x   -   35= 0

(x - 5)(x + 7) = 0

x = 5 \: or \: x =  - 7

The point (5,0) and (-7,0) lies on the circle.

When x=0

{0}^{2}   +  {y}^{2} +  2(0)  - 2y   -  35= 0

{y}^{2} - 2y   -  35= 0

(y - 7)(y + 5) = 0

y = 7 \: or \: y =  - 5

The point (0,-5) and (0,7) lie on this circle.

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((Image Included))
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Answer:

=204.13 inches.

Step-by-step explanation:

Using the side x, we can use sine to find the hypotenuse of the triangle with the angle marked 30°.

Sin 30 =x/hypotenuse.

sin 30 = 27/hyp

hyp= 27/sin 30

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We can also find the adjacent as follows.

Cos 30 = adjacent/ 54

Adjacent= 54 cos 30

=46.77 inches

Using the angles marked 45 we can find the hypotenuse of the isosceles triangle.

sin 45= x/hypotenuse

sin 45 =27/hypotenuse

hypotenuse = 27/sin 45

=38.18 inches

The hypotenuse of both the triangles making the isosceles triangle are 38.18 inches long.

Perimeter = 54+ 46.77+27+ 38.18+38.18

=204.13 inches.

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Answer:

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Step-by-step explanation:

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Answer:

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