What are the coordinates of the image of point (−1, 5) after a counterclockwise rotation of 90º about the origin?
2 answers:
Answer:
Step-by-step explanation:
We have been given the coordinates of a point and we are asked to find the coordinates of he point after a counterclockwise rotation of 90º about the origin.
We know that after rotating a point 90 degree counter-clockwise about the origin, the x and y-coordinates changes places with each other and x-coordinate of new point becomes the negative of y-coordinate.
Applying the rotation rule the coordinates of new point would be:
Therefore, the required coordinates of the given point after a counterclockwise rotation of 90º about the origin would be .
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The second derivative at the point (2,2) is 34/9
<u>Explanation:</u>
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2x⁴ = 4y³
2x⁴ - 4y³ = 0
We first need to find dy/dx and then d²y/dx²
On differentiating the equation in terms of x
dy/dx = d(2x⁴ - 4y³) / dx
We get,
dy/dx = 2x³/3y²
On differentiating dy/dx we get,
d²y/dx² = 2x²/y² + 8x⁶/9y⁵
d²y/dx² = 34/9
Therefore, the second derivative at the point (2,2) is 34/9