To find the equation of the level curve of the function h(x, y) = y ^ 3 * sin(x + pi/2) that passes through the point (r, 2), we need to follow these steps:

Step 1: Substitute the given point (r, 2) into the function h(x, y) to obtain an equation in terms of r:
h(r, 2) = 2^3 * sin(r + pi/2)
h(r, 2) = 8 * sin(r + pi/2)

Step 2: Simplify the equation obtained in step 1:
h(r, 2) = 8 * sin(r + pi/2)
h(r, 2) = 8 * sin(r) * cos(pi/2) + sin(pi/2) * cos(r)
h(r, 2) = 8 * sin(r) * 0 + 1 * cos(r)
h(r, 2) = cos(r)

Step 3: The equation of the level curve passing through the point (r, 2) is h(r, 2) = cos(r).

Question

To find the equation of the level curve of the function h(x, y) = y ^ 3 * sin(x + pi/2) that passes through the point (r, 2), we need to follow these steps:

Step 1: Substitute the given point (r, 2) into the function h(x, y) to obtain an equation in terms of r:
h(r, 2) = 2^3 * sin(r + pi/2)
h(r, 2) = 8 * sin(r + pi/2)

Step 2: Simplify the equation obtained in step 1:
h(r, 2) = 8 * sin(r + pi/2)
h(r, 2) = 8 * sin(r) * cos(pi/2) + sin(pi/2) * cos(r)
h(r, 2) = 8 * sin(r) * 0 + 1 * cos(r)
h(r, 2) = cos(r)

Step 3: The equation of the level curve passing through the point (r, 2) is h(r, 2) = cos(r).

Knowee AI · Accepted Answer

To find the equation of the level curve of the function h(x, y) = y ^ 3 * sin(x + pi/2) that passes through the point (r, 2), we need to follow these steps:

Step 1: Substitute the given point (r, 2) into the function h(x, y) to obtain an equation in terms of r:
h(r, 2) = 2^3 * sin(r + pi/2)
h(r, 2) = 8 * sin(r + pi/2)

Step 2: Simplify the equation obtained in step 1:
h(r, 2) = 8 * sin(r + pi/2)
h(r, 2) = 8 * sin(r) * cos(pi/2) + sin(pi/2) * cos(r)
h(r, 2) = 8 * sin(r) * 0 + 1 * cos(r)
h(r, 2) = cos(r)

Step 3: The equation of the level curve passing through the point (r, 2) is h(r, 2) = cos(r).

Find equation of the level curve of the function h(x, y) = y ^ 3 * sin(x + pi/2) that passes throughthe point (r.2).

Question

Find equation of the level curve of the function $h(x, y) = y^3 \sin\left(x + \frac{\pi}{2}\right)$ that passes through the point $(r, 2)$ .

Solution

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