Answer:
$9 in change
Step-by-step explanation:
Find the total cost of his purchases:
28 + 28 + 85
= 141
Find how much change he received by subtracting this from 150:
150 - 141
= 9
So, he should have received $9 in change
The point-normal form of a plane equation: (Fx(x0, y0, z0))(x - x0) + (Fy(x0, y0, z0))(y - y0) + (Fz(x0, y0, z0))(z - z0) = 0.
To find the equation of the tangent plane to a surface at a given point, follow these steps:
Step 1: Determine the function that describes the surface in the form F(x, y, z) = 0.
Step 2: Find the partial derivative of F with respect to x, denoted as Fx.
Step 3: Find the partial derivative of F with respect to y, denoted as Fy.
Step 4: Find the partial derivative of F with respect to z, denoted as Fz.
Step 5: Evaluate Fx, Fy, and Fz at the given point (x0, y0, z0).
Step 6: Use the gradient vector, which consists of the evaluated partial derivatives (Fx(x0, y0, z0), Fy(x0, y0, z0), Fz(x0, y0, z0)), as the normal vector to the tangent plane.
Step 7: Use the point-normal form of a plane equation: (Fx(x0, y0, z0))(x - x0) + (Fy(x0, y0, z0))(y - y0) + (Fz(x0, y0, z0))(z - z0) = 0. This is the equation of the tangent plane at the given point.
By following these steps, you will find the equation of the tangent plane to the surface at the specified point.
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