Question

The polynomial function defined by f(x)=π/3x³-5πx² 500πd/3 can be used to find the depth that a ball 10 cm in diameter sinks in water. The constant d is the density of the ball, where the density of water is 1. The smallest positive zero of f(x) equals the depth that the ball sinks. Approximate this depth for each material and interpret the results. a) A wooden ball with d=0.9.

Answer 1

To find the depth that a wooden ball sinks in water, we can use the polynomial function given in the question. Substitute the density of the wooden ball into the function and solve for the smallest positive zero. Approximate the depth using the value of x obtained.

Step-by-step explanation:

To find the depth that a wooden ball sinks in water, we need to find the smallest positive zero of the polynomial function f(x) = π/3x³-5πx²+(500πd)/3, where d is the density of the ball. Since the density of water is 1, we can substitute d=0.9 into the function and solve for x.

f(x) = π/3x³-5πx²+(500π(0.9))/3

Set f(x) equal to zero and solve for x to find the smallest positive zero of the function.

Approximate the depth by finding the value of x. Interpret the result to determine the depth that the wooden ball sinks.