Willis analyzed the following table to determine if the function it represents is linear or non-linear. First he found the diffe
2 answers:
He determined the y values for different x values as follows: 1, 7, 17, and 31. Willis then calculated the differences in the y values and observed they were rising by 4, concluding that the function had a constant rate of change, thus categorizing it as linear. However, his method was flawed. To establish the linearity of the function, one must assess if the slope of the graph yields a consistent rate of change, described by: where (
) denotes distinct interpolating points and their corresponding values. Hence, Willis needed to compute 
and confirm its equality for various pairs of points to substantiate that the function is indeed linear.
You might be interested in
Answer:
- The sphere has a 32 in. diameter. CORRECT: A sphere's diameter equals twice its radius; therefore, if the radius is 16, then the diameter is 32.
- The radius measures half the diameter's length. CORRECT: According to the definition, the diameter represents the greatest distance across the sphere, and its length is twice the radius since the radius extends from the center to the surface (imagining that distance across the sphere can connect two radii, which create the diameter).
- The sphere's volume (V) can be computed as
, where r is the radius. In this instance, the sphere's volume equals
, which can also be expressed as
.