How do I find the domain?
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ANSWER
The sphere is 10762 cubic centimeters bigger than the cube.
EXPLANATION
We want to find the difference in the volumes of the sphere and the cube.
To do this, we have to find the volumes of the sphere and cube and subtract that of the cube from the sphere.
The volume of a sphere is given as:
where r = radius
The radius of the sphere is 15 centimeters. Therefore, the volume of the sphere is:
The volume of a cube is given as:
where s = length of the side
The length of the side of the cube is 15 centimeters. Therefore, the volume of the cube is:
Therefore, the difference in the volumes of the sphere and cube is:
Therefore, the sphere is 10762 cubic centimeters bigger than the cube.
To find the gradient of the tangent, we must first differentiate the function.
The gradient at x = 0 is given by evaluating f'(0).
The derivative of the function at this point is negative, which tells us <em>the function is decreasing at that point</em>.
The tangent to the line is a straight line, so we will have a linear equation of the form y = mx + c. We know the gradient, m, is equal to -1, so
Now we need to substitute a point on the tangent into this equation to find c. We know a point when x = 0 lies on here. To find the y-coordinate of this point we need to evaluate f(0).
So the point (0, -1) lies on the tangent. Substituting into the tangent equation: