Slope is vertical change over horizontal change. Since coordinates conveniently give both the horizontal and vertical coordinates of a points, we can use the coordinates of both points to differentiate, or find the change horizontally and the change vertically between the two points.
9514 1404 393
Answer:
7 cm, 4.4 cm
Step-by-step explanation:
The side lengths can be found from the law of cosines. Each triangle has legs 3 cm and 5 cm. The angle between these will be 60° or 120°. Then the two sides of the parallelogram are ...
s = √(a² +b² -2ab·cos(C))
s = √(3² +5² -2·3·5·(±1/2)) = √(34 ±15) = {√49, √19}
The two side lengths are 7 cm and about 4.4 cm.
Consider the top half of a sphere centered at the origin with radius

, which can be described by the equation

and consider a plane

with

. Call the region between the two surfaces

. The volume of

is given by the triple integral

Converting to polar coordinates will help make this computation easier. Set

Now, the volume can be computed with the integral

You should get
Its 3.8 because if you add 5.9 and 10.3 is 16.2, and if you subtract it by 20, it should equal 3.8.