It's a binomial times a binomial, so you FOIL
First multiply the First numbers
3z*z = 3z(^2)
Then multiply Outers:
3z* -4 = -12z
Nest, Inners:
9*z = 9z
Finally, the Lasts:
-4*9 = -36
Then, throw it all together in descending order, starting with the variable of highest degree to lowest:
3z^2 - 12z + 9z - 36
Last of all, simplify coefficients with like terms and you're good to go:
3z^2 - 3z - 36
Hope this helps!
Answer:
Volume of a cube = side * side * side
length of 1 side = cube root of 64 = 4 cm
Therefore, each picture is 4 cm by 4 cm
Step-by-step explanation:
a) Rectangles always have 4 right angles (90 degrees), but parallelograms do not always have 4 right angles rather they can, but do not have to. Rectangles have to.
b) A square is a type of rectangle, but a rectangle is not a type of square. Both rectangles & squares have 4 right angles and are always quadrilaterals, but squares always have all sides that have the same length, but rectangles do not have to have their sides all equivalent lengths.
c) In the case of a parallelogram, the opposite sides are equal whereas in a rhombus all four sides are equal.
I assume the cone has equation 
(i.e. the upper half of the infinite cone given by 
). Take
The volume of the described region (call it 
) is
The limits on 
and 
should be obvious. The lower limit on 
is obtained by first determining the intersection of the cone and sphere lies in the cylinder 
. The distance between the central axis of the cone and this intersection is 1. The sphere has radius 
. Then satisfies
(I've added a picture to better demonstrate this)
Computing the integral is trivial. We have
