## ANT 2200 Troy University Cranium Theory of Evolution in Hominins Discussion Page 159: Scholars are still working through the actual sequence of evolutiona

ANT 2200 Troy University Cranium Theory of Evolution in Hominins Discussion Page 159:

Scholars are still working through the actual sequence of evolutionary changes in hominins that led to the development of bipedalism, large brains, social complexity, and tool-making abilities. Knowing what you now know about early hominins and how evolutionary processes work, can you theorize a possible sequence of evolutionary changes? (make sure you justify your answer)

I will send picture of the page in the book once the question is accepted. Should be at least one page Due April 24, 2020
1. Evaluate
!!
D
Math 281 – Quiz 6
Name__________________
Outside help permitted.
2
24xy dA where D is the region bounded by the graphs of y = x , and y – x = 2.
2. Reverse the order of integration and evaluate
3. Use polar coordinates to calculate
2
2
!!
D
9 3
!!
0
y
3 cos x 3 dx dy .
x dA where D is the region in the first quadrant that lies
between the circles x + y = 4 and x + y 2 = 25 .
3

4. Evaluate the integral ”
\$ \$
#0 #0
2
9% x 2
( x 2 + y 2 )3 2 dy dx by converting to polar coordinates.
Due April 24, 2020
Math 281 – Quiz 6
Outside help permitted.
1
5. Convert the integral ! !
0 0
coordinates and evaluate it.
1% x 2
!
x2 + y2
0
page 2 of 2
x 2 + y 2 dz dy dx from rectangular to cylindrical
6. Let E be the cone E = {( x, y, z ) : x 2 + y 2 & z & 4}.
a) Use cylindrical coordinates to find the volume, V, of E.
b) Find z =
1
V
!!!
E
z dV , the z-coordinate of the centroid of E.
7. Use spherical coordinates to find the volume of the solid between the sphere x 2 + y 2 + z 2 = 9 ,
and the cone z =
x 2 + y2
.
3