Answer:
C is greater
D is less
Step-by-step explanation:
Exponent rule : (a^b)^c = a^(b*c)
31. (x^2)^3 = x^(2 * 3) = x^6
32. (a^7)^5 = a^(7 * 5) = a^35
33. (y^13)^4 = y^(13 * 4) = y^52
34. (w^-21)^-15 = w^(-21*-15) = w^315
35. (5^2)^3 = 5^(2 * 3) = 5^6
36. (23^7)^8 = 23^(7 * 8) = 23^56
37. (-y^5)^4 = -y^(5 * 4) = y^20
38. (4y^3)^2 = 4^2 y^(3 * 2) = 16y^6
39. (8c^5)^2 = 8^2 c^(5 * 2) = 64c^10
40. (-3h^9)^2 = -3^2 h^(9 * 2) = 9h^18
41. (y^4d^6)^3 = y^(4 * 3)d^(6 * 3) = y^12d^18
42. (-15h^9k^7)^3 = -15^3h^(9*3)k^(7*3) = -3375h^27k^21
43. (k^9)^5(k^3)^2 = k(9 * 5)k^(3 * 2) = (k^45)(k^6) = k^51
44. (3y^6)^2 (x^5y^2z) = 3^2y^(6*2)(x^5y^2z) = 9y^12(x^5y^2z) =
9x^5y^14z
45. (4h^3)^2 (-2g^3h)^3 = 4^2h^(3*2) (-2^3g^(3*3)h^3) = 16h^6(-8g^9h^3)
= -128g^9h^9
46. (14a^4b^6)^2 (a^6c^3)^2 = 14^2a^(4*2)b^(6*2) (a^(6*2)c^(3*2) =
196a^8b^12(a^12c^6) = 196a^20b^12c^6
Given:
The height of the cylinder = 12 in
The diameter of the base of the cylinder = 8 in.
To find:
The volume of the cylinder.
Solution:
The diameter of the base of the cylinder is 8 in. The radius is half of its diameter. So,
So, the radius of the base of the cylinder is 4 in.
The height of the cylinder, h = 12 in.
Base area of the cylinder is:
Where, B is the base area and r is the radius.
So, the base area is 
square inches.
The volume of the cylinder is:
Where, r is radius, h is height, B is base area.
Putting and 
, we get
So, the volume is 
cubic inches.
Therefore, 
.
This is the concept of algebra, suppose the initial number was x, and the new number is 2x. The constant rate of growth is r and time is D, the function representing growth will be given by:
2x=x(r)D
from our choices the equations that represents the information above will be:
7.830=3.915(1.106)D
and
7.830=3.915(2)D
this is because from both equations we see the initial number was 3.915 and doubled to 7.830
