Answer:
Step-by-step explanation:
My work is in the attachment but I essentially used a hefty bit of Algebraic manipulation to turn 2^x into 4^(x-1) and then isolating that bit.
Comment if you have any questions.
Answer:
343 cm ^3
Step-by-step explanation:
A cube has 6 squares of equal sizes. 294/6 = 49
The area of one square is 49
Since the area is the length squared, the square root of 49 is 7.
Volume of a cube is area times height. 49 x 7 = 343 cm^3
A. This is an example of a situation making use of the concept of Fundamental Principles of Counting. On the first spot, Sam may choose from the five available flags. On the next spot, he can only choose from four flags. This goes on until no more flag is left. For short, there are 5! ways. This is equal to 120.
b. Since only 3 out of the five flags can be used and the arrangement is important, make use of Permutation. The answer is 5P3 = 60. There are 60 ways.
Power and chain rule (where the power rule kicks in because ):
Simplify the leading term as
Quotient rule:
Chain rule:
Put everything together and simplify:
Answer:
The ratio of planet B's volume to planet A's volume is 1:512 or 1/512
Step-by-step explanation:
Volume of sphere = 4/3 π r^3
r = d/2
Radius of palnet A = 8/2 = 4
Radius of planet B = 1/2
Since 4/3 π is same in both volumes so, they cancel out when finding ratio.
Now ratio depends on radius cube of both planets
Volume of Planet B : Volume of Planet A
4/3 π(1/2)^3 : 4/3 π(4)^3
Cancelling 4/3 π on both sides
1/8 : 64
Multiply 8 on both sides
1 : 512
So, The ratio of planet B's volume to planet A's volume is 1:512 or 1/512