Answer:
(identity has been verified)
Step-by-step explanation:
Verify the following identity:
sin(x)^4 - sin(x)^2 = cos(x)^4 - cos(x)^2
sin(x)^2 = 1 - cos(x)^2:
sin(x)^4 - 1 - cos(x)^2 = ^?cos(x)^4 - cos(x)^2
-(1 - cos(x)^2) = cos(x)^2 - 1:
cos(x)^2 - 1 + sin(x)^4 = ^?cos(x)^4 - cos(x)^2
sin(x)^4 = (sin(x)^2)^2 = (1 - cos(x)^2)^2:
-1 + cos(x)^2 + (1 - cos(x)^2)^2 = ^?cos(x)^4 - cos(x)^2
(1 - cos(x)^2)^2 = 1 - 2 cos(x)^2 + cos(x)^4:
-1 + cos(x)^2 + 1 - 2 cos(x)^2 + cos(x)^4 = ^?cos(x)^4 - cos(x)^2
-1 + cos(x)^2 + 1 - 2 cos(x)^2 + cos(x)^4 = cos(x)^4 - cos(x)^2:
cos(x)^4 - cos(x)^2 = ^?cos(x)^4 - cos(x)^2
The left hand side and right hand side are identical:
Answer: (identity has been verified)
Answer:
9.20
Step-by-step explanation:
If the ratio of red marbles to blue marbles in a jar is 3 to 8, the meaning is for every 3 red marbles there are 8 blue marbles.
3 red marbles------------------8 blue marbles.
ratio=3/8
we have 40 blue marbles; we have to compute the number of red marbles.
1) Method 1; by the rule three.
3 red marbles-----------------8 blue marbles
x----------------------------------40 blue marbles
x=(3 red marbles * 40 blue marbles) / 8 blue marbles=15 red marbles.
answer: B. 15
Method 2: the ratio of red marbles to blue marbles is
ratio=number of red marbles / number of blue marbles
ratio=3/8
if we want to compute the number of red marbles we have to multiply the number of blue marbles by this ratio.
number of red marbles=ratio (red/blue)* number of blue marbles
number of red marbles=(3/8)*40=15
Answer: B.15
563/.4 is equal to 1,407.5
