Since x - 3 < 0 for -2 < x < 3, |x-3| = -(x-3)
Since x + 2 > 0 for -2 < x < 3, |x+2| = x+2
Since x - 5 < 0 for -2 < x < 3, |x-5| = -(x-5).
So y = -(x-3) + (x+2) -(-(x-5)) = 3 - x + x + 2 + x - 5 = x.
y = x, if -2 < x < 3.
Answer:
5
Step-by-step explanation:
8x - 6 > 12 + 2x
Subtract 2x from each
8x -2x -6 > 12+2x-2x
6x -6 > 12
Add 6 to each side
6x -6+6 > 12+6
6x > 18
Divide by 6
6x/6 > 18/6
x > 3
The only value greater than 3 is 5
Distance from home to store = 4 * 0.5 = 2 miles.
Time taken to return home = (2/12) * 60 =10 minutes.
Total distance traveled = 2 * 2 = 4 miles.
Total time taken = 30 + 10 = 40 minutes.
Average speed for entire trip = total distance / total time in hours.
P(bull's-eye) = 700/30000 x 100% = 2.33% ≈ 2%
option A is the correct answer.
Yay, implicit differnentiation
when you take the derivitive of y, you multiply it by dy/dx
example
dy/dx y^2=2y dy/dx
for x, the dy/dx dissapears
ok
so differnetiate and solve for dy/dx
3y² dy/dx-(y+x dy/dx)=0
expand
3y² dy/dx-y-x dy/dx=0
3y² dy/dx-x dy/dx=y
dy/dx (3y²-x)=y
dy/dx=y/(3y²-x)
so at (7,2)
x=7 and y=2
dy/dx=2/(3(2)²-7)
dy/dx=2/(3(4)-7)
dy/dx=2/(12-7)
dy/dx=2/5
answer is 2/5