A
The velocity is found by differentiating the given cubic.
x'(t) = 2t^3 - 15t^2 + 24t This is the distance
x'(t) = 6t^2 - 20t + 24 This is the velocity (first derivative)
x"(t) = 12t - 20 This is the acceleration (second derivative)
x'(2) = 6(2)^2 - 20*2 + 24
x'(2) = 24 - 40 + 24
x'(2) = 48 - 40
x'(2) = 8 units per second.
x"(2) = 12(2) - 20
x"(2) = 24 - 20
x"(2) = 4 units per second^2
B
at t = 2 the acceleration is positive. That's a pretty good indication that the velocity is increasing.
C
When x(t) is minus, then the particle is moving left.
At t = 0 the object is not moving (x(t) = 0)
Any value less than 0 and the object is moving left. Try a couple of values.
x(-1) = 2(-1)^3 - 15(-1)^2 +24(-1) Whatever that is is minus.
t < 0 will make the object move left.
Answer:
dale is not correct
the correct angle is 30 degrees
Step-by-step explanation:
A cake is shaped like a circle
the total sum of angles in a circle is 360 degrees
If Dale and 2 friends share one fourth of a cake, the total angles they share = (1/4) X 360 = 90 degrees
If the 3 friends share the cake equally, the angles each get = (1/3) x 90 = 30 degrees
the correct angle is 30 degrees and not 45 degrees. Thus, Dale is wrong
The square root of -36 is 6i
|6x – 1| + 4 = 1
isolate the absolute value
subtract 4 from each side
|6x – 1| + 4-4 = 1-4
|6x – 1| = -3
There are no solutions since absolute value means always positive and the other side is negative
Answer:
6.24 units.
Step-by-step explanation:
Use the Pythagorean theorem.