write an equation of the line in Slope-intercept form that has a slope of -2/3 and has a Y intercept of -4
1 answer:
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(d) The particle moves in the positive direction when its velocity has a positive sign. You know the particle is at rest when and
, and because the velocity function is continuous, you need only check the sign of
for values on the intervals (0, 3) and (3, 6).
We have, for instance and
, which means the particle is moving the positive direction for
, or the interval (3, 6).
(e) The total distance traveled is obtained by integrating the absolute value of the velocity function over the given interval:
which follows from the definition of absolute value. In particular, if is negative, then
.
The total distance traveled is then 4 ft.
(g) Acceleration is the rate of change of velocity, so is the derivative of
:
Compute the acceleration at seconds:
(In case you need to know, for part (i), the particle is speeding up when the acceleration is positive. So this is done the same way as part (d).)
Answer:
A reflection in the x-axis, and a vertical translation of 8 units down
Step-by-step explanation:
The given function is
The transformed function is
To see the transformation that occurred, we can rewrite g(x) in terms of f(x).
That is:
Therefore f(x) is reflected in the x-axis and translated 8 units down.
The resulting graph decreases from left to right over its entire domain.