Answer:
10.67 m
Step-by-step explanation:
Velocity is given as;
v(t) = t² − t − 6
To get the distance, we will integrate the velocity equation.
x(t) = ∫v(t) = (t³/3) - (t²/2) - 6t
Thus, from t=0 seconds to t=4 seconds., we have;
(t³/3) - (t²/2) - 6t between 0 and 4.
Thus;
Total Distance = [(4³/3) - (4²/2) - 6(4)] - [(0³/3) - (0²/2) - 6(0)]
Total distance = (64/3) - 8 - 24 = -10.67 m
Distance can't be negative and so we take the absolute value which is 10.67 m
Here is the inequality you can enumerate:
5x >= 200, this means the money you sold for cakes must be larger or equal to your goal
x <= 100, this means you cannot sell more than 100 cakes, because you only have 100 cakes
Solve for them, you will get: 40 <= x <= 100
Answer:
II and III
Step-by-step explanation:
From statement II in the question, it is true that the standard deviations of two different samples from the same population may be the same. The population standard deviation is a fixed value calculated from every individual in the population. A sample standard deviation is calculated from only some of the individuals in a population.
Also from statement III, it is true that statistical inferences can be used to draw conclusions about the populations based on sample data. The mean of a population does not necessarily depends on the particular sample chosen. Therefore statement I is false.
The distance between a point
on the given plane and the point (0, 2, 4) is
but since
and
share critical points, we can instead consider the problem of optimizing
subject to
.
The Lagrangian is
with partial derivatives (set equal to 0)
Solve for
:
which gives the critical point
We can confirm that this is a minimum by checking the Hessian matrix of
:
is positive definite (we see its determinant and the determinants of its leading principal minors are positive), which indicates that there is a minimum at this critical point.
At this point, we get a distance from (0, 2, 4) of
