If the percent of discount is 64% and the sale price is $72 what is the original price
2 answers:
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Answer:
C. The electric car is not moving at 0 seconds and 12 seconds.
Step-by-step explanation:
Given:
The table given is:
x 0 2 4 6 8 10 12
y 0 45 72 81 72 45 0
From the above table, we observe that the car starts from rest and its speed increases from 0 to 6 seconds, the maximum speed being 81 mph.
After 6 seconds, the speed of the car goes on decreasing till it stops at time equal to 12 seconds.
So, the speed of the car at the start when is 0 mph as it is at rest at that time.
Also, when the time is , the car has come to a stop and thus its speed has reduced to 0 mph again. So, the car is not moving after 12 seconds.
From the above conclusion, we can say that only option C is correct.
The electric car is not moving at 0 seconds and 12 seconds.
Answer:
a)
Highest (-3,-3)
Lowest (2,2)
b)
Farthest (-3,-3)
Closest (2,2)
Step-by-step explanation:
To solve this problem we will be using Lagrange multipliers.
a)
Let us find out first the restriction, which is the projection of the intersection on the XY-plane.
From x+y+z=12 we get z=12-x-y and replace this in the equation of the paraboloid:
completing the squares:
and we want the maximum and minimum of the paraboloid when (x,y) varies on the circumference we just found. That is, we want the maximum and minimum of
subject to the constraint
Now we have
Let be the Lagrange multiplier.
The maximum and minimum must occur at points where
that is,
we can assume (x,y)≠ (-1/2, -1/2) since that point is not in the restriction, so
Replacing in the constraint
from this we get
<em>x=-1/2 + 5/2 = 2 or x = -1/2 - 5/2 = -3 </em>
<em> </em>
and the candidates for maximum and minimum are (2,2) and (-3,-3).
Replacing these values in f, we see that
f(-3,-3) = 9+9 = 18 is the maximum and
f(2,2) = 4+4 = 8 is the minimum
b)
Since the square of the distance from any given point (x,y) on the paraboloid to (0,0) is f(x,y) itself, the maximum and minimum of the distance are reached at the points we just found.
We have then,
(-3,-3) is the farthest from the origin
(2,2) is the closest to the origin.