The Lagrangian,
has critical points where its partial derivatives vanish:
tells us , so that
Then with , we get
and tells us
Then there are two critical points, . The critical point with the negative -coordinates gives the maximum value, .
Answer:
Explanation:
You need to use derivatives which is an advanced concept used in calculus.
<u>1. Write the equation for the volume of the cone:</u>
<u />
<u>2. Find the relation between the radius and the height:</u>
- r = diameter/2 = 5m/2 = 2.5m
<u>3. Filling the tank:</u>
Call y the height of water and x the horizontal distance from the axis of symmetry of the cone to the wall for the surface of water, when the cone is being filled.
The ratio x/y is the same r/h
The volume of water inside the cone is:
<u>4. Find the derivative of the volume of water with respect to time:</u>
<u>5. Find x² when the volume of water is 8π m³:</u>
m²
<u>6. Solve for dx/dt:</u>
<u />
<u>7. Find dh/dt:</u>
From y/x = h/r = 2.08:
That is the rate at which the water level is rising when there is 8π m³ of water.
Answer:
The polygon that is made is a triangle
Step-by-step explanation:
Answer:
4:7
Edit: I just saw the multiple choice options, in this case the right answer is:
<h2>
8:14</h2>
but they're both equal
Step-by-step explanation:
The ratio you are looking for is
freestyle laps : (freestyle + butterfly) laps
so:
8 : (6+8)
8:14
Divide by 2 to simplify
4:7