<h3>Given</h3>
- a cone of height 0.4 m and diameter 0.3 m
- filling at the rate 0.004 m³/s
- fill height of 0.2 m at the time of interest
<h3>Find</h3>
- the rate of change of fill height at the time of interest
<h3>Solution</h3>
The cone is filled to half its depth at the time of interest, so the surface area of the filled portion will be (1/2)² times the surface area of the top of the cone. The filled portion has an area of
... A = (1/4)(π/4)d² = (π/16)(0.3 m)² = 0.09π/16 m²
This area multiplied by the rate of change of fill height (dh/dt) will give the rate of change of volume.
... (0.09π/16 m²)×dh/dt = dV/dt = 0.004 m³/s
Dividing by the coefficient of dh/dt, we get
... dh/dt = 0.004·16/(0.09π) m/s
... dh/dt = 32/(45π) m/s ≈ 0.22635 m/s
_____
You can also write an equation for the filled volume in terms of the filled height, then differentiate and solve for dh/dt. When you do, you find the relation between rates of change of height and area are as described above. We have taken a "shortcut" based on the knowledge gained from solving it this way. (No arithmetic operations are saved. We only avoid the process of taking the derivative.)
Note that the cone dimensions mean the radius is 3/8 of the height.
V = (1/3)πr²h = (1/3)π(3/8·h)²·h = 3π/64·h³
dV/dt = 9π/64·h²·dh/dt
.004 = 9π/64·0.2²·dh/dt . . . substitute the given values
dh/dt = .004·64/(.04·9·π) = 32/(45π)
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xXxGolferGirlxXx
Answer:
Translate the graph 14 units horizontally to the left by adding to the x-variable the constant 14.
Step-by-step explanation:
Translations of "c" units in the horizontal axis are obtained by adding or subtracting the constant value "c" to the variable x itself. When we want to translate the graph to the right, we subtract c, and when we want to move the graph horizontally to the left , we add c.
In this case, to go from the radicand (x-9) to the radicand (x+5), an addition of 14 units has to be performed, and such corresponds to a horizontal displacement to the left in 14 units.
Answer:
<h2>
4x+4</h2>
Basic fact:
<em>all sides of a square are equal</em>
Step-by-step explanation:
1 side is x+1 so all sides are x+1
there are 4 sides so times everything by 4
4(x+1) which is 4x+4
Answer:
Step-by-step explanation:
Given the algebraic expression;
To make n the subject of formula.
Cross-multiplying, we have;
Rearranging the equation, we have;
