they receive 25 per entry but 5 goes towards the cost of the race
so 25-5 = 20 per entry is for the charity
so 20x + 5000 = 25000
subtract 5000 from each side
20x= 20000
divide both sides by 20
x = 20000/ 20
x = 1000
they need at least 1000 entries to make 25000
so to make more than 25000, they need 1001 entries
<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)
3
he could use:
1x55 cent coin
1x10 + 1x25 cent coins
4x10 cent coins
4-1=3
What r the options so i can get an idea
It will take the Ostrich 64 minutes to run 40 miles, at the same speed
The distance-time ratio is given as:
Distance : Time = 25 miles : 40 minutes
When the distance is 40 miles, the ratio equation becomes
40 miles : Time = 25 miles : 40 minutes
Express as fraction
Multiply both sides by 40
Solve for times
Hence, it will take 64 minutes to run 40 miles
Read more about speed at:
brainly.com/question/4931057
