Answer:
a. 318.2k
b. 45.2kj
Explanation:
Heat transfer rate to an object is equal to the thermal conductivity of the material the object is made from, multiplied by the surface area in contact, multiplied by the difference in temperature between the two objects, divided by the thickness of the material.
See attachment for detailed analysis
The Lamborghini SCV12 has 830 horse power.
Answer:
The population size would be 
The yield would be 
Explanation:
So in this problem we are going to be examining the application of a population dynamics a fishing pond and stock fishing and objective would be to obtain the maximum sustainable yield and and the population of the fish at the obtained maximum sustainable yield, so basically we would be applying an engineering solution to fishing
So the current yield which is mathematically represented as

Where dN is the change in the number of fish
and dt is the change in time
So in order to obtain the solution we need to obtain the rate of growth
For this we would be making use of the growth rate equation which is
![r = \frac{[\frac{dN}{dt}] }{N[1-\frac{N}{K} ]}](https://tex.z-dn.net/?f=r%20%3D%20%5Cfrac%7B%5B%5Cfrac%7BdN%7D%7Bdt%7D%5D%20%7D%7BN%5B1-%5Cfrac%7BN%7D%7BK%7D%20%5D%7D)
Where N is the population of the fish which is given as 4,000 fishes
and K is the carrying capacity which is given as 10,000 fishes
r is the growth rate
Substituting these values into the equation
![r = \frac{[\frac{2000}{year}] }{4000[1-\frac{4000}{10,000} ]} =0.833](https://tex.z-dn.net/?f=r%20%3D%20%5Cfrac%7B%5B%5Cfrac%7B2000%7D%7Byear%7D%5D%20%7D%7B4000%5B1-%5Cfrac%7B4000%7D%7B10%2C000%7D%20%5D%7D%20%20%3D0.833)
The maximum sustainable yield would be dependent on the growth rate an the carrying capacity and this mathematically represented as

So since the maximum sustainable yield is 2082 then the the population need to be higher than 4,000 so in order to ensure a that this maximum yield the population size denoted by
would be
Answer:
<u><em>note:</em></u>
<u><em>solution is attached in word form due to error in mathematical equation. furthermore i also attach Screenshot of solution in word due to different version of MS Office please find the attachment</em></u>
Answer:
Explanation:
There are three points in time we need to consider. At point 0, the mango begins to fall from the tree. At point 1, the mango reaches the top of the window. At point 2, the mango reaches the bottom of the window.
We are given the following information:
y₁ = 3 m
y₂ = 3 m − 2.4 m = 0.6 m
t₂ − t₁ = 0.4 s
a = -9.8 m/s²
t₀ = 0 s
v₀ = 0 m/s
We need to find y₀.
Use a constant acceleration equation:
y = y₀ + v₀ t + ½ at²
Evaluated at point 1:
3 = y₀ + (0) t₁ + ½ (-9.8) t₁²
3 = y₀ − 4.9 t₁²
Evaluated at point 2:
0.6 = y₀ + (0) t₂ + ½ (-9.8) t₂²
0.6 = y₀ − 4.9 t₂²
Solve for y₀ in the first equation and substitute into the second:
y₀ = 3 + 4.9 t₁²
0.6 = (3 + 4.9 t₁²) − 4.9 t₂²
0 = 2.4 + 4.9 (t₁² − t₂²)
We know t₂ = t₁ + 0.4:
0 = 2.4 + 4.9 (t₁² − (t₁ + 0.4)²)
0 = 2.4 + 4.9 (t₁² − (t₁² + 0.8 t₁ + 0.16))
0 = 2.4 + 4.9 (t₁² − t₁² − 0.8 t₁ − 0.16)
0 = 2.4 + 4.9 (-0.8 t₁ − 0.16)
0 = 2.4 − 3.92 t₁ − 0.784
0 = 1.616 − 3.92 t₁
t₁ = 0.412
Now we can plug this into the original equation and find y₀:
3 = y₀ − 4.9 t₁²
3 = y₀ − 4.9 (0.412)²
3 = y₀ − 0.83
y₀ = 3.83
Rounded to two significant figures, the height of the tree is 3.8 meters.