The final magnification will be 400-fold or 400 times the original size of the object.
For magnifying smaller objects, a compound microscope is used.
A compound microscope consists of an objective and an eyepiece, whose diagram is shown in the adjoining image.
The lens near the object is called an objective and the other one is the eyepiece.
Let the magnification of the objective be m1
Let the magnification of the eyepiece be m2
The final magnification by the microscope, M, will be
M = m1 x m2
Putting the values in the above equation
M = 40 x 10
M= 400
Thus, the final magnification will be 400-fold or 400 times the original size of the object.
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Newton's third law is: For every action, there is an equal and opposite reaction. The statement means that in every interaction, there is a pair of forces acting on the two interacting objects. The size of the forces on the first object equals the size of the force on the second object.
Answer:
a) The population of prairie dogs after nine months is 280.
b) P(t) = 30 + 30 · t - t²/4 for 0 ≤ t ≤ 60
Explanation:
Hi there!
We have the following information:
The initial population is P(0) = 30.
The rate of growth of the population is the following:
P´(t) = 30 - t/2 where
a) Let´s find the function of the population of prairie dogs P(t). For that, let´s integrate the P´(t) function between t = 0 and t and between P = 30 and P
P(t) = ∫P´(t)
P´(t) = dP/dt = 30 - t/2
Separating variables:
dP = (30 - t/2) dt
∫dP = ∫(30 - t/2) dt
P - 30 = 30 · t - t²/4
P(t) = 30 + 30 · t - t²/4
The population of prairie dogs at t = 9 months will be equal to P(9):
P(9) = 30 + 30(9) - (9)²/ 4
P(9) = 280 prairie dogs
The population of prairie dogs after nine months is 280.
b) P(t) = 30 + 30 · t - t²/4 (it was obtained in part a).