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The function r(t)= 0.5 + t cos(πt³/80) is an illustration of a cosine function
The depth of water in the rain gauge increases by 1.466cm from t = 0 to t = 3
<h3>How to determine the increase in water depth?</h3>
The function is given as:
r(t)= 0.5 + t cos(πt³/80)
When t = 0, the depth of water is:
r(0)= 0.5 + 0 * cos(π *0³/80)
Evaluate
r(0) = 0.5
When t = 3, the depth of water is:
r(3)= 0.5 + 3 * cos(π *3³/80)
Evaluate
r(3)= 1.966
Calculate the difference (d) in the depths
d = r(3) - r(0)
So, we have:
d = 1.966 - 0.5
Evaluate
d = 1.466
Hence, the depth of water in the rain gauge increases by 1.466cm from t = 0 to t = 3
Read more about cosine functions at:
brainly.com/question/17075439
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Considering the data in the question, the focal length of the objective lens that will give a total magnification of 200x is <u>0.8cm focal length.</u>
The whole question is:
You are using a microscope with a 10x eyepiece. What focal length of the objective lens will give a total magnification of 200x? Assume a length L = 160mm.
<h3>How was the answer derived?</h3>
Given that total magnification is 200
And the Assume length is 160
Since we used a microscope with a 10x eyepiece, the magnification would be divided by 10.
=> 200 ÷ 10 = 20.
Also, the focal length is measured in centimeters or meters; we would change the millimeters of focal length to centimeters. Therefore, we have 160 ÷ 10 = 16
The formula for the focal length of the objective lens = assumed length ÷ total magnification.
=> 16 ÷ 20 = 0.8cm.
Hence, in this case, it is concluded that the correct answer is "0.8cm."
Learn more about the focal length of the objective lens here: brainly.com/question/15744335
