<h3>
Answer: 25/12</h3>
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Work Shown:
![\displaystyle S_n = \sum_{k=1}^{n} \frac{1}{k}\\\\\\\displaystyle S_4 = \sum_{k=1}^{4} \frac{1}{k}\\\\\\\displaystyle S_4 = \frac{1}{1}+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}\\\\\\\displaystyle S_4 = \frac{12}{12}+\frac{6}{12}+\frac{4}{12}+\frac{3}{12}\\\\\\\displaystyle S_4 = \frac{12+6+4+3}{12}\\\\\\\displaystyle S_4 = \frac{25}{12}\\\\](https://tex.z-dn.net/?f=%5Cdisplaystyle%20S_n%20%3D%20%5Csum_%7Bk%3D1%7D%5E%7Bn%7D%20%5Cfrac%7B1%7D%7Bk%7D%5C%5C%5C%5C%5C%5C%5Cdisplaystyle%20S_4%20%3D%20%5Csum_%7Bk%3D1%7D%5E%7B4%7D%20%5Cfrac%7B1%7D%7Bk%7D%5C%5C%5C%5C%5C%5C%5Cdisplaystyle%20S_4%20%3D%20%5Cfrac%7B1%7D%7B1%7D%2B%5Cfrac%7B1%7D%7B2%7D%2B%5Cfrac%7B1%7D%7B3%7D%2B%5Cfrac%7B1%7D%7B4%7D%5C%5C%5C%5C%5C%5C%5Cdisplaystyle%20S_4%20%3D%20%5Cfrac%7B12%7D%7B12%7D%2B%5Cfrac%7B6%7D%7B12%7D%2B%5Cfrac%7B4%7D%7B12%7D%2B%5Cfrac%7B3%7D%7B12%7D%5C%5C%5C%5C%5C%5C%5Cdisplaystyle%20S_4%20%3D%20%5Cfrac%7B12%2B6%2B4%2B3%7D%7B12%7D%5C%5C%5C%5C%5C%5C%5Cdisplaystyle%20S_4%20%3D%20%5Cfrac%7B25%7D%7B12%7D%5C%5C%5C%5C)
Note: in step 3, I'm adding terms in the form 1/k where k ranges from k = 1 to k = 4 (k being an integer)
135-60=75.1 75.1-22.50=52.6 52.6-45=7.6 the answer is $7.06
BD is congruent to BD by the reflexive property
AD is congruent to DC because they are both created by the midpoint D
so with all the together you can say the triangle are similar by SSS
Answer:
a) $2,641,885.90
b) $264,188.59
Step-by-step explanation:
The total profit is the integral of the marginal profit. The marginal profit is the difference between marginal revenue and marginal cost.
![\displaystyle P(t)=\int^t_0 {(R'(t)-C'(t))} \, dt=\int^t_0{(120e^t-120+0.6t)}\,dt\\\\P(t)=120(e^t-1)-120t+0.3t^2](https://tex.z-dn.net/?f=%5Cdisplaystyle%20P%28t%29%3D%5Cint%5Et_0%20%7B%28R%27%28t%29-C%27%28t%29%29%7D%20%5C%2C%20dt%3D%5Cint%5Et_0%7B%28120e%5Et-120%2B0.6t%29%7D%5C%2Cdt%5C%5C%5C%5CP%28t%29%3D120%28e%5Et-1%29-120t%2B0.3t%5E2)
a) To find the total profit for the first 10 days, we evaluate P(10):
P(10) = 120(e^10 -1) -120(10) +0.3(10^2) = 120(22026.4658 -1) -1200 +30
P(10) = 2,641,885.90 . . . . rounded to cents
The total profit from day 0 to day 10 is $2,641,885.90.
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b) The average daily profit is the total profit divided by the number of days:
average profit per day = P(10)/10 = $264,188.59
The average daily profit for the first 10 days is $264,188.59.
Answer:
I believe the answer would be 6
Step-by-step explanation:
Area = length x width
4 x 3 = 12
12/2= 6 because only half of the rectangle is shaded