Answer:
Step-by-step explanation:
Equation for this problem: Total 3 cubed / (L x W)
So 18.5cm x 15cm = 277.5 is the product of L and W. Now you need to devide the total by 277.5 which is 14. So the aquarium is 14 cm deep.
∫(t = 2 to 3) t^3 dt
= (1/4)t^4 {for t = 2 to 3}
= 65/4.
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∫(t = 2 to 3) t √(t - 2) dt
= ∫(u = 0 to 1) (u + 2) √u du, letting u = t - 2
= ∫(u = 0 to 1) (u^(3/2) + 2u^(1/2)) du
= [(2/5) u^(5/2) + (4/3) u^(3/2)] {for u = 0 to 1}
= 26/15.
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For the k-entry, use integration by parts with
u = t, dv = sin(πt) dt
du = 1 dt, v = (-1/π) cos(πt).
So, ∫(t = 2 to 3) t sin(πt) dt
= (-1/π) t cos(πt) {for t = 2 to 3} - ∫(t = 2 to 3) (-1/π) cos(πt) dt
= (-1/π) (3 * -1 - 2 * 1) + [(1/π^2) sin(πt) {for t = 2 to 3}]
= 5/π + 0
= 5/π.
Therefore,
∫(t = 2 to 3) <t^3, t√(t - 2), t sin(πt)> dt = <65/4, 26/15, 5/π>.
The percentage of tardiness among the 102 pupils is 2.94.
<h2>Calculation of the percentage</h2>
According to the query,
Course A: Total number of students = 102
Number of tardy students = 3
Percent of students tardy in course A = (number of tardy students/total
number of students) * 100
=(3/102)*100
= 2.941
≈2.94
In case of course B: Total number of students = 85 & tardy student = 5
So, the percent of tardy student = (5/85)*100 = 5.88 %
Therefore, it is concluded that the percentage of student tardiness in course A is 2.94.
Learn more about the percentage here:
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