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Answer is linear function
It's top left
Answer:
New mean length of these 17 people=11.62
Step-by-step explanation:
<em>Step 1: Determine the total length of children's fingers</em>
L=l×n
where;
L=total length (cm)
l=mean length (cm)
n=number of children
replacing;
L=6.7×6=40.2 cm
The total children's fingers length=40.2 cm
<em>Step 2: Determine the total length of adults fingers</em>
total length of adults fingers=mean length of adults fingers×number of adults
where;
mean length of adults=14.3
number of adults=11
replacing;
total length of adults fingers=(14.3×11)=157.3 cm
<em>Step 3: Determine the new mean length</em>
new mean length=total length of adults and children fingers/number of adults and children
where;
total length of adults and children fingers=157.3+40.2=197.5 cm
number of adults and children=11+6=17
replacing;
new mean length=197.5/17=11.62
∫(t = 2 to 3) t^3 dt
= (1/4)t^4 {for t = 2 to 3}
= 65/4.
----
∫(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.
----
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>.
