Let us suppose missing term is y
so it becomes - ( x-1) + 5 = 2 ( x+3) - y
let us now try solving it for x ( in terms of y )
-x + 1 + 5 = = 2x + 6 - y
-x + 6 = 2x + 6 -y
6 + y = 2x + 6 +x
y = 3x
y / 3 = x
but x is given to be infinite . let us try placing y= the given options
x= x/3 which is not possible
x= 3x/3 which is giving valid statement
x= 1/3 which is a finite value
x= 5/3 again a finite value
so it is only y= 3x which could be the answer
Answer : option second that is 3x
∫(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>.
That would be 5/913. As a percent, that would be 0.5%.
I hope this answer helped you! If you have any further questions or concerns, feel free to ask! :)
Let n be unknown number, then 1/5 of this number is 1/5n. When you add these two numbers, you get
You know that this sum is equal to 24, so
1. Multiply this equation by 5:
2. Solve it:
Answer: n=20, correct choice is B.
a.
Scottie = 30
Top of the lighthouse = 45 (30+15)
The boat = 0
The fish = -10
b.
10 + 30 = 40
