Hey there, 2 out of 5 is 2/5. There are a lot of fractions that is equivalent to 2/5, so I am only going to give you 3, 2/5=4/10, 6/15, and 8/40, 2*2=4 and 5*2=10.
The answer would be B because the sum of the squares of the 2 shorter sides equal the square of the longer side, which is the pythagoream theorem of a^2+b^2=c^2.
Answer:
The highest common factor for both 102 and 153 is
GCF- 51
Step-by-step explanation:
51*3= 153
51*2=102
∫(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>.
X^2/y + x^2/z =
10^2/(-5) + 10^2/(-2) =
100/(-5) + 100/(-2) =
-20 - 50 =
-70
