It is 6 because 6x6x6=216
To solve this questions, we can turn 2 into a fractions.
2 as a fraction is 2/1 (because 2 divide by 1 is still 2)
We can now use this to get our answer.
1/3 ÷ 2/1
= 1/3 × 1/2 (flip the fraction and then multiply)
= 1/6 (1 x 1 / 3 x 6)
Or 0.16666.. as a decimal
The answer is (1/2)xe^(2x) - (1/4)e^(2x) + C
Solution:
Since our given integrand is the product of the functions x and e^(2x), we can use the formula for integration by parts by choosing
u = x
dv/dx = e^(2x)
By differentiating u, we get
du/dx= 1
By integrating dv/dx= e^(2x), we have
v =∫e^(2x) dx = (1/2)e^(2x)
Then we substitute these values to the integration by parts formula:
∫ u(dv/dx) dx = uv −∫ v(du/dx) dx
∫ x e^(2x) dx = (x) (1/2)e^(2x) - ∫ ((1/2) e^(2x)) (1) dx
= (1/2)xe^(2x) - (1/2)∫[e^(2x)] dx
= (1/2)xe^(2x) - (1/2) (1/2)e^(2x) + C
where c is the constant of integration.
Therefore,
∫ x e^(2x) dx = (1/2)xe^(2x) - (1/4)e^(2x) + C
The answer is 3 yards.
There are 3 feet in a yard, so if we divide 9 (the length of the rope in feet) by 3, then we get the amount of yards in the rope: 9/3=3.
