Answer: 10
Step-by-step explanation:
Since integral from 1 to 4 of f(x) =10
To evaluate integral from 2 to 8 of 2 times f(2x), using substitution method
Let U = 2x, dU = 2dx, dx = dU/2
Evaluate the limit, upper limit gives dU = 2*4 = 8, lower limit gives dU = 2*1 = 2.
Since this limit are the same as the limit for the question,
Therefore, F(4) - F(1) = F(8) - F(2) = 10
Substituting dx=dU/2
Gives,
Integral from 2 to 8 of 2 times f(2x)= (1/2)(2)(F(8)-F(2)) = 10
-2/3-(-1 1/3) =
-2/3 + 1 1/3 =
4/3 - 2/3 =
<em>2/3</em>
12 - (-5) =
12 + 5 =
<em>17</em>
-1 - (-6) =
-1 + 6 =
6 - 1 =
<em>5</em>
-3 3/8 - 7/8 =
27/8 - 7/8 =
20/8 =
2 4/8 =
<em>2</em><em> </em><em>1/2</em>
Answer:
x = 2
Step-by-step explanation:
The product of distances from the intersection of secants to the near and far intersections with the circle are the same. For a tangent, the near and far points of intersection with the circle are the same. This relation tells us ...
(2√3)(2√3) = x(x +4)
12 = x² +4x
16 = x² +4x +4 . . . . . add the square of half the x-coefficient to complete the square
4² = (x +2)² . . . . . . . . write as squares
4 = x +2 . . . . . . . . . . positive square root
2 = x . . . . . . . . . . . . . subtract 2
_____
<em>Alternate solution</em>
If you believe x to be an integer, you can look for factors of 12 that differ by 4.
12 = 1×12 = 2×6 = 3×4
The factors 2 and 6 differ by 4, so x=2 and x+4=6.
Answer:
1/4 chance (this is equal to 25% as a percentage or 0.25 as a decimal)
Step-by-step explanation:
There are 4 balls and only one can be first. As there is only 1 yellow ball, there is 1/4 chance that the yellow ball is picked first.
