Jill has ran 36 yards.
We run 5, 10, 15, 20, 25, 30
Jill runs 6, 12, 18, 24, 30, 36
Answer:
Step-by-step explanation:
<em>Refer to picture</em>
Added angles a and b as interior angles of same triangle with angle x to make solving simple.
Angle a is same as 42° since both angles intercept same arc AB.
Angle b is supplementary with 64° angle as linear pair
Some of the interior angles of a triangle is 180
- x + 42° + 116° = 180°
- x + 158° = 180°
- x = 180° - 158°
- x = 22°

Recall that a circle of radius 2 centered at the origin has equation

where the positive root gives the top half of the circle in the x-y plane. The definite integral corresponds to the area of the right half of this top half. Since the area of a circle with radius

is

, it follows that the area of a quarter-circle would be

.
You have

, so the definite integral is equal to

.
Another way to verify this is to actually compute the integral. Let

, so that

. Now

Recall the half-angle identity for cosine:

This means the integral is equivalent to
Answer:
x = 0, π/3, π, 5π/3
Step-by-step explanation:
sec(x)sin(x) - 2sin(x) = 0
factor out sin(x)
sin(x)[sec(x) - 2] = 0
then solve by splitting into two parts:
sin(x) = 0 and sec(x) - 2 = 0
x = 0, π and x = π/3, 5π/3 then plug in to original equation to check