Answer:
x=4
Step-by-step explanation:
Consider ΔKLJ:
sinθ=opposite/hypotenuse
sin30=LJ/8√2
LJ=0.5*8√2=4√2
Consider ΔMLJ:
sinθ=opp/hyp
sin45=x/4√2
1/√2=x/4√2
4√2/√2=x
x=4
We know in these kind of triangles that have a 90 degrees angle, we can do:

so the first question:

and then:

so , when you want to rationalize , usually you must multiply the irrational factor as 1:

so , now multiply:

in the next question,we know negative numbers in radical don't have any solution so 2 is correct,
Angle 8,2 that’s the answer
Answer:
Angular velocity:
(
)
Linear velocity:
(
)
Step-by-step explanation:
The gear experiments a pure rotation with axis passing through its center, the angular (
), in radians per second, and linear velocities (
), in inches per second, of a point on the outer edge of the element are, respectively:
(1)
(2)
Where:
- Rotation rate, in revolutions per minute.
- Radius of the gear, in inches.
If we know that
and
, then the linear and angular velocities of the gear are, respectively:

(
)

(
)