We are given the function
, and we are told to solve for
. Basically, we need to plug in
into all the variable spots in the given expression for
.
Therefore, the value of
when
is
. Hope this helps and have a phenomenal day!
Answers:
a)
b)
Step-by-step explanation:
a) The area of the sector of a circle is given by:
(1)
and
(2)
Where:
is the radius
(3) is the length of arc
is the angle in radians
In this case we have to find the value of . So, let's begin substituting the known values in (1):
(4)
Isolating :
(5)
Substituting (5) in (3):
(6)
Solving:
(7) At this point we have , but we need to find the value of in order to have the actual value of the length of arc.
Making (1)=(2):
(8)
Isolating :
(9)
Substituting (7) and (5) in (9):
(10)
Finding :
(10) Now that we have the value of the radius, we can substitute it in (7) and finally find the value of the
(11)
(12)
b) In this second case we have:
is the length of arc
is the angle in radians
the radius
We have to find the area of the sector and we will use equations (1) and (2):
(13)
(14)
(15)
(16)
Knowing :
This is the area of the sector of the circumference.
I think 24! Have a nice day :))
Center of circle 1 = (-4,-2)
Center of circle 2 = (5,3)
From -4 to 5 is a 9 unit move to the right.
From -2 to 3 is a 5 unit move up.
You would need to add 9 to the x value and 5 to the y value.
The transformation rule would be (x+9, y+5)
The radius of circle 2 is twice the length of circle 1, so to make the radius of circle 1 the same as circle 2 multiple it by 2, this is the scale factor.
Scale factor = 2