Answer:
1. PNT
2.RNM
3.QNM
4.UYZ
5. None
6.VYZ
7.none
Step-by-step explanation:
suplametery means when you add to angles together it will equal 180
while complementery is when to angels are added together to make 90 degrees
Radius of curvature = 10'
Diameter of circle = 2 * 10' = 20'
height of segment = 2'
Let semi-chord be x.
Then by the intersecting chord property,
2*(20-2)=x^2
x^2=36
x=sqrt(36)=6
=>
chord=2x=2*6=12'
Answer:
x = 0, x = 3
Step-by-step explanation:
Given
- 4x² = - 12x ( add 12x to both sides )
- 4x² + 12x = 0 ← factor out - 4x from each term
- 4x(x - 3) = 0
Equate each factor to zero and solve for x
- 4x = 0 ⇒ x = 0
x - 3 = 0 ⇒ x = 3
Since you mentioned calculus, perhaps you're supposed to find the area by integration.
The square is circumscribed by a circle of radius 6, so its diagonal (equal to the diameter) has length 12. The lengths of a square's side and its diagonal occur in a ratio of 1 to sqrt(2), so the square has side length 6sqrt(2). This means its sides occur on the lines
and
.
Let
be the region bounded by the line
and the circle
(the rightmost blue region). The right side of the circle can be expressed in terms of
as a function of
:

Then the area of this circular segment is


Substitute
, so that 


Then the area of the entire blue region is 4 times this, a total of
.
Alternatively, you can compute the area of
in polar coordinates. The line
becomes
, while the circle is given by
. The two curves intersect at
, so that


so again the total area would be
.
Or you can omit using calculus altogether and rely on some basic geometric facts. The region
is a circular segment subtended by a central angle of
radians. Then its area is

so the total area is, once again,
.
An even simpler way is to subtract the area of the square from the area of the circle.

Answer:
y = -3/8x -41/8
Step-by-step explanation:
Perpendicular lines intersect at 90° and their slopes are opposite reciprocals.
Therefore the slope changes from 8/3 to -3/8.
Now we must solve for the new y-intercept (b) by plugging in the given coordinate (-3,-4).
The result is b = -41/8 so our new equation is:
y = -3/8x -41/8