Answer:

and x=4
Step-by-step explanation:
We are given that a curve

We have to find the equation of tangent at point (4,2) on the given curve.
Let y=f(x)
Differentiate w.r.t x

By using the formula 
Substitute x=4
Slope of tangent

In given question


By comparing we get a=4
Point-slope form

Using the formula
The equation of tangent at point (4,2)




Answer:
Step-by-step explanation:
You see that there’re angles with 30 and 90 degrees that means that -> 180-(90+30)=60 (measurement of the third angle)
Here you’ll need to use the 30,60,90 degree triangle rule:
The opposite side of 30 degree will be y
30->y
90->2y->12√3 => y=6√3
60->y√3->x => 6√3x√3=6x3=18
To understand the rule better you can check the picture below.Wish it will help you!Good luck!
Answer:
4y+3
Step-by-step explanation:
Answer:
Part 1) 
Part 2) 
Part 3) 
Part 4) 
Part 5) 
Part 6) 
Step-by-step explanation:
Part 1) we know that
The shaded region is equal to the area of the complete rectangle minus the area of the interior rectangle
The area of rectangle is equal to

where
b is the base of rectangle
h is the height of rectangle
so



Part 2) we know that
The shaded region is equal to the area of the complete rectangle minus the area of the interior square
The area of square is equal to

where
b is the length side of the square
so



Part 3) we know that
The area of the shaded region is equal to the area of four rectangles plus the area of one square
so



Part 4) we know that
The shaded region is equal to the area of the complete square minus the area of the interior square
so



Part 5) we know that
The area of the shaded region is equal to the area of triangle minus the area of rectangle
The area of triangle is equal to

where
b is the base of triangle
h is the height of triangle
so



Part 6) we know that
The area of the shaded region is equal to the area of the circle minus the area of rectangle
The area of the circle is equal to

where
r is the radius of the circle
so


Answer:
a^2 - 3
Step-by-step explanation:
(3a^2 + 1) - (4 + 2a^2)
3a^2 + 1 - 4 - 2a^2
a^2 - 3