For the following exercises, find the exact area of the region bounded by the given equations if possible. If you are unable to determine the intersection points analytically, use a calculator to approximate the intersection points with three decimal places and determine the approximate area of the region. x= √4-y^2 and y^2=1+x^2

Points of intersection: (1.225,-1.58) and (1.225,1.58)

Step-by-step explanation:

Given

Required

The region area

Plot the graphs of and

Make y the subject in both equations

Square both sides

Rewrite

Take square roots

So, we have:

Take square roots

So, we have:

The point of intersection is:

Square both sides

Collect like terms

Divide by 2

Take square roots

So, the point of intersection is at: (1.225,-1.58) and (1.225,1.58)

See attachment

From the attached image, we can see that the curves do not enclose

Hence:

step-by-step explanation:

if x = 2 you have to find x to finish the problem

step-by-step explanation:

given that there are two triangles j'k'l' and jkl>

the former is got by dilating the second one.

when drawn on a grid, (graph paper) coordinates of vertices of first triangle is

(6,12)j, (9,6)k and (12,9)l

side jk has length = distance between j and k

=

side j'k'=distance between j' and k'

=

ie j'k'l' has sides 1/3 of that of corresponding sides of jkl.

hence scale factor of 1/3 is used to get j'k'l'from jkl