Answer:
y
=
x
2
−
2
x
,
y
=
x
Step-by-step explanation:
Rewrite the boundary lines <em>y</em> = -1 - <em>x</em> and <em>y</em> = <em>x</em> - 1 as functions of <em>y </em>:
<em>y</em> = -1 - <em>x</em> ==> <em>x</em> = -1 - <em>y</em>
<em>y</em> = <em>x</em> - 1 ==> <em>x</em> = 1 + <em>y</em>
So if we let <em>x</em> range between these two lines, we need to let <em>y</em> vary between the point where these lines intersect, and the line <em>y</em> = 1.
This means the area is given by the integral,

The integral with respect to <em>x</em> is trivial:

For the remaining integral, integrate term-by-term to get

Alternatively, the triangle can be said to have a base of length 4 (the distance from (-2, 1) to (2, 1)) and a height of length 2 (the distance from the line <em>y</em> = 1 and (0, -1)), so its area is 1/2*4*2 = 4.
If the graphs of the equations do not intersect
Answer:
Step-by-step explanation:
The opposite side (the one not connected to A) = 4
The hypotenuse is 5
The adjacent side needs to be found for the cosine and the tangent.
a^2 + b^2 = c^2
a = opposite side = 4
b = adjacent side = ?
c = hypotenuse = 5
4^2 + x^2 = 5^2
16 + x^2 = 25
x^2 = 25 - 16
x^2 = 9
x = sqrt(9)
x = 3
cos(A) = adjacent / hypotenuse = 3/5
Tan(A) = opposite / adjacent = 4/3
cos(A) + tan(A) = 3/5 + 4/3
cos(A) + tan(A) = 9/15 + 20/15 = 29/15
Answer:
a=m-x^2/k^2
Step-by-step explanation:
(k^2(m-a)) /x=x
K^2(m-a)=x^2
m-a=x^2/k^2
a=m-x^2/k^2