The answer is C.(-2,3)<span />
Look at the picture.
The polygon is a right-angled trapezoid.
The area is:

The points (-2,-1) and (6,-1) lie on the same horizontal line, so the distance between them is 6-(-2)=6+2=8. The length of a is 8 units.
The points (-2,5) and (3,5) lie on the same horizontal line, so the distance between them is 3-(-2)=3+2=5. The length of b is 5 units.
The points (-2,5) and (-2,-1) lie on the same vertical line, so the distance between them is 5-(-1)=5+1=6. The length of h is 6 units.

The area is
39 square units.
39×2÷6=13
13-5=8 mm. The other base of the trapezoid is 8 mm. Let check it:
1/2(8+5)×6
=1/2×13×6
=39 square mm. Hope it help!
Answer:
y=t−1+ce
−t
where t=tanx.
Given, cos
2
x
dx
dy
+y=tanx
⇒
dx
dy
+ysec
2
x=tanxsec
2
x ....(1)
Here P=sec
2
x⇒∫PdP=∫sec
2
xdx=tanx
∴I.F.=e
tanx
Multiplying (1) by I.F. we get
e
tanx
dx
dy
+e
tanx
ysec
2
x=e
tanx
tanxsec
2
x
Integrating both sides, we get
ye
tanx
=∫e
tanx
.tanxsec
2
xdx
Put tanx=t⇒sec
2
xdx=dt
∴ye
t
=∫te
t
dt=e
t
(t−1)+c
⇒y=t−1+ce
−t
where t=tanx
Answer:
1. Option A
2. Option B
Step-by-step explanation:
I would like to elaborate on the answer to the second question, since the first answer is actually option a. Why? The question asks for a parametric equation, not set, so it would be choice a.
2. x=3t + 5 - isolate t
t=(x-5)/3 - substitute into the second equation
y = [(x-5)/3]^2 - 1
your solution is option b