Step-by-step explanation:
y=-2
y=0.2x
y=0.2(-2)
y=-0.4
y=0
y=0.2x
y=0.2(0)
y=0
y=2
y=0.2x
y=0.2(2)
y=0.4
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:
45 degrees
Step-by-step explanation:
The formula to find the sum of all the interior angles in an "n-gon" (n is a variable that stands for the numbers of sides, ex) 20-gon --> 20 sided polygon) is .
Let's plug in 100 to find the sum of all the interior angles in a 100-gon.
I would rather distribute than simplify the parentheses and have to multiply 180 by 98.
So:
= degrees
[REMEMBER, IT WAS NOT GIVEN THAT THIS POLYGON IS REGULAR, SO <u>DO NOT</u> DIVIDE 17640 BY 100]
Now to find the last angle, we can just subtract since we are given the value of 99 of the 100 angles (17595 degrees).
So the last angle is degrees
Area of square = s^2
Area of Rectangle = lw
l = 2s
w+3 = s
solve for w, w=s-3
Now we have l and w.
Plug both into area of rectangle formula so: (2s)(s-3)
Since both areas are equal set both equations equal to each other:
(2s)(s-3)=s^2
Now simplify
2s^2-6s=s^2
s^2-6s=0, Solve for s.
Factor polynomial. s(s-6)=0 , s can be equal to 0 or 6. HOWEVER, you cannot have a side length of 0 therefore the side length has to be 6.
Now plug in s for the length formula for the rectangle:
l = 2s so... l = 2(6) so length of rectangle = 12.
Now plug in s for the width formula for the rectangle:
w+3=s so... w+3=6 so width of rectangle = 3.
Now the dimensions of the rectangle are 12 by 3. 12 being length and 3 width.
To CHECK:
Find area of rectangle:
A=lw so A=3 times 12 so A=36
Find area of square:
We know the side is equal to 6 so
A=s^2 so 6^2 = 36
The areas are equal that verifies the answer of 12 by 3.