The summand (R?) is missing, but we can always come up with another one.
Divide the interval [0, 1] into 
subintervals of equal length 
:
![[0,1]=\left[0,\dfrac1n\right]\cup\left[\dfrac1n,\dfrac2n\right]\cup\cdots\cup\left[1-\dfrac1n,1\right]](https://tex.z-dn.net/?f=%5B0%2C1%5D%3D%5Cleft%5B0%2C%5Cdfrac1n%5Cright%5D%5Ccup%5Cleft%5B%5Cdfrac1n%2C%5Cdfrac2n%5Cright%5D%5Ccup%5Ccdots%5Ccup%5Cleft%5B1-%5Cdfrac1n%2C1%5Cright%5D)
Let's consider a left-endpoint sum, so that we take values of 
where 
is given by the sequence
with 
. Then the definite integral is equal to the Riemann sum
Interesting problem ...
The key is to realize that the wires have some distance to the ground, that does not change.
The pole does change. But the vertical height of the pole plus the distance from the pole to the wires is the distance ground to the wires all the time. In other words, for any angle one has:
D = L * sin(alpha) + d, where D is the distance wires-ground, L is the length of the pole, alpha is the angle, and 'd' is the distance from the top of the (inclined) pole to the wires:
L*sin(40) + 8 = L*sin(60) + 2, so one can get the length of the pole:
L = (8-2)/(sin(60) - sin(40)) = 6/0.2232 = 26.88 ft (be careful to have the calculator in degrees not rad)
So the pole is 26.88 ft long!
If the wires are higher than 26.88 ft, no problem. if they are below, the concerns are justified and it won't pass!
Your statement does not mention the distance between the wires and the ground. Do you have it?
The diameter is approximately 32.72 cm.
The corners of a door
The edge of a table
corners of a book
basically any corner of a rectangular or square object
Answer:
x = -19/2 y = -33/2
Step-by-step explanation:
x - (3x + 12) = 7
x - 3x - 12 = 7
-2x - 12 = 7
-2x = 19
x = -19/2
x - y = 7
-19/2 - y = 7
-y = 33/2
y = -33/2
