Answer:
14.3 feet.
14.3 feet
Step-by-step explanation:
The problem forms a right triangle in which:
The Vertical Leg of the Right Triangle = 3 feet
The Horizontal Leg of the Right Triangle =14 feet
We are to determine the length of the broken part of the tree. This is the Hypotenuse of the Right Triangle,
Using Pythagoras Theorem

Split up the interval [0, 2] into <em>n</em> equally spaced subintervals:
![\left[0,\dfrac2n\right],\left[\dfrac2n,\dfrac4n\right],\left[\dfrac4n,\dfrac6n\right],\ldots,\left[\dfrac{2(n-1)}n,2\right]](https://tex.z-dn.net/?f=%5Cleft%5B0%2C%5Cdfrac2n%5Cright%5D%2C%5Cleft%5B%5Cdfrac2n%2C%5Cdfrac4n%5Cright%5D%2C%5Cleft%5B%5Cdfrac4n%2C%5Cdfrac6n%5Cright%5D%2C%5Cldots%2C%5Cleft%5B%5Cdfrac%7B2%28n-1%29%7Dn%2C2%5Cright%5D)
Let's use the right endpoints as our sampling points; they are given by the arithmetic sequence,

where
. Each interval has length
.
At these sampling points, the function takes on values of

We approximate the integral with the Riemann sum:

Recall that

so that the sum reduces to

Take the limit as <em>n</em> approaches infinity, and the Riemann sum converges to the value of the integral:

Just to check:

line given slope = x coefficient = 1/3
Perpendicular slopes must be opposite reciprocals of each other: m1 * m2 = –1
line slope (m) = -3
line equation formula = y = mx + b
y = -3x + b
from the point given
x = 3
y= 3
3 = -9 + b
b = 12
y = -3x + 12
The pounds is 1.875 I'm not sure about oz
Answer:
Ted and Fred
Step-by-step explanation:
As per the question,
Ted and Fred are the owners of a gas station that is they are the owner of their own firm.
As being the owner of their own company, they are the one who is responsible for their loss. That is the firm’s owners always suffer the firm’s risk.
Business Risk: Risk that a business will not be able to cover its operating costs.
So in this case, Lawrence is the employee and legally he is not responsible to suffer any kind of the loss.
So he must be paid his salary on time and in full whether or not the firm is running a profit, a loss, or just breaking even.
As being owner Ted and Fred are responsible to withstand the business risk.
Hence, the person who is legally responsible for bearing the $40,000 loss is Ted and Fred.