To draw the 2 dimensional representation, we just "open" the box and flatten it. Once we have it opened, we find the area of each side and add them up for the total surface area. See the pic. Let me know if you have questions. :)
The points A(2,1), B(3,6), C(5,-2) and D (1,-2) are the vertices of a parallelogram.fine |AC| and |BD|.are they equal in length?
1 answer:
Answer:
|AC| =√18 and |BD| =√68. They are not equal in length.
Step-by-step explanation:
To find |AC| and |BD| of the parallelogram, we will simply use the distance formula.
Using the line distance formula;
D = √(-
)² + (
-
)²
A(2,1) C(5,-2)
=2
=1
= 5
=-2
|AC| = √(-
)² + (
-
)²
=√(-2-1)² + (5-2)²
=√(-3)² + (3)²
=√9+9
=√18
Distance |AC| =√18
B(3,6) D (1,-2)
=3
=6
= 1
=-2
|BD| = √(-
)² + (
-
)²
=√(-2-6)² + (1-3)²
=√(-8)² + (-2)²
=√64+4
=√68
Distance |BD| =√68
|AC| and |BD| are not equal in length
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Answer:
The Jonathon and Raymond need to sell 6000 sales to earn the same amount each month.
Step-by-step explanation:
Given data
Let no. of sales = x
Jonathon earning = $ 1500 +
Raymond earning = $ 1200 +
Given that the earnings of Jonathon & Raymond are same.
1500 + = 1200 +
300 =
x = 6000 sales
Therefore the Jonathon and Raymond need to sell 6000 sales to earn the same amount each month.
First of all, when I do all the math on this, I get the coordinates for the max point to be (1/3, 14/27). But anyway, we need to find the derivative to see where those values fall in a table of intervals where the function is increasing or decreasing. The first derivative of the function is 
. Set the derivative equal to 0 and factor to find the critical numbers. 
, so x = -3 and x = 1/3. We set up a table of intervals using those critical numbers, test a value within each interval, and the resulting sign, positive or negative, tells us where the function is increasing or decreasing. From there we will look at our points to determine which fall into the "decreasing" category. Our intervals will be -∞<x<-3, -3<x<1/3, 1/3<x<∞. In the first interval test -4. f'(-4)=-13; therefore, the function is decreasing on this interval. In the second interval test 0. f'(0)=3; therefore, the function is increasing on this interval. In the third interval test 1. f'(1)=-8; therefore, the function is decreasing on this interval. In order to determine where our points in question fall, look to the x value. The ones that fall into the "decreasing" category are (2, -18), (1, -2), and (-4, -12). The point (-3, -18) is already a min value.