Mid point b/w pair of coordinate (xo ,yo) ,(x1,y1)
X = xo+x1/2
y= yo+y1/2
thus mid point between (-8,-8),(4,8)
X = -8+4/2= -2
y= -8+8/2 = 0
(-2,0) will be the midpoint
Answer:
Martha is 29
Step-by-step explanation:
48=AX+MX+10
-10=-10
38=AX+MX
÷2=÷2
19=X
M(19)+10=29
48=19+29
Answer: 7 pigeons sitting on the branches, 5 pigeons under the tree
=12 in total
Step-by-step explanation:
Upper branch has x pigeons, lower has y.
Top branch said: "If one of you flies up to us our number will be double yours":
Well, if one of the bottom branch flies up, the top branch will have x+1 birds and the bottom will have (y−1). The top will have double the bottom, so:
x+1=2(y−1)
Top branch said: "If one of us flies down to you, our numbers will be equal":
Now, the top branch will have x−1 and the bottom y+1. The numbers should be equal:
x−1=y+1
Answer:
$180000
Step-by-step explanation:
Let's c be the number of chair and d be the number of desks.
The constraint functions:
- Unit of wood available 4d + 3c <= 2000 or d <= 500 - 0.75c
- Number of chairs being at least twice of desks c >= 2d or d <= 0.5c
c >= 0
d >= 0
The objective function is to maximize the profit function
P (c,d) = 400d + 250c
We draw the 2 constraint functions (500 - 0.75c and 0.5c) on a c-d coordinates (witch c being the horizontal axis and d being the vertical axis) and find the intersection point 0.5c = 500 - 0.75c
1.25c = 500
c = 400 and d = 0.5c = 200 so P(400, 200) = $250*400 + $400*200 = $180,000
The 500 - 0.75c intersect with c-axis at d = 0 and c = 500 / 0.75 = 666 and P(666,0) = 666*250 = $166,500
So based on the available zones in the chart we can conclude that the maximum profit we can get is $180000
Answer:
(C) 50π
Step-by-step explanation:
For this problem, we need to find a way to relate the inner circle, to the square, to the outer circle.
Given that we know the area of a circle is πr^2, and our inner circle has a area of 25π, we can find the radius.
25π = πr^2
25 = r^2
5 = r
Note, that the diameter of the inner circle is parallel to the side of the square, meaning that the diameter of the inner circle is the length of the side of the square.
diameter = 2 * radius
d = 2 * 5 = 10.
Now that we know the value of the side of the square, we can find the length of the diagonal of the square, which is the diameter of the outer circle.
Using the properties of the 45-45-90 right triangle, we can say that the diagonal of the square is the length of the side times sqrt(2).
Outer_Diameter = 10 * sqrt(2)
Now to find the outer area, we need the formula for the area of a circle. Note that the diameter is twice the radius, so we will simply divide by 2.
A = πr^2
A = π * [ ( 10 * sqrt(2) ) / 2 ]^2
A = π * [ 5 * sqrt(2) ] ^2
A = π * 25 * 2
A = 50π
So the area of the outer circle is 50π.
Cheers.
