Consider the following sets. U = {ordered pairs on a coordinate plane} A = {ordered pair solutions to y = x} B = {ordered pair s
2 answers:
Answer:
(0,0)
Step-by-step explanation:
We have,
U = { (x,y) : x,y belong to real numbers }
A = { (x,y) : (x,y) is a solution of y=x }
B = { (x,y) : (x,y) is a solution of y=2x }
We need to find the ordered pair (x,y) that belong to AB.
Let, (x,y) belong to AB
i.e. (x,y) belong to A and (x,y) belong to B
i.e. y = x and y = 2x
i.e. x = 2x
i.e. x = 0
Now, substitute x= 0 in any of the equation say y = x, we get y = 0.
Hence, the ordered pair satisfying AB is (0,0).
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Answer:
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Step-by-step explanation:
The general point slope of line passing through and having slope as m.
The given equation of the straight line,
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Answer:
minimum cost of construction box are x = x = 3.4199 in and y = 10.2598 in and z = 4.2750 in
Step-by-step explanation:
given data
volume = 150 in³
base material costing = 5 cents/in²
front cost = 10 cents/in²
remainder sides cost = 2 cents/in²
to find out
the dimensions that will minimize the cost
solution
we consider here length = x and breadth = y and height = z
and
area of base = xy
area of front = xz
and area of remaining side = xz + 2yz .....................1
so
cost of base will be = 5xy
cost of front = 10xz
cost of remaining side = 2 ( xz+ 2yz)
and
total cost will be
total cost TC = 5xy + 10xz + 2 ( xz+ 2yz)
total cost TC = 5xy + 10xz + 2xz+ 4yz
total cost TC = 5xy + 12xz + 4yz ....................2
and total volume will be = xyz
150 = xyz
z = .......................3
now put z value in equation 2
total cost TC = 5xy + 12xz + 4yz
total cost TC = 5xy + 12x + 4y
total cost TC = 5xy + +
...........4
now differentiate TC w.r.t x and y
TC (x) = 5y -
TC (x) = 5x -
now equating with 0 these
5y - = 0
x² =
and
5x - = 0
x =
solve we get
y = 10.2598
x = 3.4199
now put x and y value in equation 3
z =
z =
z = 4.2750
so minimum cost of construction box are x = x = 3.4199 in and y = 10.2598 in and z = 4.2750 in