A relation is (also) a function if every input x is mapped to a unique output y.
In terms of graphical representation, this implies that a graph represents a function if there doesn't exist a vertical line that intersects the graph more than once. So:
- The first graph is exactly a vertical line, so it's not a function.
- The second graph represents the function y=x, so it's a function: you can see that every possible vertical line crosses the graph only once.
- The third graph is not a function, because you can draw vertical lines that cross the graph twice.
- Similarly, in the fourth graph you can draw vertical lines that cross the graph twice
- The fifth graph is a function, because every vertical line crosses the graph once
- The last graph is a function, although discontinuous, for the same reason.
Answer:
C = -13.78
Step-by-step explanation:
There are 2! = 2 ways to arrange the names of two basketball players in a hat.
Since, the are going to throw alphabetically, there is 1 way for the names to be arranged alphabetically.
Therefore, <span>the probability that they shoot free throws in alphabetical order is
</span>
Answer:
Length l = 15 - 2x = 15 - 2(1.5) = 12.00 in
Breadth b = 7 - 2x = 7 - 2(1.5) = 4.00 in
Height h = x = 1.50 in
Step-by-step explanation:
The volume of a box can be written as;
V = l×b×h
Where;
Length = l
Breadth = b
Height = h
Let x represent the length of the cube cut out of the four edges.
Using the attached image;
Length l = 15 - 2x
Breadth b = 7 - 2x
Height h = x
Substituting the values to the volume equation;
V = (15-2x)(7-2x)(x)
V = 105x - 30x^2 - 14x^2 + 4x^3
V = 105x - 44x^2 + 4x^3
At Maximum volume, V' = dV/dx = 0
V' = 105 - 88x + 12x^2 = 0
Solving the quadratic equation, we have;
x = 5.83 or x = 1.50
x cannot be 5.83 since 2x > 7 (greater than the breadth of cardboard)
Therefore ;
Length l = 15 - 2x = 15 - 2(1.5) = 12.00 in
Breadth b = 7 - 2x = 7 - 2(1.5) = 4.00 in
Height h = x = 1.50 in
