Let
x---------> the rate of the boat in still water in mph
y--------> the rate of the current in mph
we know that
Upstream
equation
Downstream
equation
Adds equation and equation
Find the value of y
therefore
the answer is
the rate of the boat in still water is
the rate of the current is
PART A (1 in diagram)
Each mapping diagram represents a function because none of the elements in the inputs maps on to two different elements in the outputs.
1. The domain of the given function f(x) is the set {10, 20, 30}.
All we can say about
is that, it has a range of {10, 20, 30}.
This is because the domain of a function becomes the range of its inverse function.
2. If the graph of a function f(x) includes the point (3, 0), then the graph of the inverse function ,
will contain the point (0,3).
Reason:The point on the graph of the inverse function is obtained by reflecting the corresponding point on the graph of the function in the line y=x. We just have to swap the coordinates.
In simple terms the domain of the function becomes the range of the inverse function and vice versa.
3. If the first term in an arithmetic sequence is 2.
Then we have a=2.
If the twelfth term is 211, then
Put a=2 into this equation.
Solve for d.
If
then
Substitute a=2 and d=19
Therefore n=8
Answer:
1) 1 element
2) 13 elements
3) 22 elements
4) 40 elements
Step-by-step explanation:
1) Only one element will have no tails: the event that all the coins are heads.
2) 13 elements will have exactly one tile. Basically you have one element in each position that you can put a tail in.
3) There are elements that have exactly 2 tails. From those elements we have to remove the only element that starts and ends with a tail and in the middle it has heads only and the elements that starts and ends with a head and in the 11 remaining coins there are exactly 2 tails. For the last case, there are
possibilities, thus, the total amount of elements with one tile in the border and another one in the middle is 78-55-1 = 22
4) We can have:
For the first possibility there are 2 * 11 = 22 possibilities (first decide if the pair starts or ends and then select the remaining tail)
For the second possibility, we have 2*9 = 18 possibilities (first, select if there is a tail at the end or at the start, then put a head next to it and on the other extreme, for the remaining 10 coins, there are 9 possibilities to select 2 cosecutive ones to be tails).
This gives us a total of 18+22 = 40 possibilities.