A boat sails 150km on a bearing of 042degree and then 250km due east . How far is the boat from the starting point
The answer is 368 km using cosine rule
The bearing of a point A from a point B is 042 degree calculate the bearing from A
370°
Please what rule are we using
We can assume that there exists a linear relationship between x and y. That is:
y = mx + b
where m is the slope of the line and b is the y-intercept.
Using the point given, we can solve for b:
5 = m(9) + b
b = 5 - 9m
Now that we know b, we can use the slope to find y when x is 4:
m = (y - 5)/(x - 9)
Since we are asked to find y when x is 4 and we know that m is the same, we can plug in the values we know and solve for y:
m = (y - 5)/(4 - 9)
m = (y - 5)/(-5)
Multiplying both sides by -5, we get:
-5m = y - 5
Adding 5 to both sides, we get:
-5m + 5 = y
Now, substituting the value we found for b earlier:
y = -5m + 5 - 9m
Simplifying the right-hand side, we get:
y = -14m + 5
Now, we can solve for m:
5 = 9m + b
5 = 9m + (5 - 9m)
5 = 5
This is true for any value of m, because the equation for the line is not unique with only one point. However, we can choose any value for m and still find a valid value for y. Let's choose m = 1:
y = -14(1) + 5
y = -9
Therefore, when x is 4, y is -9.
A truth table is a table that displays all possible inputs and outputs for a Boolean function. Boolean functions are functions that take one or more binary inputs (0 or 1) and produce a binary output. The truth table shows all the possible combinations of input values and the corresponding output values.
The columns of a truth table are typically labeled with the input variables and the output variable. The rows of the truth table show all possible combinations of input values. For each row of the truth table, the values of the input variables are specified and the corresponding output value is computed using the Boolean function.
For example, consider the Boolean function AND, which takes two binary inputs and produces a binary output that is 1 if both inputs are 1, and 0 otherwise. The truth table for this function would have two input columns and one output column, and would look like this:
```
Input1 | Input2 | Output
------------------------
0 | 0 | 0
0 | 1 | 0
1 | 0 | 0
1 | 1 | 1
```
The first row of the truth table shows the result when both input variables are 0, which produces an output of 0. The second row shows the result when one input variable is 0 and the other is 1, which produces an output of 0. The third row shows the result when the first input variable is 1 and the second is 0, which produces an output of 0. Finally, the last row shows the result when both input variables are 1, which produces an output of 1.
The truth table provides a complete and systematic way to specify the behavior of Boolean functions. It is a valuable tool for designing and analyzing digital circuits, for encoding Boolean expressions, and for testing the correctness of logic designs.
Thank you! I'm here to help with any questions you may have, so feel free to ask me anything. :)
D = 150km[42o]+250km[90o].
D = (150*sin42+250*sin90)+(150*cos42+250*cos90)i
D = 350+112i = 367km[72o].
368 km
We are using the cosine rule (a.k.a. the law of cosines) to find the distance between the two points. The cosine rule is a formula that relates the length of the sides of a triangle to the cosine of one of its angles. It can be used to find the length of any side of a triangle if the lengths of the other two sides and the included angle are known.
The formula for the cosine rule is:
c^2 = a^2 + b^2 - 2ab*cos(C)
Where c is the length of the side opposite angle C, and a and b are the lengths of the other two sides.