Given that a line passes through the point , and that the line is perpendicular to the line Determine the equation of the line
If sin(20-30)-cos(30-40) then the value of is 0
In a class of 40 boys, 18 passed Business Mathematics, 19 passed Accounts, 10 passed Economics, 6 passed Accounts only, 5 passed Business Mathematics and Accounts only, 2 Passed Accounts and Economics only. How many passed in all three papers.
To determine the equation of a line that passes through a given point and is perpendicular to another line, you need to know the slope of the given line.
1. Find the slope of the given line:
Use the formula for slope (m) which is (change in y) divided by (change in x). If you have the equation of the line in the form y = mx + b, then the slope (m) is the coefficient of x.
2. Calculate the negative reciprocal of the slope:
Since the line you want to find is perpendicular to the given line, the slope of the line you want to find will be the negative reciprocal of the slope of the given line. The negative reciprocal of a number is found by flipping the fraction and changing the sign.
3. Use the point-slope form to write the equation:
Once you have the slope and the given point, you can use the point-slope form to write the equation of the line.
The point-slope form is: y - y1 = m(x - x1)
Plug in the given point (x1, y1) and the negative reciprocal slope (m) to get the equation of the line.
For the second question about the value of an expression, you need to simplify the given expression and determine the value:
1. Simplify the expression:
Follow the order of operations (PEMDAS) and perform the calculations. Start with any parentheses, then exponents, then multiplication/division from left to right, and finally addition/subtraction from left to right.
2. Determine the value:
After simplifying the expression, you should have a numerical value. Check if there are any variable expressions or unknowns that need to be evaluated. Substitute the given values into the expression and calculate the final result.
For the third question about determining the number of students who passed in all three papers:
1. Use a Venn diagram:
Create a Venn diagram with three overlapping circles representing each subject: Business Mathematics, Accounts, and Economics. Use the given information to fill in the numbers in each section of the circles.
2. Use the principle of Inclusion-Exclusion:
Apply the principle of Inclusion-Exclusion to count the total number of students who passed in all three papers. Start by adding the numbers in the intersection of all three circles.
3. Calculate the number of students who passed in all three papers:
Count the total number of students in the intersection of all three circles to find the answer to the question.