Questions
Given that a line passes through the point , and that the line is perpendicular to the line Determine the equation of the line
If then the value of is
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.
Don't give much away on the line and point, do you?
For the other, just draw a 3-circle Venn diagram, and start filling in the pieces.
To determine the equation of a line passing through a given point and perpendicular to another line, you'll need to follow these steps:
1. Find the slope of the given line. Let's call this slope "m".
2. Since the line you want to determine is perpendicular to the given line, the slope of the new line will be the negative reciprocal of "m". Let's call this new slope "m_perpendicular".
3. Use the point-slope form to write the equation of the new line. The point-slope form is: y - y1 = m_perpendicular(x - x1), where (x1, y1) is the given point.
Similarly, if you want to find the number of students who passed all three papers in a given scenario, here's how you can approach it:
1. Identify the number of students who passed each individual paper. Let's call these numbers "A" (Business Mathematics), "B" (Accounts), and "C" (Economics).
2. Determine the number of students who passed any combination of two papers: A ∩ B (Business Mathematics and Accounts), A ∩ C (Business Mathematics and Economics), and B ∩ C (Accounts and Economics).
3. Finally, calculate the number of students who passed all three papers by subtracting the sum of the two-paper combinations from the total number of students who passed any individual paper: A ∩ B ∩ C = Total - (A + B + C - A ∩ B - A ∩ C - B ∩ C).
Now, let's solve the given questions step by step:
Question 1: Given that a line passes through a point and is perpendicular to another line, determine the equation of the line.
To find the equation of the line, you need the coordinates of the given point and the slope of the given line.
Question 2: If a^2 + b^2 = c^2, then the value of c is:
To find the value of c, you need to use the Pythagorean theorem, where c represents the length of the hypotenuse of a right triangle and a and b are the lengths of the other two sides.
Question 3: In a class of 40 boys, the number of students passing three different papers is given. To find the number of students who passed all three papers, you need to identify the students who passed each individual paper and the students who passed any combination of two papers, and then use the formula explained above.