Question
A line passes through the point (4, 3) and is
perpendicular to the line 3x + 4y = 12. Find the equation of the new line.Solution
The slope of the line 3x + 4y = 12 is given by rearranging it into slope-intercept form: 3x + 4y = 12Â 4y = -3x + 12Â y = -3/4 * x + 3. Thus, the slope of the given line is -3/4. The slope of the perpendicular line will be the negative reciprocal, i.e., 4/3. Now, using the point-slope form of the equation of a line: y - y1 = m(x - x1), Substitute the point (4, 3) and slope 4/3: y - 3 = 4/3(x - 4), Multiply both sides by 3 to eliminate the fraction: 3(y - 3) = 4(x - 4), 3y - 9 = 4x - 16, 3y = 4x - 7, Thus, the equation of the line is: 4x - 3y = 7. Answer: c)
‘a’ is directly proportional to ‘b’. If at a=30, the value of ‘b’ is 20% greater than ‘a’, then find the value of ‘a’ when b=54.
...If a + `1/b` = 1 and b + `1/c` =1 , then the value of c + `1/a` is
The average of three numbers a, b and c is 2 more than c. The average of a and b is 48. If d is 10 less than c, then the average of c and d is:
√(92×8 ×52+700) = ?
If x4 + x - 4 = 47 then find the value of (x + x-1).
If a + b + c = 5, a³ + b³ + c³ = 85 and abc =25, then find the value of a² + b² + c² – ab –bc – ca
- If x + 4y = 26 and 4x + y = 41, then find the value of (x - y).
- If p = 25 - q - r and pq + r(p + q) = 256, then find the value of (p² + q² + r²).
If 10x2 – 6xy+y² – 4x+4= 0, then find the value of (3x+2y).
Find the value of ‘x’ in the given expression:
(49/16)x × (64/343)x-1 = 4/7
