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1) Find distance between two parallel lines 3x+2y-5=0 and 3x+2y-6=0 2) Find the acute angle between the lines 2x+3y=13 & 2x-5y+7=0 3) Find the slope and intercepts of the line 3x+4y=12. 4) Find the equation of line passi

Concept: Distance between parallel lines

Question

1) Find distance between two parallel lines 3x+2y-5=0 and 3x+2y-6=0
2) Find the acute angle between the lines 2x+3y=13 & 2x-5y+7=0
3) Find the slope and intercepts of the line 3x+4y=12.
4) Find the equation of line passing through (-1,-2) & (-3, 8).
5) Find the equation of line passing through the point of intersection of lines 4x+3y=8 &
x+y=1 & parallel to the line 5x-7y=3.
6) State whether the function is even or odd if f(x)=3x⁴-2x⁴+cos x.
7) Find dy/dx if y=x¹⁰+10⁶+e⁸
8) If f(x)=x²+6x+10 find f(2)+f(-2).
9) Find dy/dx if x²+y²=4xy.
10) Find the range & coefficient of range for the following data, 120, 100, 130, 50, 150.
11) Find the mean deviation for the following data.
C.I. 0-10 10-20 20-30 30-40 40-50
Fi 5 8 15 16 6
12) From the following data investigate which set is more consistent.
Set X SD.=σ
Set 1 82.5 7.3
Set II 98.75 8.35
13) Calculate Standard Deviation for the following data:
Marks 5 10 15 20 25
No.of Students 6 16 28 38 46
14) Find the Standard Deviation & Coefficient of Variation from the following data:
C.I. 0-10 10-20 20-30 30-40 40-50
Frequency 3 5 8 3 1
d=∣C1−C2∣A2+B2d = \frac{|C_1 - C_2|}{\sqrt{A^2 + B^2}}

Try it yourself first

Hint: Start by identifying the coefficients A, B, C1, and C2 from the given equations of the parallel lines.

Step-by-step solution

  1. 1

    Identify coefficients

    Line 1: Ax+By+C1=0 • Line 2: Ax+By+C2=0 • A=3, B=2, C1=-5, C2=-6
  2. 2

    Recall distance formula

    d = |C1 - C2| / A2+B2\sqrt{A^2 + B^2} • Absolute difference of C • Divide by A2+B2\sqrt{A^2+B^2}
    d=∣C1−C2∣A2+B2d = \frac{|C_1 - C_2|}{\sqrt{A^2 + B^2}}
  3. 3

    Substitute and calculate

    d = |-5 - (-6)| / 32+22\sqrt{3^2 + 2^2} • d = |1| / 9+4\sqrt{9 + 4} • d = 1 / 13\sqrt{13}
    d=∣−5−(−6)∣32+22d = \frac{|-5 - (-6)|}{\sqrt{3^2 + 2^2}}

Final answer

0.2774

Remember: Use the specific formula for distance between parallel lines.

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