1. Express the following in logarithmic form:
10-3 = 0.001
Solve, using cross-multiplication:
8x + 5y = 9
3x + 2y = 4
Solve, using cross-multiplication:
√2x – √3y = 0
√5x + √2y = 0
2. The value of expression mx – ny is 3 when x = 5 and y = 6. And its value is 8 when x = 6 and y = 5. Find the values of m and n.
Find the value of m, if x = 2, y = 1 is a solution of the equation 2x + 3y = m.
3. A train travels from city A to city B with constant speed of 36 kmph and returns back to city A with constant speed of 72 kmph. Find average speed during the entire journey.
2. A rifle bullet loses 1/20th of the initial velocity in passing through a plank. Find out the least number of similar planks required to stop the bullet.
Distance travelled in fifth second = distance travel in 2.5 sec - distance travel in 2 sec
= 0.5 * a { (T1)^2 - (T2)^2 }
= 0.5 * 2 { (2.5)^2 - (2)^2 }
= 2.25m
Please solve the questions
5. Find x, if:
[∛(⅔)]x-1 = 27/8
SOLUTION
[(?)1/3]x-1 = (3 × 3 × 3)/(2 × 2 × 2)
(?)(x-1)/3 = (3/2)3
(?)(x-1)/3 = (2/3)-3
Now, if the bases are equal, then the powers must be equal
So, on comparing the exponents, we get
(x – 1)/3 = -3
x – 1 = -9
x = -9 + 1
x = -8
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