51\(\frac{3}{7}\)km per hour
72km per hour
37\(\frac{1}{2}\) km per hour
66km per hour
75km per hour
Correct answer is B
Distance travelled by both x and y = 150 km.
Speed of y = 60km per hour, Time = \(\frac{dist.}{Speed}\)
Time spent by y = \(\frac{150}{60}\)
= 2\(\frac{3}{6}\)hrs
= \(\frac{1}{2}\) hrs
if x arrived at p 25 minutes earlier than y, then time spent by x = 2 hour 5 mins
= 125 mins
x average speed = \(\frac{150}{125}\) x \(\frac{60}{1}\)
= \(\frac{9000}{125}\)
= 72 km\hr
Given that 10x = 0.2 and log102 = 0.3010, find x
-1.3010
-0.6990
0.6990
1.3010
0.02
Correct answer is B
Given that log102 = 0.3010, If 10x = 0.2
log1010x = log10 0.2 = log10
xlog10 10 = log10 2 - log1010 since log10 10 = 1
x = 0.3010 - 1
x = -0.6990
If \(\log_{2} y = 3 - \log_{2} x^{\frac{3}{2}}\), find y when x = 4.
8
\(\sqrt{65}\)
4\(\sqrt{2}\)
3
1
Correct answer is E
\(\log_{2} y = 3 - \log_{2} x^{\frac{3}{2}}\)
When x = 4,
\(\log_{2} y = 3 - \log_{2} 4^{\frac{3}{2}}\)
\(\log_{2} y = 3 - \log_{2} 2^{3}\)
\(\log_{2} y = 3 - 3 \log_{2} 2 = 3 - 3 = 0\)
\(\log_{2} y = 0 \implies y = 2^{0} = 1\)
1.5cm
2.5cm
3cm
4cm
None of the above
Correct answer is A
Let XW = a, a :7
\(\frac{a}{5 - a}\) = \(\frac{3}{7}\)
7a = 15 - 3a
10a = 15
a = \(\frac{15}{10}\)
= \(\frac{3}{2}\)
= 1.5cm
Solve \(\frac{1}{x + 1}\) - \(\frac{1}{x + 3}\) = \(\frac{1}{4}\)
x = -1 or 3
x = 1 or 3
x = 1 or -5
x = -1 or 5
x = -1 or -3
Correct answer is C
\(\frac{1}{x + 1}\) - \(\frac{1}{x + 3}\) = \(\frac{1}{4}\)
\(\frac{x + 3 - x - 1}{(x + 1)(x + 3)}\) = \(\frac{1}{4}\)
\(\frac{2}{x^2 + 4x + 3}\) = \(\frac{1}{4}\)
= x2 + 4x + 3 = 8
x2 + 4x - 5 = 0
= (x - 1)(x + 5) = 0
x = 1 or -5