If 2\(^{x + y}\) = 16 and 4\(^{x - y} = \frac{1}{32}\), find the values of x and y
x = \(\frac{3}{4}\), y = \(\frac{11}{4}\)
x = \(\frac{3}{4}\), y = \(\frac{13}{4}\)
x = \(\frac{2}{3}\), y = \(\frac{4}{5}\)
x = \(\frac{2}{3}\), y = \(\frac{13}{4}\)
Correct answer is B
2\(^{x + y}\) = 16 ; 4\(^{x - y}\) = \(\frac{1}{32}\).
\(\implies 2^{x + y} = 2^4\)
\(x + y = 4 ... (1)\)
\(2^{2(x - y)} = 2^{-5} \)
\(2^{2x - 2y} = 2^{-5}\)
\(\implies 2x - 2y = -5 ... (2)\)
Solving the equations (1) and (2) simultaneously, we have
x = \(\frac{3}{4}\) and y = \(\frac{13}{4}\)
Evaluate \((\frac{6}{0.32} \div \frac{2}{0.084})^{-1}\) correct to 1 decimal place.
1.3
2.5
4.6
3.2
Correct answer is A
\((\frac{6}{0.32} \div \frac{2}{0.084})^{-1}\)
= \((\frac{600}{32} \div \frac{2000}{84})^{-1}\)
= \((\frac{600}{32} \times \frac{84}{2000})^{-1}\)
= \((\frac{63}{80})^{-1}\)
= \(\frac{80}{63}\)
= 1.3 (to 1 decimal place)
15.5%
18.2%
14.8%
16.7%
Correct answer is D
Actual weight = 0.18g
Error = 0.21g - 0.18g
= 0.03g
% error = \(\frac{0.03}{0.18} \times 100%\)
= 16.7%
The angles of a polygon are given by 2x, 5x, x and 4x respectively. The value of x is
31°
30°
26°
48°
Correct answer is B
Since there are 4 angles given, the polygon is a quadrilateral.
Sum of angle in a quadrilateral = 360°
∴∴ 2x + 5x + x + 4x = 360°
12x = 360°
x = 30°
If S = (4t + 3)(t - 2), find ds/dt when t = 5 secs.
50 units per sec
35 units per sec
22 units per sec
13 units per sec
Correct answer is B
\(s = (4t + 3)(t - 2)\)
\(\frac{\mathrm d s}{\mathrm d t} = (4t + 3)(1) + (t - 2)(4)\)
= \(4t + 3 + 4t - 8\)
= 8t - 5
\(\frac{\mathrm d s}{\mathrm d t} (t = 5 secs) = 8(5) - 5\)
= 40 - 5
= 35 units per sec