The first term of a geometric progression (G.P) is 3 and the 5th term is 48. Find the common ratio.
2
4
8
16
Correct answer is A
T\(_5\) = ar\(^4\)
\(\frac{48}{3} = \frac{3r^4}{3}\)
16 = r\(^4\)
r = \(4\sqrt{16}\)
= 2
~ y \(\to\) ~ x
y \(\to\) ~ x
~ x \(\to\) ~ y
y \(\to\) x
Correct answer is C
No explanation has been provided for this answer.
Solve 3x - 2y = 10 and x + 3y = 7 simultaneously
x = -4 and y = 1
x = -1 and y = -4
x = 1 and y = 4
x = 4 and y = 1
Correct answer is D
3x - 2y = 10 - - x 3
x + 3y = 7 ---x 2
------------------------
9x - 6y = 30
2x + 6y = 14
-------------------------
\(\frac{11x}{11} \frac{44}{11}\)
x = 4
From x + 3y = 7
3y = 7 - 4
\(\frac{3y}{3}\) = \(\frac{3}{3}\)
y = 1
If x = 3 and y = -1, evaluate 2(x\(^2\) - y\(^2\))
24
22
20
16
Correct answer is D
2(\(x^2 - y^2\))
= 2(x + y)(x - y)
= 2(3 + (-1))(3 - (-1))
= 2(2)(4) = 16
Given that \(\frac{\sqrt{3} + \sqrt{5}}{\sqrt{5}}\) = x + y\(\sqrt{15}\), find the value of (x + y)
1\(\frac{3}{5}\)
1\(\frac{2}{5}\)
1\(\frac{1}{5}\)
\(\frac{1}{5}\)
Correct answer is C
\(\frac{\sqrt{3} + \sqrt{5}}{\sqrt{5}}\) = x + y\(\sqrt{15}\)
cross multiply to have: \(\sqrt{3}\) + \(\sqrt{5}\) = x\(\sqrt{5}\) + 5y\(\sqrt{3}\)
Collect like roots : x\(\sqrt{5}\) = \(\sqrt{5}\) → x = 1
5y\(\sqrt{3}\) = \(\sqrt{3}\) → y = \(\frac{1}{5}\)
∴ ( x + y ) = 1 + \(\frac{1}{5}\)
= 1\(\frac{1}{5}\)