If y varies directly as \(\sqrt{n}\) and y = 4 when n = 4, find y when n = 1\(\frac{7}{9}\)
\(\sqrt{17}\)
\(\frac{4}{3}\)
\(\frac{8}{3}\)
\(\frac{2}{3}\)
Correct answer is C
y \(\propto \sqrt{n}\)
y = k\(\sqrt{n}\)
when y = 4, n = 4
4 = k\(\sqrt{4}\)
4 = 2k
k = 2
Therefore,
y = 2\(\sqrt{n}\)
y = 2\(\sqrt{\frac{16}{9}}\)
y = 2\((\frac{4}{3})\)
y = \(\frac{8}{3}\)
Solve for x and y in the equations below
x2 - y2 = 4
x + y = 2
x = 0, y = -2
x = 0, y = 2
x = 2, y = 0
x = -2, y = 0
Correct answer is C
x2 - y2 = 4 .... (1)
x + y = 2 .... (2)
Simplify eqn (1)
(x + y)(x - y) = 4
From eqn (2)
x + y = 2 so substitute it into simplified eqn (1), we have
2 (x - y) = 4
therefore,
x - y = 2 ... (1)
x + y = 2
---------
2x = 4
---------
x = 2, when y = 0
Find the remainder when 2x3 - 11x2 + 8x - 1 is divided by x + 3
-871
-781
-187
-178
Correct answer is D
Hence f(x) = 2x3 - 11x2 + 8x - 1
f(-3) = 2(-3)3 - 11(-3)2 + 8(-3) - 1
= 2(-27) - 11(9) + 8(-3) - 1
= -54 - 99 - 24 - 1
= -178
Make 'n' the subject of the formula if w = \(\frac{v(2 + cn)}{1 - cn}\)
\(\frac{1}{c}(\frac{w - 2v}{v + w})\)
\(\frac{1}{c}(\frac{w - 2v}{v - w})\)
\(\frac{1}{c}(\frac{w + 2v}{v - w})\)
\(\frac{1}{c}(\frac{w + 2v}{v + w})\)
Correct answer is A
w = \(\frac{v(2 + cn)}{1 - cn}\)
2v + cnv = w(1 - cn)
2v + cnv = w - cnw
2v - w = -cnv - cnw
Multiply through by negative sign
-2v + w = cnv + cnw
-2v + w = n(cv + cw)
n = \(\frac{-2v + w}{cv + cw}\)
n = \(\frac{1}{c}\frac{-2v + w}{v + w}\)
Re-arrange...
n = \(\frac{1}{c}\frac{w - 2v}{v + w}\)
1
2
3
4
Correct answer is A
n(f \(\cap\) v) + n(f) + n(v) + n(f \(\cap\) v) = 46
3 + 19 + 23 + x = 46
22 + 23 + x = 46
45 + x = 46
x = 46 - 45
x = 1