Write the decimal number 39 to base 2
10011 base 2
110111 base 2
111001 base 2
100101 base 2
19.5 base 2
Correct answer is A
\(\begin{array}{c|c} 2 & 39\\ 2 & 19 R 1\\ 2 & 9 R 1\\2 & 4 R 0\\2 & 1 R 0\\ 2 & 1 R 1\end{array}\)
= 10011 base 2
x varies inversely as w2
x varies directly as w2
x varies directly as w
x varies inversely as w
x varies directly as square root of w
Correct answer is B
No explanation has been provided for this answer.
\(\frac{6600}{7}\)cm3
270cm3
660cm3
\(\frac{4224}{7}\)cm3
\(\frac{1980}{7}\)cm3
Correct answer is D
V = \(\pi\)r2h
= \(\frac{22}{7}\) x 52 x 12 - \(\frac{22}{7}\) x 32 x 12
= \(\frac{22}{7}\) x 12(52 - 32)
= \(\frac{4224}{7}\)
If a function is defined by f(x + 1) = 3x2 - x + 4, Find f(0).
4
6
9
8
2
Correct answer is D
f(x + 1) = 3x2 - x + 4
f(0) = f(x + 1)
x + 1 = 0 ===> x = -1
f(0) = 3(-1)2 - (-1) + 4
f(0) = 3 + 1 + 4
= 8
c = 4 and d = -9
c = -4 and d = 9
c = -20 and d = -15
c = 20 and d = -15
c = -20 and d = 15
Correct answer is C
F(X) = x\(^3\) - 4x\(^2\) + cx + d
= (X + 1) Q(X) + R
x = -1, R = 0,f(-1) = -1\(^3\) - 4(-1)\(^2\) + c(-1) + d = 0
-1 - 4 - c + d = 0
d - c = 5................(i)
f(-2) = -2\(^3\) - 4(-2)\(^2\) + c(-2) + d = 1
= -8 - 16 - 2c + d
= 1
-8 - 16 - 2c + d = 1
-24 - 2c + d = 1
d - 2c = 1 + 24
d - 2c = 25.................(ii)
\(\frac{d - c = 5}{-c = 20}\) d - c = 5
c = -20
d - (-20) = 5
d + 20 = 5
d = 5 - 20
= -15
c = -20, d = -15