The sides of two cubes are in the ratio 2:5. What is the ratio of their volumes?
4:5
8:15
6:125
8:125
Correct answer is D
The ratio of the two cubes = 2:5
Volume of the two cubes = 2\(^3\) : 5\(^3\) = 8 : 125
I only
II only
III only
I, II and III
Correct answer is C
No explanation has been provided for this answer.
Given that \(P\propto \frac{1}{\sqrt{r}}\) and p = 3 when r = 16, find the value of r when p = 3/2
48
64
72
324
Correct answer is B
\(P \propto \frac{1}{\sqrt{r}} P=3\hspace{1mm}r=16\\
P = \frac{k}{\sqrt{r}}\Rightarrow 3 = \frac{k}{\sqrt{16}}\Rightarrow \frac{3}{1} = \frac{k}{4} \\ \Rightarrow K = 12 \Rightarrow K = 12; P\sqrt{r} = k \Rightarrow \sqrt{r} = \frac{k}{p}\\
r = \frac{(k)^2}{P}=12^2 \div \frac{3}{2}=\left(\frac{12}{1}\times \frac{2}{3}\right)=8^2\\
r = 64\)
the perpendicular bisector of the line segment X Y
a line parallel to the line segment XY
a circle with XY as diameter
the line perpendicular to the line segment XY
Correct answer is A
No explanation has been provided for this answer.
Which of the following quadratic equations has \(-\frac{1}{2}\) and \(\frac{3}{4}\) as its roots?
8x2 + 11x - 3 = 0
8x2 -11x – 3 = 0
8x2 + 2x -3 = 0
8x2 - 2x – 3 = 0
Correct answer is D
X2 - (sum of the roots)x + (product of the roots) = 0
Sum of the roots \(= -\frac{1}{2}+\frac{3}{4} = \frac{-2+3}{2}=\frac{1}{4}\)
Product of the roots = \(-\frac{1}{2}\times \frac{3}{4}=\frac{-3}{8}\\
X^2-\left(\frac{1}{4}\right)x-\frac{3}{8} = 0. Taking \hspace{1mm}the\hspace{1mm} common\)
\(8x^2-2x-3=0\);