A square is inscribed in an equilateral triangle of side length 1 cm. Find the side length of the square, x.
\(\sqrt3\over(\sqrt3+2)\)
\(1\over\sqrt3\)
\(\sqrt3\over2\)
\(1\over2\)
\(1\over\sqrt3+2\)
A regular tetrahedron has side length x. Find the distance from the centre of one face to the opposing vertex.
\(x \sqrt 3 \over 6\)
\(x \sqrt 5 \over 6\)
\(x \sqrt 3 \over 16\)
\(x \sqrt 3 \over 8\)
\(x \sqrt 6 \over 3\)
8000 cuboids of dimensions 2x, x and x are melted and formed into a similar cuboid. Find the ratio of the total surface area of the individual cuboids to that of the new cuboid.
8000:1
20:1
9:20
200:9
46:2
What is the ratio of the total surface area of an open hemisphere to the total surface area of a closed hemisphere?
1:3
2:3
4:3
3:4
3:2
\(\int_{0}^{2}{{(x-\sqrt x)}^2dx}.\)Calculate the following integral:
\(\frac{14}{3}-\frac{16}{5}\sqrt2\)
\(\frac{14}{3}+\frac{16}{5}\sqrt2\)
\(4-\frac{16}{5}\sqrt2\)
\(\frac{14}{3}\)
None of the above
What is the minimum of the following function?
\(f\left(x\right)=x^4-2x^2\)
-2
-1
0
-1.5
1
Determine the equation of the line which contains the origin O(0,0) and the intersection point between the lines:
\(y_1:4x-3y-1=0 \)
and
\(y_2:6x-6y-1=0\)
\(2x-3y=0\)
\(4x-3y=0\)
\(x-y=0\)
\(3x-2y=0\)
\(3x-3y=0\)
Considering that \(f\left(x\right)=\left(x^2-1\right)\bullet\ln(x).\)
If f(x) is the derivative of F(x) where: \(F\left(x\right)=x\left({ax}^2-1\right)\bullet\ln{\left(x\right)}-x(\frac{x^2}{9}-b)\)
Find a and b.
\(a=\frac{1}{3}\ ,\ b=1\)
\(a=\frac{2}{3}\ ,\ b=2\)
\(a=1\ ,\ b=\frac{1}{3}\)
\(a=\frac{1}{3}\ ,\ b=2\)
\(a=\frac{1}{4}\ ,\ b=4\)
Of all the articles in a box, 80% are satisfactory, while 20% are not. The probability of obtaining exactly five good items out of eight randomly selected articles is:
0.003
0.013
0.132
0.147
0.8
A company offers you the use of its computer for a fee. Plan A costs 6 pounds to join and 9 pounds per hour to use the computer. Plan B costs 25 pounds to join and then 2.25 pounds per hour to use the computer. After how many minutes of use would the cost of plan A be the same as the cost of Plan B?
180
173
169
160
154
