Find the length of a side of a rhombus whose diagonals are 6cm and 8cm
8cm
5cm
4cm
3cm
Correct answer is B
The diagonal of a rhombus is a line segment that joins any two non-adjacent vertices.
A rhombus has two diagonals that bisect each other at right angles.
i.e this splits 6cm into 3cm each AND 8cm to 4cm
Using Hyp\(^2\) = adj\(^2\) + opp\(^2\)
Hyp\(^2\) = 3\(^2\) + 4\(^2\)
Hyp\(^2\) = 25
Hyp = 5
∴ Length (L) is 5cm because a rhombus is a quadrilateral with 4 equal lengths
The angle of a sector of s circle, radius 10.5cm, is 48°, Calculate the perimeter of the sector
8.8cm
25.4cm
25.6cm
29.8cm
Correct answer is D
Length of Arc AB = \(\frac{\theta}{360}\) 2\(\pi\)r
= \(\frac{48}{360}\) x 2\(\frac{22}{7}\) x \(\frac{21}{2}\)
= \(\frac{4 \times 22 \times \times 3}{30}\) \(\frac{88}{10}\) = 8.8cm
Perimeter = 8.8 + 2r
= 8.8 + 2(10.5)
= 8.8 + 21
= 29.8cm
At what value of x is the function x\(^2\) + x + 1 minimum?
-1
\(-\frac{1}{2}\)
\(\frac{1}{2}\)
1
Correct answer is B
x\(^2\) + x + 1
\(\frac{dy}{dx}\) = 2x + 1
At the turning point, \(\frac{dy}{dx}\) = 0
2x + 1 = 0
x = -\(\frac{1}{2}\)
Find the sum of the first 18 terms of the progression 3, 6, 12......
3(217 - 1)
3(218 - 1)
3(218 + 1)
3(217 - 1)
Correct answer is B
3 + 6 + 12 + .....18thy term
1st term = 3, common ratio \(\frac{6}{3}\) = 2
n = 18, sum of GP is given by Sn = a\(\frac{(r^n - 1)}{r - 1}\)
s18 = 3\(\frac{(2^{18} - 1)}{2 - 1}\)
= 3(2^18 - 1)
Find the sum of the first twenty terms of the progression log a, log a2, log a3.....
log a20
log a21
log a200
log a210
Correct answer is D
No explanation has been provided for this answer.