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Solve the following system of equations by the method of cross-multiplication:
$\text{bx}+\text{cy}=\text{a}+\text{b}$
$\text{ax}\Big(\frac{1}{\text{a}-\text{b}}-\frac{1}{\text{a}+\text{b}}\Big)+\text{cy}\Big(\frac{1}{\text{b}-\text{a}}-\frac{1}{\text{b}+\text{a}}\Big)=\frac{2\text{a}}{{\text{a}+\text{b}}}$
→$\text{bx}+\text{cy}=\text{a}+\text{b}$
$\text{ax}\Big(\frac{1}{\text{a}-\text{b}}-\frac{1}{\text{a}+\text{b}}\Big)+\text{cy}\Big(\frac{1}{\text{b}-\text{a}}-\frac{1}{\text{b}+\text{a}}\Big)=\frac{2\text{a}}{{\text{a}+\text{b}}}$
Two vertical poles of height 9m and 14m stand on a plane ground. If the distance between their feet is 12m, find the distance between their tops.
The $6^{th}$ and $17^{th}$ terms of an A.P. are $19$ and $41$ respectively, find the $40^{th}$ term?
→A rocket is in the form of a circular cylinder closed at the lower end and a cone of the same radius is attached to the top. The radius fo the cylinder is 2.5m, its height is 21m and the slant height of the cone is 8m. Calculate the total surface area of rocket.
Prove the following identities:
$\frac{\tan\theta}{\big(1+\tan^2\theta\big)}+\frac{\cot\theta}{\big(1+\cot^2\theta\big)}=\sin\theta\cos\theta$
→$\frac{\tan\theta}{\big(1+\tan^2\theta\big)}+\frac{\cot\theta}{\big(1+\cot^2\theta\big)}=\sin\theta\cos\theta$
If the volumes of two bones are in the ratio of 1 : 4 and their iameters are in the ratio of 4 : 5, find the ratio of their heights.
Side of a triangular field are 15m, 16m and 17m. With the three corners of the field a cow, a buffalo and tied separately with ropes of length 7m each to graze in field. Find the area of the field which cannot be grazed by three animals.
Graphically, solve the following pair of equations:
→$2x + y = 6$
$2x - y + 2 = 0$
Find the ratio of the areas of the two triangles formed by the lines representing these equations with the x axis and the lines with the y-axis.In an A.P. the first term is – 5 and last term is 45. If sum of all numbers in the A.P. is 120, then how many terms are there? What is the common difference?
Solve the following quadratic equations by factorization:
$4\sqrt{3}\text{x}^2+5\text{x}-2\sqrt{3}=0$
→$4\sqrt{3}\text{x}^2+5\text{x}-2\sqrt{3}=0$