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Preeti Dabral 1 year, 8 months ago
Let distance between the two towers = AB = x m
and height of the other tower = PA = h m
Given that, height of the tower = QB = 30 m and {tex}\angle{/tex}QAB = 60°, {tex}\angle{/tex}PBA = 30°.
Now, in {tex}\Delta Q A B, \tan 60^{\circ}=\frac{Q B}{A B}=\frac{30}{x}{/tex}
{tex}\Rightarrow \sqrt{3}=\frac{30}{x}{/tex}
{tex}x=\frac{x^{2}}{3}-\frac{x}{3}-\frac{x-3}{3}-x+0.5 \pi{/tex}
and in {tex}\Delta P B A{/tex}
{tex}\tan 30^{\circ}=\frac{P A}{A B}=\frac{h}{x}{/tex}
{tex}\Rightarrow \frac{1}{\sqrt{3}}=\frac{h}{10 \sqrt{3}}{/tex} {tex}[\because x=10 \sqrt{3} \mathrm{m}]{/tex}
{tex}\Rightarrow h = 10 m{/tex}
Hence, the requied distance and height are {tex}10\sqrt3{/tex} and 10m, respectively.
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Posted by Vinayak Guleria. 1 year, 8 months ago
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Preeti Dabral 1 year, 8 months ago
h = 20t - 16t²
= (20 x 3/2) - 16 x (3/2)²
= 30 - ( 16 x 9/4)
= 30 - 36 = -6
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Few rules to keep homework help section safe, clean and informative.
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Posted by Parth Patel 1 year, 8 months ago
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Preeti Dabral 1 year, 8 months ago
Let’s consider the number of 20 rupee notes to be x
And the number of 5 rupee notes be y
Then, according to the given conditions, we have
20x+5y=380 … (i) and
5x+20y=380−60
⇒5x+20y=320 … (ii)
Now, multiplying eq(i) by 4 and subtracting with eq(ii), we get
(80x+20y)−(5x+20y)=1520−320
⇒75x=1200
{tex}\begin{aligned} & \Rightarrow \mathrm{x}=\frac{1200}{75} \\ & \Rightarrow \mathrm{x}=16 \end{aligned}{/tex}
On substituting the value of x in eq(i), we get
20(16)+5y=380
⇒320+5y=380
⇒5y=380−320=60
{tex}\begin{aligned} & \Rightarrow y=\frac{60}{5} \\ & \Rightarrow y=12 \end{aligned}{/tex}
Therefore,
The number of 20 rupee notes =16 and
The number of 5 rupee notes =12
Posted by Manisha Choudhary 1 year, 8 months ago
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Preeti Dabral 1 year, 8 months ago
Given A circle with centre O and an external point T and two tangents TP and TQ to the circle, where P, Q are the points of contact.
To Prove: {tex}\angle{/tex}PTQ = 2{tex}\angle{/tex}OPQ
Proof: Let {tex}\angle{/tex}PTQ = {tex}\theta{/tex}
Since TP, TQ are tangents drawn from point T to the circle.
TP = TQ
{tex}\therefore{/tex} TPQ is an isoscles triangle
{tex}\therefore{/tex} {tex}\angle{/tex}TPQ = {tex}\angle{/tex}TQP = {tex}\frac12{/tex} (180o - {tex}\theta{/tex}) = 90o - {tex}\fracθ2{/tex}
Since, TP is a tangent to the circle at point of contact P
{tex}\therefore{/tex} {tex}\angle{/tex}OPT = 90o
{tex}\therefore{/tex} {tex}\angle{/tex}OPQ = {tex}\angle{/tex}OPT - {tex}\angle{/tex}TPQ = 90o - (90o - {tex}\frac12{/tex} {tex}\theta{/tex}) = {tex}\fracθ2{/tex}= {tex}\frac12{/tex}{tex}\angle{/tex}PTQ
Thus, {tex}\angle{/tex}PTQ = 2{tex}\angle{/tex}OPQ
Posted by Vikash Yadav 1 year, 8 months ago
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