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Megha Prasadan
Subject: Maths
, asked on 16/3/18
Q) Why didn't we change the units or keep it same?
Let y m be the height of the wall at which the ladder touches. Also, let the foot of the ladder be x
m away from the wall.
Then, by Pythagoras theorem, we have:
x
^{2}
+ y
^{2}
= 25 [Length of the ladder = 5 m]
$y=\sqrt{25-{x}^{2}}$
Then, the rate of change of height (y) with respect to time (t) is given by,
$\frac{dy}{dx}=\frac{-x}{\sqrt{25-{x}^{2}}}.\frac{dx}{dt}$
It is given that dx/dt = 2 cm/s
$\frac{dy}{dt}=\frac{-2x}{\sqrt{25-{x}^{2}}}$
Now, when x = 4 m, we have:
$\frac{dy}{dt}=\frac{-2\times 4}{\sqrt{25-16}}=-\frac{8}{3}$
Hence, the height of the ladder on the wall is decreasing at the rate of 8/3 cm/s.
Answer
5
Arnapurna Paikaray
Subject: Maths
, asked on 16/3/18
Please dont provide link.
Answer
3
Arnapurna Paikaray
Subject: Maths
, asked on 16/3/18
Please explain these step by step .
Answer
1
Ranjit Singh
Subject: Maths
, asked on 16/3/18
Q.28. Find the shortest distance between the line x - y + 1 = 0 and the curve
${y}^{2}=x$
.
Answer
1
Vibhav
Subject: Maths
, asked on 16/3/18
In this question, if I have to verify that pi/3 is the point of maxima via first derivative test then why does it give this as the point of minima???
Prove that pi/3 is the point of maxima via first derivative test???
Q.25 If the sum of lengths of the hypotenuse and a side of a right angles triangle is given, then show that the area of triangle is maximum, where the angle between them is
$\frac{\mathrm{\pi}}{3}$
,
Answer
1
Vibhav
Subject: Maths
, asked on 16/3/18
How is the rate at which the tip of shadow moving equal to x+y????
Please explain via figure
Answer
0
Manasi Mujumdar
Subject: Maths
, asked on 16/3/18
what is the difference between strictly increasing and increasing and strictly decreasing and decreasing. pls explain using an example and not statements
Answer
2
Laieeqa
Subject: Maths
, asked on 16/3/18
Solve this:
Q. Find the equation of tangent to the curve
$3{x}^{2}-{y}^{2}=8$
which pass through point
$\left(\frac{4}{3},0\right)$
Answer
1
Kurian J
Subject: Maths
, asked on 15/3/18
$Thefunctionsfandgarerespectivelydecrea\mathrm{sin}gandincrea\mathrm{sin}gin(-\infty ,O]to(-\infty ,0].Leth=g\circ f.Ifh\left(0\right)=0,thenwhatcanbesaidaboutthevalueofh\left(x\right)-h(-1)?\phantom{\rule{0ex}{0ex}}\left(A\right)alwayspositive\phantom{\rule{0ex}{0ex}}\left(B\right)alwaysnegative\phantom{\rule{0ex}{0ex}}\left(C\right)strictlyincrea\mathrm{sin}g\phantom{\rule{0ex}{0ex}}\left(D\right)noneofthese$
Answer
1
Shubhrajyoti Ghosh
Subject: Maths
, asked on 15/3/18
$ThetimeTofacompleteoscillationofasimplependulumoflengthIisgivenbytheequationT=2\pi \sqrt{\frac{l}{g}},wheregiscons\mathrm{tan}t.WhatisthepercentageerrorinTwhen/isincreasdby1\%.$
Answer
1
Devi Das
Subject: Maths
, asked on 14/3/18
Solve this:
$If,x\sqrt{1+y}+y\sqrt{1+x}=0\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}Showthat,\frac{dy}{dx}=-\frac{1}{{\left(1+x\right)}^{2}}$
Answer
1
Sahil Hariani
Subject: Maths
, asked on 28/2/18
Find the approximate volume of hollow spherical shell whose external and inernal radius is 3cm and 3.0005 respectively
Answer
2
Shanaya
Subject: Maths
, asked on 26/2/18
26
Answer
1
Vinuthna Terala
Subject: Maths
, asked on 25/2/18
17q pls solve n send asap
Answer
2
Vinuthna Terala
Subject: Maths
, asked on 25/2/18
16q or one...find point that q,....pls solve n send
Answer
1
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What are you looking for?

Let y m be the height of the wall at which the ladder touches. Also, let the foot of the ladder be x

m away from the wall.

Then, by Pythagoras theorem, we have:

x

^{2}+ y^{2}= 25 [Length of the ladder = 5 m]$y=\sqrt{25-{x}^{2}}$

Then, the rate of change of height (y) with respect to time (t) is given by,

$\frac{dy}{dx}=\frac{-x}{\sqrt{25-{x}^{2}}}.\frac{dx}{dt}$

It is given that dx/dt = 2 cm/s

$\frac{dy}{dt}=\frac{-2x}{\sqrt{25-{x}^{2}}}$

Now, when x = 4 m, we have:

$\frac{dy}{dt}=\frac{-2\times 4}{\sqrt{25-16}}=-\frac{8}{3}$

Hence, the height of the ladder on the wall is decreasing at the rate of 8/3 cm/s.

Prove that pi/3 is the point of maxima via first derivative test???

Q.25 If the sum of lengths of the hypotenuse and a side of a right angles triangle is given, then show that the area of triangle is maximum, where the angle between them is $\frac{\mathrm{\pi}}{3}$,

Please explain via figure

Q. Find the equation of tangent to the curve $3{x}^{2}-{y}^{2}=8$ which pass through point $\left(\frac{4}{3},0\right)$

$If,x\sqrt{1+y}+y\sqrt{1+x}=0\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}Showthat,\frac{dy}{dx}=-\frac{1}{{\left(1+x\right)}^{2}}$