The length of a rectangle is decreasing at a rate of 3 cm/sec and breadth is increasing at a rate of 4 cm/sec. Find the rate of change of its (a) perimeter (b) area, when the length and breadth of rectangle are 7 cm and 8 cm respectively.
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ABCD is a rectangle with `A(-1,2),B(3,7)` and `AB:BC=4:3`. If P is the centre of the rectangle, then the distance of P from each corner is equal to
Correct Answer - D Since ABCD is a rectangle, `(AC)^2=(AB)^2+(BC)^2` `=(AB)^2[1+(9)/(16)]=(25)/(16)(AB)^2` and `PA=(AC)/(2)=(5AB)/(8)` `(5)/(8)sqrt((-1-3)^2+(2-7)^2)=5(sqrt41)/(8)`
2 Answers 6 views
`d/(dx)sqrt((1-sin2x)/(1+sin2x))i se q u a lto,(0<x<pi/2),` `sec^2x` (b) `-sec^2(pi/4-x)` `sec^2(pi/4+x)` (d) `sec^2(pi/4-x)`
`y=sqrt((1-sin 2x)/(1+ sin 2x))=(cos x - sin x)/(cos x + sin x)=(1-tan x)/(1+ tan x)=tan ((pi)/(4)-x)` `therefore (dy)/(dx)=-sec^(2)((pi)/(4)-x)`
2 Answers 1 views
The diagonal of a rectangle is 10 units. The formula to find the diagonal is `d=sqrt(l^(2)+b^(2))`. Where l and b are length and breadth respectively.
Correct Answer - `l^(2)`
2 Answers 1 views
(i) The radius of a circle is increasing at the rate of 5 cm/sec. Find the rate of increasing of its perimeter. (ii) If the area of a circle increases
Correct Answer - `10 pi cm//sec`
2 Answers 2 views
If the perimeter of a rectangle is 10 cm and the difference between its length and breadth is 1 cm, then its length is ______ and its breadth is _____
Correct Answer - 3 cm and 2 cm
2 Answers 1 views
The length of a cuboid is 2 cm more than its height, whereas its breadth is 2 cm less than the height. Its height is equal to the side of a square hav
Correct Answer - 960 `cm^(3)`
2 Answers 3 views
The sides of a rectangle are given by the equations x=-2, x = 4, y=-2 andy=5. Find the equation of the circle drawn on the diagonal of this rectangle
Correct Answer - ` x ^(2) + y ^(2) - 2x - 3y - 18 =0`
2 Answers 1 views
Find the area of rectangle whose length is 5.3cm and breadth is 3 cm.
Correct Answer - `17.1cm^(2)`
2 Answers 1 views
(a) The length of Rameshs notebook is 9 cm 5 mm. What will be its length in cm? (b) The length of a young gram plant is 65 mm. Express its length in c
Correct Answer - (a) 9.5 सेमी: `" "`(b) 6.5 सेमी:
2 Answers 1 views
The perimeter of rectangle is 34cm and length of its diagonal is 13cm. Find the length and breadth of rectangle
let length of the rectangle be L and breadth be B so by the problem perimeter 2(IL+B)=34 => L+B =17 .......(1) => L2+B2+2LB=289 ..........(2) and the square of the diagonal = L2+B2=132 =169 .....(.3) By...
2 Answers 1 views