Let `x` be the length of one of the equal sides of an isosceles triangle, and let `theta` be the angle between them. If `x` is increasing at the rate (1/12) m/h, and `theta` is increasing at the rate of `pi/(180)` radius/h, then find the rate in `m^3` / `h` at which the area of the triangle is increasing when `x=12ma n dtheta=pi//4.`

Let x be the length of one of the equal sides of an isosceles triangle, and let theta be the angle between them. If x is increasing at the rate (1/12) m/h, and theta is increasing at the rate of pi/(180) radius/h, then find the rate in m^3 / h at which the area of the triangle is increasing when x=12m and theta=pi//4.

The length x of a rectangle is decreasing at the rate of 5 cm/minute and the width y is increasing at the rate of 4 cm/minute. When x = 8cm and y = 6cm, find the rates of change of (a) the perimeter, and (b) the area of the rectangle.

The length x of a rectangle is decreasing at the rate of 3 cm/minute and the width y is increasing at the rate of 2cm/minute. When x =10cm and y = 6cm, find the rates of change of (a) the perimeter and (b) the area of the rectangle.

The base of an isosceles triangle measures 4 units base angle is equal to 45^(@) . A straight line cuts the extension of the base at a point M at the angle theta and bisects the lateral side of the triangle which is nearest to M. The length of portion of straight line inside the triangle may lie in the range

The base of an isosceles triangle measures 4 units base angle is equal to 45^(@) . A straight line cuts the extension of the base at a point M at the angle theta and bisects the lateral side of the triangle which is nearest to M. The length of portion of straight line inside the triangle may lie in the range

The base of an isosceles triangle measures 4 units base angle is equal to 45^(@) . A straight line cuts the extension of the base at a point M at the angle theta and bisects the lateral side of the triangle which is nearest to M. The area of quadrilateral which the straight line cuts off from the given triangle is

For the straight lines 4x+3y-6=0 and 5x+12 y+9=0, find the equation of the bisector of the obtuse angle between them, bisector of the acute angle between them, and bisector of the angle which contains (1, 2)

Column I, Column II a)A circular plate is expanded by heat from radius 6 cm to 6.06 cm. Approximate increase in the area is, b)If an edge of a cube increases by 2%, then the percentage increase in the volume is, c)If the rate of decrease of (x^2)/2-2x+5 is thrice the rate of decrease of x , then x is equal to (rate of decrease in nonzero)., d)The rate of increase in the area of an equailateral triangle of side 30c m , when each side increases at the rate of 0. 1c m//s , is, p. 5 q. 0.72 pi r. 6 s. (3sqrt(3))/2

Sand is pouring from a pipe at the rate of 12 cm^(3) /s. The falling sand forms a cone on the ground in such a way that the height of the cone is always one-sixth of the radius of the base. How fast is the height of the sand cone increasing when the height is 4 cm?

One angle of an isosceles triangle is 120^0 and the radius of its incircle is sqrt(3)dot Then the area of the triangle in sq. units is (a) 7+12sqrt(3) (b) 12-7sqrt(3) (c) 12+7sqrt(3) (d) 4pi