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To warn ships for underwater rocks, a lighthouse spreads a red coloured light over a sector of angle `80o`to a distance of 16.5 km. Find the area of the sea over which the ships are warned.

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To find the area of the sea over which ships are warned by the lighthouse, we can use the formula for the area of a sector of a circle. The formula is: \[ \text{Area} = \frac{\theta}{360} \times \pi r^2 \] where: - \(\theta\) is the angle of the sector in degrees, ...
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To warn ships for underwater rocks, a lighthouse spreads a red coloured light over a sector of angle 80^@ to a distance of 16.5 km. Find the area of the sea over which the ships are warned.

To warn ships for underwater rocks, a light house throws a red coloured light over a sector of 80^o angle to a distance of 16.5 km. Find the area of the sea over which the ships are warned.

A driver having a definite reaction time is capable of stopping his car over a distance of 30 m on seeing a red traffic signal, when the speed of the car is 72 km/hr andover a distance of 10 m when the speed is 36 km/hr. Find the distance over which he can stop the car if it were running at a speed of 54 km/hr. Assume that his reaction time and the deceleration of the car remains same in all the three cases.

Two ships are there in the sea on either side of a light house in such a way that the ships and the light house are in the same straight line. The angles of depression of two ships are observed from the top of the light house are 60^@ and 45^@ respectively. If the height of the light house is 200 m, find the distance between the two ships. (U s e\ \ sqrt(3)=1. 73)

A cargo ship is 4.2 miles from a lighthouse, and a fishing boat is 5.0 miles from the lighthouse, as shown below. The angle between the straight lines from the lighthouse to the 3 vessels is 5^(@) . The approximate distance in miles, from the cargo ship to the fishing boat is given by which of the following expressions? (Note: The law of cosines states that for any triangle with vertices A, B and C adn the sides opposite those vertices with length a, b, and c, respectively. c^(2) = a^(2) + b^(2) - 2ab cos C ).

From the top of a 75m high lighthouse from the sea level the angles of depression of two ships are 30^@ and 45^@ . If the two ships are on the opposite sides of the light house then find the distance between the two ships.

As observed from the top of a light house, 100m above sea level, the angle of depression of a ship, sailing directly towards it, changes from 30o to 45o . Determine the distance travelled by the ship during the period of observation.

A ship is moving at a constant speed of 10 km//hr in the direction of the unit vector hat(i) . Initially. Its position vector, relative to a fixed origin is 10(-hat(i)+hat(j)) where hat(i) & hat(j) are perpendicular vectors of length 1 km. Find its position vector relative to the origin at time t hours later. A second ship is moving with constant speed u km//hr parallele to the vector hat(i)+2hat(j) and is initially at the origin (i) If u=10 sqrt(5) km//h . Find the minimum distance between the ships and the corresponding value of t (ii) Find the value of u for which the shipd are on a collision course and determine the value of t at which the collision would occur if no avoiding action were taken.

An agricultural field is in the form of a rectangle of length 20 m and width 14 mdot A pit 6mlong,3mw i d ea n d2. 5 md e e p is dug in a corner of the field and the earth taken out of the pit is spread uniformly over the remaining area of the field. Find the extent to which the level of the field has been raised.

An agricultural field is in the form of a rectangle of length 20 m\ and width 14\ mdot A pit 6m\ long,\ 3m\ w i d e\ a n d\ 2. 5 m\ d e e p is dug in a corner of the field and the earth taken out of the pit is spread uniformly over the remaining area of the field. Find the extent to which the level of the field has been raised.

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