A cow-trough has a triangular cross-section of height 25cm and base 30cm and is 2m long. A cow is drinking steadily, and when the water level is 5cm below the top it is being loward at the rate of 1cm/min. Find the rate if consumption in litres per minute.

The width of the water surface when it has depth y is 6/5 y. So, the cross-sectional area is (1/2)(y)(6/5 y) = 3/5 y^2

Thus, the volume at depth y is 120y^2 cm^3

We have

dv/dt = 240y dy/dt
Now plug in the numbers and we have

dv/dt = 240(20)(-1) = -4800 cm^3/min

Or, 4.8 L/min

Find the area whose vertcises are in polar coordinates (1,30),(2,60)and(3,90)

Suggest the colour emitted for the first line in the balmer series

To find the rate of water consumption in liters per minute, we need to calculate the volume of water being consumed per minute.

First, let's calculate the volume of the trough:
The trough has a triangular cross-section, so its volume can be found using the formula for the volume of a triangular prism: V = (base x height x length) / 2.

Given:
Base of the triangular cross-section = 30 cm
Height of the triangular cross-section = 25 cm
Length of the trough = 2 m = 200 cm

Volume of the trough = (30 cm x 25 cm x 200 cm) / 2
Volume of the trough = 75,000 cm³

Now, let's calculate the rate of consumption in cm³/minute:
The water level is decreasing at a rate of 1 cm/minute when the water level is 5 cm below the top. This means that the volume of water consumed per minute is equal to the area of the triangular cross-section multiplied by the rate of change in height.

The area of the triangular cross-section can be calculated using the formula for the area of a triangle: A = (base x height) / 2.

Given:
Base of the triangular cross-section = 30 cm
Height of the triangular cross-section = 25 cm - 5 cm (since the water level is 5 cm below the top)

Area of the triangular cross-section = (30 cm x 20 cm) / 2
Area of the triangular cross-section = 300 cm²

The volume of water consumed per minute = Area of the cross-section x rate of change in height
Volume of water consumed per minute = 300 cm² x 1 cm/minute
Volume of water consumed per minute = 300 cm³/minute

Now, let's convert the volume from cm³ to liters:
1 liter = 1000 cm³

Volume of water consumed per minute = 300 cm³/minute ÷ 1000 cm³/liter
Volume of water consumed per minute = 0.3 liters/minute

Therefore, the rate of water consumption is 0.3 liters per minute.