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2 years ago

obtain the equation of two points passing of lines 4x-3y-1=0 and 2x-3y+3=0 and equally inclined to the axes

Mathematics

1 answer:

klasskru [66]2 years ago

8 0

Answer:By 8(4)P.5, the slope of the line equally inclined to axes is tan(±45

)=±1. Hence by P+λQ=0,

5λ+3

2λ+4

=±1

⇒λ=

,−1. Putting for λ, the two lines are

x−y=0,x+y−2=0.

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The carnival tent can be filled to 85% of its volume and not exceed the weight limit

<h3>The volume of the hopper bin</h3>

The given parameters are:

Height of cylinder, H = 20 ft
Diameter of cylinder, D = 36 feet
Angle, θ = 52°

Start by calculating the radius (r) of the cones.

r = D/2 -------- because the cones and the cylinder have equal diameters.

So, we have:

r = 36/2 = 18

The height (h) of the cones is:

tan(θ) = h/r

This gives

tan(52) = h/18

Make h the subject

h = 18 * tan(52)

Evaluate

h = 23.04

The volume is then calculated as:

Volume = Volume of cylinder + 2 * Volume of cone

This gives

Volume = πr^2H + 2 * 1/3πr^2h

Volume = πr^2H + 2/3πr^2h

Factor out πr^2

Volume = πr^2(H + 2/3h)

Substitute known values

Volume = 3.14 * 18^2 * (20 + 2/3 * 23.04)

Evaluate

Volume = 35973.85 cubic feet

Hence, the volume of the hopper bin is 35974 cubic feet

<h3>The weight limit of the hopper bin</h3>

The given parameters are:

Maximum weight = 500000 pounds
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For a feed that weighs 22 pounds per cubic feet, the weight of the hopper bin would be:

Weight = 22 * 35974 pounds

Weight = 791428 pounds

At 85% full, the weight wuld be:

Weight = 85% * 791428 pounds

Weight = 672713.8 pounds

672713.8 pounds is greater than the weight limit of 500000 pounds.

Hence, the carnival tent can be filled to 85% of its volume and not exceed the weight limit

obtain the equation of two points passing of lines 4x-3y-1=0 and 2x-3y+3=0 and equally inclined to the axes​

obtain the equation of two points passing of lines 4x-3y-1=0 and 2x-3y+3=0 and equally inclined to the axes