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Featured 1 month ago

Option (C)

Given family of lines

Rearranging we get

Obviously the all lines of the family mus pass through the point of intersection of two lines represented by the following two equations

and

#3x-y-1=0........[2]

Subtracting [2] from [1] we get

Inserting

So the coordinates of common point of intersection of all lines of the family will be

Any line passing through this common point

Now rearranging [3] in intercept form we get

So area of the triangle made by this line with the positive semi axes will be given by

Differentiating w r, to m we get

Imposing the condition of minimization of

Hence minimum area of the the triangle should be for m=-2##

[It matches with Option (C)]

Featured 1 month ago

# "Arc Length" = (10pi)/3 ~~ 10.47 \ m #

If the circle has radius

# P_"Total" = 2 pi r #

# \ \ \ \ \ \ \ \ \ = 2 xx pi xx 5 #

# \ \ \ \ \ \ \ \ \ = 10 pi #

We require the length of the arc of a sector of

# P_"Sector" = 120^0/360^0 xx P_"Total" #

# \ \ \ \ \ \ \ \ \ \ = 1/3 xx P_"Total" #

# \ \ \ \ \ \ \ \ \ \ = 1/3 xx 10 pi #

# \ \ \ \ \ \ \ \ \ \ = (10pi)/3 #

# \ \ \ \ \ \ \ \ \ \ ~~ 10.47 \ m #

Featured 1 month ago

Let

Let the coordinates of the third point of the triangle be

As

Again

So coordinates of

Now height of the isosceles triangle

And the base of the isosceles triangle

So by the problem its area

By [2] and [1] we get

So

when

when

So the coordinates of third point will be

OR

Featured 4 weeks ago

Well now I have to look up what the double quote means. Probably minutes or seconds.

OK, Wikipedia says **For example, 40.1875Â° = 40Â° 11' 15"** .

That's 40 degrees, 11 minutes, 15 seconds, a minute being 1/60th of a degree and a second being 1/60th of a minute. (Thank you Babylonians.)

So we're to understand 1920" as

So we're looking at a diameter

Check: Google

Featured 4 days ago

option (1)

**Q92**

Given that G is the centroid of

AP median is produced such that

As

Again

So

Now

and

So

So

So

Area of

Featured 2 days ago

See below.

This question is a little ambiguous. I'm guessing you mean a volume of revolution. If this is the case then a rectangle rotated about a line could be a solid cylinder or a hollow cylinder ( Tube) if the line of rotation is parallel or perpendicular to the sides of the rectangle. If the line of rotation is neither parallel nor perpendicular then a vast number of different solids could result. A big problem here is on the definition. Strictly a prism has a base that is a polygon and faces that are flat, but you could say a cylinder has a polygonal base with an in finite number of sides and an infinite number of faces.

Here are two rotations of a rectangle around different lines.

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