The puzzle can be solved by logic, without any guessing.

Row 1 solves logically, as Bob said, and leads to multiple elimination of duplicates in the lower rows.

From there, eliminating the 2 from R3C2 ('R' = row, 'C' = column) leaves {3,4} in both R3C2 and R3C3, which enables us to eliminate the 3 from R3C1 and R3C4 because the 3 must be in either R3C2 or R3C3.

...etc, etc.

]]>knowledge on sines and cosines would help:

https://www.mathsisfun.com/algebra/trigonometry.html

]]>I need to draw a logo representing the earth in the solar system

It looks like this:

1) An perfect circle to represent the earth

2) a 22.5 degree slanted ellipsoid to represent the equater on the earth

3) several longitude lines from north pole to south pole that intersects with equater

Can you model equater and longitude lines by elliptic equations?

Any help is appreciated

]]>EDIT: never mind, this problem is due and I'll just roll with what you've written. I didn't want to waste your time further.

]]>Is, there any problem with MIFF, cuz its not recognizing latex equations?

]]>Bob

]]>(x, y, 1-x-y)'

Thus if you multiply the transformation matrix to this vector

It will be:

x+y-1+x+y

3x+3y-1+x+y

5x+5y-1+x+y

=

2(x+y)-1

4(x+y)-1

6(x+y)-1

=

2p-1

4p-1

6p-1

=

t

2t+1

3t+2

i x i = j x j = k x k = 0

i x j = k j x i = -k and four more like these.

CO = - OC etc.

I've just realised that using k for the multiplier was a poor use of symbol. Sorry if that is confusing. Fortunately I haven't actually used k as a unit vector in my proof, so all the ks are multipliers.

Bob

]]>Carlycan’tdomath03 wrote:

4. Write a counterexample for the converse of "Cats make great pets."

My answer: A tiger is a cat, and it’s not a great pet.

This is not correct. The sentence can be rewritten “All cats are great pets”; the converse is then “All great pets are cats”. Now give an example of an animal that is a great pet but not a cat.

Carlycan’tdomath03 wrote:

6. Write a counterexample for the converse of "Cars have four wheels."

My answer: The aptera is a car, and it has three wheels.

Again, not correct. The converse is “All things with four wheels are cars”. Give an example of something that has four wheels but is not a car.

]]>Please see the link below:

.

Hope it helps.

]]>1) By factorization:

.

.

.

x = -4 or 2.

2) By quadratic equation formula,

Here,

a = 1, b = 2, and c = -8.

]]>

Let's say you have a regular polygon with n sides. Centre point A.

Draw lines out from A to each of the vertices of the polygon. This makes n identical isosceles triangles. Label one with points B and C. Mark the midpoint of BC as point D.

Angle BAC = 360/n, and angle BAD = (360/n)/2 = 180/n

Angle ADB = 90 so we can use trig. on the triangle ADB. AD = height of a triangle.

BD/AD = tan(BAD) , so AD = BD / tan (BAD) (note BD = half a side = s/2)

area of one triangle = 1/2 side x height = 1/2 . s . s/2 .1/tan(BAD)

area of polygon = n . 1/2 . s . s/2 / tan(180/n)

Hope that helps,

Bob

]]>