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Note : 

Area of triangle  AOB = (1/2)c * r

Area of triangle AOC = (1/2)b * r

Area of triangle BOC  = (1/2)a * r

So....areae of triangle ABC  = " K"   =

(1/2)c*r  + (1/2)b*r  + (1/2)a *r  =

(1/2)r [ a + b + c ]  =

r  [(a + b + c)  / 2 ]  =

r * s

how to factor 14x^2/y*5y^2/xy=70x

Press the 2nd button and you will see it in the top row.

1) Because: Sum of: 1/1 + 1/2 + 1/4 + 1/8 + 1/16..........converges to 2!

2) Because: Sum of: 1/1 + 1/2 + 1/3 + 1/4 + 1/5............diverges to infinity. This is the Harmonic series.

3*10^-3 = 0.003

You move the decimal point 3 places to the left.

THAT IS TRUE!! The series converges to ln(2).

I hope the image makes it. (Look at the bottom ...left and right)    Angle B = 180-90-30 =60 degrees  

Angle D2 = 180-90-30 = 60

Since DC = BC in a right triangle (GIVEN in the problem) then  angles D1 and B1 are EQUAL too  180- 90 -2x  yields the fact that these two angles are 45 degrees

If ANGLE B is 60 degrees and ANGLE B1 is 45 degrees angle DBK = 60 - 45 = 15 degrees.

All this because DC = BC !

2(a-5)(a+5)=21a

solve for a.

just so i won't cunfuse you:

2(a-5)(a+5)=(2a-10)(a-5)

that means:

(2a-10)(a-5)=

2a²-10a-10a-50=

2a²-20a-50=

21a

divide both sides by a:

2a-10-(50/a)=21

add 10:

2a-(50/a)=31

divide by two:

a-(25/a)=15.5

multiply by a:

a²-25=15.5/a

subtract 25 and take the square root:

a=sqrt((15.5/a)-25)

idk how to get the rest, but, at least it might help.

If you want to know if it can EVENLY be divided by 7...you'll just have to divide it by 7 ...either in your head, on paper or with a calculator......if thee is NO REMAINDER , it is EVENLY divisible by 7 ......I do not know of any shortcuts like there is for 3

(If you add all of the numbers up and THEY are divisible by 3 then the number is too

Example: Is 513 divisible by 3?   Add 5 + 1 + 3 = 9     9 is divisible by 3, so 513 is too)

If you want to know if it can EVENLY be divided by 7...you'll just have to divide it by 7 ...either in your head, on paper or with a calculator......if thee is NO REMAINDER , it is EVENLY divisible by 7 ......I do not know of any shortcuts like there is for 3

(If you add all of the numbers up and THEY are divisible by 3 then the number is too

Example: Is 513 divisible by 3?   Add 5 + 1 + 3 = 9     9 is divisible by 3, so 513 is too)

Ahhhhhhh!   I got to that point and it seemed like it was gonna be big a drawn out ordeal squaring both of those factors...THAT is when I 'trial and error'ed'  it !       Thanx again !

any number can!

What do you mean by "i"?

 \(2(a^2-25)=21a\\ a^2-25=10.5a\\ a^2-10.5a-25=0\)

Do the rest by yourself then write the answer

If it isn't in your textbook, then google it.

The sum isn't but the product is.

\(\sqrt{5}+\sqrt{2}\ne \sqrt{10} \\ \sqrt{5}\times \sqrt{2}=\sqrt{10}\)

.

This might help illustrate example a:

.

For example a.

fx = 15*cos(65°) + 37*cos(142°)  so fx =  --22.817

fy = 15*sin(65°) + 37*sin(142°)  so fy = 36.374

f = sqrt((-22.817)^2 + 36.374^2)    so  f = 42.938

Angle theta = tan^-1(fy/fx)   = tan^-1(36.374/-22.817) = -57.9°  However, because fy is positive and fx is negative this is in the second quadrant, so the angle from the positive x-direction going anti-clockwise around to the resulatnt is 180°-57.9° = 122.1°

can you give me some example to solve it Sir? :)

The neutrino is one of the smallest elementary particles.

I just used a piece of software to do it for me!  However, here is the derivation:

.

Yea that is bad luck isn't it.      

You do not have a member name so how could you have a member birthday?    

My appology to all members who do not get their birthdays recognised.  :)

I hope that all members and guest, including you, enjoy 'their day'.    

Though I got the same answer via trial and error, I wanted to do it mathematically like you did...but you lost me between the step 4 lines from the bottom and the step 3 lines form the bottom.....how did you 'simplify' that?

Thanx !

Thanks guest and Alan i guess

1.  3x >= 2    

3x - 2 = 4   

3x = 6

x = 2

2. 3x<2

-(3x-2) = 4

3x-2 = -4

3x = -2

x = -2/3