CPhill

There are infinite possibilities here...but....since these are roots of a quadratic, we have

y = a(x - 2) (x + 4)

Where a is some real number

y = 3x + 1    line      

y = x^2 + 1   parabola   

x^2 + y^2 = 1    circle   

y = x^2 - 1  parabola

P.S.  - you need to be able to recognize these by sight.....

My grandson is about as many days as my son in weeks, and my grandson is as many months as I am in years. My grandson, my son and I together are 120 years. Can you tell me my age in years ? 

I'm assuming a 30 day month and a 360 day year in this problem...other assumptions may produce "round numbers" at the end..(I don't know, and don't really care)..but...we'll get close enough...besides...it's the idea of the thing that counts......

Let the son's age in years be x

Then, the son's age in weeks= 52 weeks per year times the number of years he has lived = 52x = the grandson's age in days

The grandson's age in months is (assuming a 30 day month) = the number of days he has lived/30 days in a month =  (52x)/30.  So the grandson's age in years  = (52x)/(12months*30 days in a month)  = (52x)/360

Let the grandfather's age in years = y  And this = the grandson's age in months

So  y = (52x)/30 ....and we have

The son's age in years + the grandson's age in years + the grandfather's age in years = 120   ...or....

x + (52x)360 + (52x)/30 = 120            

[360x + 52x + 624x]  = 43200

[1036]x = 43200

x =  41.7 years =    and this is the son's age...we'll call it 42

And the grandson's age iin years  = (52*41.7)/ 360  = about 6 years old

And the grandfather's age is   (52*41.7)/ 30 = about 72.28 years....and we'll call this 72

So

42 + 6 + 72  = 

48 + 72 =

120

Close enough!!!

2.) Find the value of the constant A so that y = Asin3t satisfies the equation d^2y/dt^2 + 2y = 4sin3t 

I assume this is

d²y/dt² + 2y= 4sin3t

If y= Asin3t

dy/dt = 3Acos3t

And  

d²y/dt²  = -9Asin3t

So

d²y/dt² + 2y= 4sin3t

-9Asin3t + 2(Asin3t) = 4sin3t

-7Asin3t = 4sin3t

A = -4/7

I'm going to amend Melody's answer a bit

cos x  = ±1/√2    at   pi/4 ± n (pi/2)

Using the Pythagorean Theorem, we have

AB² + BC² = AC²

5² + 8² = AC²

25 + 64  = AC²

89 = AC²

√89  = AC

C(15,3)  = 455 different committees

So...I assume we have   

780x = y   and

.08(y + x ) = 3,000,000     ????

Divide the second equation on both sides by .08

y + x =  37,500,000     (2)  

And since 780x = y, let's substitute this  into (2)  for y

780x + x = 37,500, 000

781x  = 37,500,000     divide both sides by 781

x = about 48015.3649167733674776

And using (2) to find y, we have

y + 48015.3649167733674776  = 37,500,000

y = about 37,451,984.6350832266325224