Math Is Fun Forum

nycguitarguy

Member

Registered: 2024-02-24

Posts: 542

General Formula For Variation...2

Write a general formula to describe each Variation.

1.  y varies inversely with sqrt{x}; y = 4 when x = 9

y = k/sqrt{x}

4 = k/sqrt{9}

4 = k/3

4•3 = (k/3)(3)

12 = k

y = 12/sqrt{x}

YOU SAY?

2. T varies jointly with the cube root of x and the square of d;
T = 18 when x = 8 and d = 3

Let cr = cube root

T = cr{x}•(d^2)k

18 = cr{8}•(3)^2k

18 = 2(9)k

18 = 18k

18/18 = k

1 = k

T = cr{x}(d)^2(1)

T = cr{x}(d)^2

You say?

Last edited by nycguitarguy (2024-03-04 22:27:28)

KerimF

Member

From: Aleppo-Syria

Registered: 2018-08-10

Posts: 165

Re: General Formula For Variation...2

y varies inversely with sqrt{x}.
But y = k/x means: y varies inversely with x, not sqrt(x), got it?

T varies jointly with the cube root of x and the square of d.
But T = cr{x}•sqrt{d}•k means: T varies jointly with the cube root of x and the square root of d, not square of d, got it?

Your time is short so you can't avoid misreading sometimes.

nycguitarguy

Member

Registered: 2024-02-24

Posts: 542

Re: General Formula For Variation...2

y varies inversely with sqrt{x}.
But y = k/x means: y varies inversely with x, not sqrt(x), got it?

T varies jointly with the cube root of x and the square of d.
But T = cr{x}•sqrt{d}•k means: T varies jointly with the cube root of x and the square root of d, not square of d, got it?

Your time is short so you can't avoid misreading sometimes.

Write a general formula to describe each Variation.

1.  y varies inversely with sqrt{x}; y = 4 when x = 9

y = k/sqrt{x}

4 = k/sqrt{9}

4 = k/3

4•3 = (k/3)(3)

12 = k

y = 12/sqrt{x}

YOU SAY?

2. T varies jointly with the cube root of x and the square of d;
T = 18 when x = 8 and d = 3

Let cr = cube root

T = cr{x}•(d^2)k

18 = cr{8}•(3)^2k

18 = 2(9)k

18 = 18k

18/18 = k

1 = k

T = cr{x}(d)^2(1)

T = cr{x}(d)^2

You say?

Last edited by nycguitarguy (2024-03-04 22:28:53)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,196

Re: General Formula For Variation...2

Yes, those look good to me,

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

nycguitarguy

Member

Registered: 2024-02-24

Posts: 542

Re: General Formula For Variation...2

Yes, those look good to me,

Bob

Bob,

Solving math problems at 58 years old keep my aging mind alive and well.

KerimF

Member

From: Aleppo-Syria

Registered: 2018-08-10

Posts: 165

Re: General Formula For Variation...2

Being 75 now, I try my best to let my brain's cells be active by keeping them busy, as long as possible, in solving new things.
So, when I don't have a new design to think of (for the local market), I simply work on a new product which could be useful to me.
After all, my brain is the remaining organ in my living body that didn't reach its end of service

nycguitarguy

Member

Registered: 2024-02-24

Posts: 542

Re: General Formula For Variation...2

Being 75 now, I try my best to let my brain's cells be active by keeping them busy, as long as possible, in solving new things.
So, when I don't have a new design to think of (for the local market), I simply work on a new product which could be useful to me.
After all, my brain is the remaining organ in my living body that didn't reach its end of service

If you at 75 answer math problems, then it is ok for me to do likewise at 58.