Math Is Fun Forum

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

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 mathxyz (2024-03-04 22:27:28)

KerimF

Member

From: Aleppo-Syria

Registered: 2018-08-10

Posts: 256

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.

---

Every living thing has no choice but to execute its pre-programmed instructions embedded in it (known as instincts).
But only a human may have the freedom and ability to oppose his natural robotic nature.
But, by opposing it, such a human becomes no more of this world.

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

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 mathxyz (2024-03-04 22:28:53)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

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

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

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: 256

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

---

Every living thing has no choice but to execute its pre-programmed instructions embedded in it (known as instincts).
But only a human may have the freedom and ability to oppose his natural robotic nature.
But, by opposing it, such a human becomes no more of this world.

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

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.