Math Is Fun Forum

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: 10 second questions

Hi ganesh;

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,395

Re: 10 second questions

Hi bobbym,

The reply to the problem #2349 is perfect. Well done!

#2350. Two persons X and Y appeared in an interview for two vacancies in an office. The chance for X's selection is 1/5 and the chance for Y's selection is 1/7. Find the chance that
(i) both of them are selected
(ii) only one of them is selected
(iii) none of them is selected.

#2351. Two dice are thrown. What is the probability of getting the same number on both dice or the total of the numbers on the faces as 6?

---

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: 10 second questions

Hi ganesh;

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,395

Re: 10 second questions

Hi bobbym,

Regarding

The solution to 2350 is perfect. Congratulations!

#2352. Prove that the points (4,2), (3,8), and (5,-4) are collinear.

---

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: 10 second questions

Hi ganesh;

Sorry about 2351, I misread the question.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,395

Re: 10 second questions

Hi bobbym,

That is understandable.

Regarding the three points, it can also be shown by finding the area of the triangle being nil.

#2353. If the lines 3x+y+2=0, 2x-y+3=0, and x+my-3=0 are concurrent,  find the value of m.

#2354. If the distance s described by the particle in time t is given by s=t[sup]3[/sup]-3t[sup]2[/sup]+4, then find the velocity at time t.

#2355. If s=5t[sup]2[/sup]+4t-8, then what are the initial velocity and acceleration.

#2356. If s=5+2t-t[sup]2[/sup], then the particle comes to rest when time t is __________________.

---

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: 10 second questions

Hi;

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,395

Re: 10 second questions

Hi bobbym,

The solutions 2353, 2354, 2355, and 2356 are perfect. Well done!

#2357. Fatorize: x[sup]3[/sup]-3x[sup]2[/sup]-10x+24.

#2358. The side of a square is increasing at a constant rate of 2 cm per second. When each side is 8 cm long, what is the rate of increase in its area?

#2359. The radius of a sphere is r cm at time t seconds. If the rates of surface area and the radius are numerically equal, find the radius.

#2360. The side of an equilateral triangle is 10 cm and is increasing at the rate of

cm per second. Find the rate of increase of the area.

---

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: 10 second questions

Hi;

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,395

Re: 10 second questions

Hi bobbym,

The solutions to 2357 2358, and 2360 are perfect. Brilliant!

Regarding 2359, the solution is

as radius.

#2361. A particle is moving in a straight line. Its distance at time t is given by

. Find

(i) the initial velocity
(ii) when the velocity is zero
(iii) when the acceleration is zero

#2362. A stone thrown upwards has its equation of motion s=490t-4.9t[sup]2[/sup] in meters and seconds. What is the maximum height reached by it?

#2363. The age of the father is square of the age of his daughter Veronica. Five years hence, the father would be three times as old as Veronica. Find their present ages.

---

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: 10 second questions

Hi ganesh;

Thanks for providing #2359.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,395

Re: 10 second questions

Hi bobbym,

The solutions 2361, 2362, and 2363 are perfectly okay.

#2364. The area of a circular plate metal is expanded by heat. When the radius passes through the value 2 cubic cm., it is increasing at the rate of 0.01 cm/sec. How fast is the area increasing?

#2365. The volume of a sphere is increasing at the rate of 2 cubic cm. per second. Find the rate at which its surface is increasing when the radius is 3 cm.

---

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: 10 second questions

Hi ganesh;

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,395

Re: 10 second questions

Hi bobbym,

The solution I get for
#2364. 

#2365.

---

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: 10 second questions

Hi ganesh;

Muffed these pretty good. Seems like I have totally forgotten how to do a relative rate problem and get the right answer. Do you have the method on how you got your answers?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,395

Re: 10 second questions

Hi bobbym,

I am sorry I had given the wrong solutions to 2364 and 2365. The solutions you had given is perfectly in order. I apologize again. I continue.

#2366.Find the equations of the tangent and notmal to the curve y=x[sup]3[/sup] at the point (1,1).

#2367. Find the equations of the tangent and normal to the curve y=x[sup]2[/sup]-x-2 at the point (1,-2).

---

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: 10 second questions

Hi ganesh;

No problem, no apologies are necessary.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,395

Re: 10 second questions

Hi bobbym,

The answers to 2366 and 2367 are perfect. Kudos!

#2368. Find the equation of the tangent at the point (a,b) to the curve xy = c[sup]2[/sup].

#2369. Find the equation of the tangent to the parabola y[sup]2[/sup] = 20x which forms an angle 45 degrees with the x-axis.

---

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: 10 second questions

Hi ganesh;

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,395

Re: 10 second questions

Hi bobbym,

The solution to 2369 is perfect. Well done!

Regarding #2368, I get

---

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: 10 second questions

Hi ganesh;

How did you eliminate the c^2 ? In mine I first manipulated it to explicit form:

So the c^2 remained in all the later work. Your answer is working as well as mine but is shorter. So it is a better answer.
I think you implicitly differentiated and that is what eliminated the c^2. Amazing that the c^2 is not necessary in the final answer.
Bravo, good answer!

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,395

Re: 10 second questions

Hi bobbym,

The elimination of c^2 is exactly as you thought I did.

#2370. Solve : x[sup]2[/sup] + 6x - 7 = 0.

#2371. The sum of a number and its square is 90. Find the number.

---

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: 10 second questions

Hi ganesh;

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,395

Re: 10 second questions

Hi bobbym,

The solutions 2370 and 2371 are correct. Very well done!

#2372. Solve :

.

#2373. Solve 2(x + 1)[sup]2[/sup] - 5(x + 1) = 12.

---

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: 10 second questions

Hi gaesh;

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.