Search results

Then I stongly recommend you hire a bookkeeper to do the arithmetic for you!

Samojit, this is what they mean: Let "w" be the amount of work does in one day and let "m" be the amount of work a man does in one day. "It takes 6 days for 3 women and 2 men working together to complete a work." 3(6)w+ 2(6)m= 18w+ 12m= 1 work. "3 men would do the same work 5 days sooner than...

Really doesn't matter what you think- there's reality! (It occurs to me that your post might be interpreted "I never thought I was a prodigy and then found out I was"!)

That makes no sense. Numbers have averages, not points! Of course, it is true that there exist a unique line through two given points. Is that what you mean? That is a basic property, in fact, a postulate, of Euclidean Geometry.

Do you understand what these questions mean? The first asks you to use the "bisection method" to numerically solve the equation x^3- 3= 0. Do you understand what the "bisection method" is? I notice that if x= 0, x^3- 3= 0- 3= -3 which is less than 0 and that if x= 2, x^3- 3= 8- 3= 5 which is...

The "characteristic equation" for this differential equation is r^2- 5r+ 6= (r 3)(r- 2)= 0 so the "characteristic numbers" are 2 and 3. That means that the general solution to the "associated homogeneous equation, y''- 5y'+ 6y= 0, is Ae^{2x}+ Be^{3x}. Normally, with the "non-homogeneous" part...

First, you can't "convert a non-linear differential equations into vector form" because vector spaces are necessarily linear. The best you can do is approximate the non-linear differential equations by linear equations then convert them to vector form. For these equations the best...

I don't see anywhere in what you have posted that gives the actual original cone!

For x< 5, \frac{x^2- 25}{x- 5}= \frac{(x- 5)(x+ 5)}{x- 5}= x+ 5 so the limit, as x goes to 5 from below is 5+ 5= 10. The limit, as x goes to 5 from below, of f is 10d+ c. Cosine is always between -1 and 1 and x- 5 goes to 0 as x goes to 0 so the limit, as x goes to 5 from above, of this function...

I presume you know the basics of integration: \int a dx= ax+ c \int ax dx= \frac{a}{2}x^2+ c \int ax^2 dx= \frac{a}{3}x^3+ c and in general \int ax^n dx= \frac{a}{n+1}x^{n+1}+ c. That is, the integral of a polynomial of degree n is a polynomial of degree n+ 1. (Notice that I am using the word...

Do you understand what a "tangent" is? The tangent to a graph at a point is a straight line that passes through that point and has the same slope (derivative) there. Do you understand what "y= 3" means? Since y is always 3 any (x, y) point is (x, 3). The graph is a horizontal straight line...

First, since dividing P by quadratic polynomials leaves first degree remainders, P itself must be cubic: P(x)= ax^3+ bx^2+ cx+ d \frac{ax^3+ bx^2+ cx+ d}{x^2- 2x- 8}= Q(x)- x+ 5 so [

I once thought I was a prodigy but reality soon slapped me in the face!

If you do not assume that then it is impossible to do this problem.

There were initially 670 grams. Since it decays by 27.3% per minute, there is left (100- 27.3)%= 72.7% per minute. That means that after one minute there is 72.7% of 670= 0.727(670)= 487.09 grams left. And after the second minute there is 72.7% of 487.09= 0.727(487.09)= 354.11443 grams left...

Yes, and subtracting the second equation from the first eliminates a: a- b- (a- 2b)= (a- a)- (b- 2b)= b= 4-(-6)= 4+ 6= 10 and a- b= a- 10= 4 so a= 4+ 10= 14. There are 14 children in bus A and 10 children in bus B. Check: Transfering two children from bus A to bus B leaves 14- 2= 12 children...

While there are 2 values of x such that x^2= a^2, x= a and x= -a, \sqrt{a^2} is specifically defined as the positive root, |a|.

Do you know that the Laplace Transform of f(x) is defined as F(t)= \int_0^\infty f(s)e^{-st}ds? With this f that is \int_0^2 -t e^{-st}dt. To integrate that, use "integration by parts" with u= -t and dv= e^{-st}. du= -dt v= -(1/s)e^{-st} (t/s)e^{-st}|_0^2+ (1/s)\int_0^2 e^{-st}dy...

You have 14(2x+ 4)^6(3x- 2)^5+ 15(2x+ 4)^7(3x- 2)^4. Do you see that there is a "(2x+ 4)" in both terms? One is to the 6th power and the other is to the 7th power. (2x+ 4)^7= (2x+ 4)^6(2x+ 4) so there is (2x+ 4)^6 in both terms and we can factor that out, leaving 2x+ 4 to the first power in...

How about someone who is no prodigy buit knows what "base 12" is? In any case what is this "super cool task"?