# hard

1. ### hard integral

compute \int_0^{ + \infty } {e^{ - x^2 } \ln xdx}

I have no idea. Can you show me the answer step by step, please. The Arrhenius equation is given by k = A exp (-E/RT), where k is the rate constant, A is called the pre-exponential factor, E is called the activation energy, R is the ideal gas constant and T is the...
3. ### Two variables calculus-not too hard

1. Given the function: f(x,y) = \frac{xy^{2}}{x^{4}+y^{2}} Does the limit \lim_{(x,y)\to(0,0)} f(x) exist? 2. For positive \alpha , \beta , show that: \lim_{(x,y)\to(0,0)} x^{\alpha}y^{\beta}ln(x^{4}+y^{2}) =0 I'll be delighted to get some guidance in these two... In the first...
4. ### hard optimisation problem cylinder.

A cylindrical can open at one end is to have a fixed outside surface area of S -) show that the can has a height of H and a radius R then h = (S - pi r^2 )/ 2 pi r Find an expression for the volume of the cylinder in terms of R and hence show that the maximum possible volume is...
5. ### Hard question involving trig and circles

A radius of a circle divides a chord in the ratio 2:1 and is bisected by the chord. Show that the cosine of the angle between the radius and the chord is \frac{\sqrt{6}}{4}
6. ### Hard multivariable calculus problem..

Hi. :) I have this one in my textbook. It is really hard!!! I can't do anything. Problem: For what values of the number r is the function f(x,y,z)=\frac{(x+y+z)^r}{x^2+y^2+z^2} \, if \, (x,y,z) \neq 0 f(x,y,z) = 0 \, if \, (x,y,z)=0 continuous on R ? the problem here is that the...
7. ### [SOLVED] Hard difference quotient problem for me *pic*

http://i46.tinypic.com/28i7wuh.jpg So with the typical: F(a+h) - F(a) ____________ (h) I did two trials of: F(1993 + 33) - F(1993) / 33 and F(2026 + 6) - F(2026) / 6 Is that the right method? Please help, thank you.
8. ### Very Hard Bonus Question

A boy and a ball are at rest at the top of an incline. The ball rolls down the incline with an acceleration of 0.2m/s^2. Twelve seconds later the boy chases after the ball with an acceleration of 9.0m/s^2. The length the incline is 60m. Draw a diagram before solving the problem. Given...
9. ### Very hard inequality

Use the inequalities \sin \theta < \theta < \tan \theta for a suitable value of \theta to show that \pi lies between 3 and 2\sqrt{3}.
10. ### Hard question

A region of the xy plane is defined by the inequalities 0\leq y\leq \sin x, 0\leq x\leq \pi Find: (a) the area of the region (b) The first moment of area about the x-axis, (c) the coordinates of the centroid of this area. Find Also: (d)The volume obtained when this area is rotated completely...
11. ### hard fraction

hi this is my question: what number when multiplyed by 2/5 gives an answer of 1? i have no idea how to work this question out so can anyone help me to work it out please?
12. ### Reading from a table of statistics, hard to find the %

Hi all, The following is a short problem i'm desperately trying to work out. Here is a table of figures: Total Population is 20 million. Now, the first question asks: What percentage of the population live in either Tokyo, Yoko or Hiro? I can choose from four answers: a. 52% b. 11.8% c. 45%...
13. ### Volume of a region problem (hard to decipher)

Let R be the region bounded by the graphs of y= Square rt of x, y=e^-x, and the y- axis. The Region R is the base of a solid. For this solid, each cross section perpendicular to the x-axis is a semicircle whose diameter runs from the graph of y=square rt x to the graph of y=e^-x. Find the Volume...
14. ### [SOLVED] very hard standard form

Hi, i need to find the standard form of this: The largest number of dominoes ever toppled by one person is 281,581 although 30 set up and toppled 1,382,101. can some one help me to work this out please?
15. ### Help with Hard Root Problem

Can anyone help me do number one from the document I uploaded? I am having some real trouble doing it. Thank you. EDIT: Cold you do 2a too? :]
16. ### Kinematics in 1d question- very hard

Here is the question: A cyclist starts from rest and accelerates at 1.6ms^2 for 10 seconds along a straight horizontal road and then continues at a constant speed. A motorist sets off from the same point as the cyclist at the same time and accelerates at a constant rate for 8 seconds, reaching...
17. ### very hard inversely proportional

Hi this is my question: The grant avalible to a section of society was inversely proportional to the number of people needing the grant. When 30 people needed a grant, the received £60 each. i worked out that K=1800 But: a) what would the grant have been if 120 people had needed one? i get...

find :
19. ### Is math hard, or is it just me?

:/ Can someone please help me? I'm not sure if this is the right section, but I am in Pre-Algebra, and this is what our teacher assigned us. This is one of the questions I was stuck on. We have to use a2+b2=c2 formula...basically the pythagorean Theorem. Billy and Sam drew a...
20. ### hard question

Consider non-collinear vectors a and b. Suppose A=(x+4y)a+(2x+y+1)b and B=(y-2x+2)a+(2x-3y-1)b Find x and y such that 3A=2B