Member: Cyphersum

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+22

You have to first find the acceleration from the initial velocity, time and distance and then use the equation for acceleration to find the final velocity. So you just have to remember two things:

A)d=vt+(1/2)at², where d is the total distance traveled, t is the time taken to travel said distance and v is the initial velocity.

B)a=(vf-vi)/t, where again t is total time, a is acceleration and vf and vi are final velocity and initial velocity respectively.

You already have the values of d, t and vi so you all have to do is plug those values into the first formula, solve for a then set the second formula equal to that value of a that you solved for in the first equation. Plug in the values of vi and t that you already have into the formula and then solve for final velocity. If you need help with the calculations let me know and I'll see if I can help.

CyphersumNov 4, 2013

+22

Well the speed of light is roughly 3*10^8 meters per second. Which means that after every second passes light will have traveled about 3*10^8 meters(which is 3 with eight zero's behind it or 300 000 000). Ringing any bells yet? If you still need some help let me know and I will try to explain further. By the way just in case you need the answer real quick it travels 1.05*10^9 meters(or one billion fifity million meters). Now try and find out how I got that number. After all you shouldn't trust strangers on the internet

CyphersumNov 4, 2013

+22

Yes you did do that correctly towards the end, but that first bit had nothing to do with the question. What you did in the beginning is what you would do if you were trying to find the mass of 1.5mol of fluorine, not the number of atoms.

CyphersumNov 3, 2013

+22

Well first you have to simplify each term individually then put them all together. In my explanation I'm going to assume you already have a general idea of how simplifying complex roots works. If that's not the case you might want to look into that first and then come back to this. So right off the bat we know that 2*root2 cannot be simplified since 2 does not have any square factors, 3*root20 on the other hand can be simplified since 20 is 4*5 and 4 is a square number.

3*root20 3*root(4*5) 3(2*root5) 6*root5

Then we look at the next term root45. This can also be simplified since 45 can also be expressed as 9*5 and 9 is 3². So,

root45 root(9*5) 3*root5

And last but not least we look at root288. Now if your sharp you can just realize that 288 is 144*2 and 144 is 12². Unfortunately I'm not that good so I just did it gradually. You can just start with the smallest square number you know that you think might be a factor, factor it out then square it to bring it out of the root and then just keep simplifying until you can't simplify anymore. Since 288 has 4 as a factor we can start there.

root288 root(4*72) 2*root72 2*root(4*18) 2(2*root18) 4*root18 4*root(9*2) 4(3*root2) 12*root2

Now going back to the original expression we just replace each root with it's simplified form.

2*root2+3*root20-root45-root288 2*root2+6*root5-3*root5-12*root2

Then just combine like terms.

2*root2+6*root5-3*root5-12*root2 2*root2+3*root5-12*root2 3*root5-10*root2

and that would be the simplified form of that expression. Hope that helps and that it wasn't too long

CyphersumOct 31, 2013

+22

Since subtracting a negative is the same as adding a positive 3 minus -1 is the same as 3 + 1, which is of course 4.

CyphersumOct 21, 2013

+22

Well after you subtract A from both sides the equation becomes V-A=Prh+h. So in order to isolate the h you first need to factor it out of the two different h terms that you have and then divide.

V-A=Prh+h V-A=h(Pr+1)

then divide both sides by Pr+1 to find the value of h,

V-A=h(Pr+1) V-A/Pr+1=h.

The problem with what you did was that after subtracting A from both sides you divided by Pr which wouldn't give you the equation 2h=V-A/Pr, instead the equation would become V-A/Pr=h+h/Pr which wouldn't help you at all really. That's why you need to factor first in order to consolidate the h variables and then divide by it's coefficient.

CyphersumSep 25, 2013

+22

This isn't as much a math problem as it is just a problem about basic chemical concepts. In order to solve it all you have to do is recognize that 6.02 x 10^23 is Avogadro's number, in other words the number of atoms or molecules contained in one mole of any substance. So since the amount of copper that you have has 6.02 x 10^23 atoms of copper in it, it must mean that you have a mole of copper. Meaning that 63.5g is the molar mass of copper. Therefore all you have to do is remember what the definition of a mole is or how to find the molar mass of a substance to realize that if the molar mass of copper is 63.5g, the atomic mass of copper must be 63.5 amu. If you really wanted to do this arithmetically you'd have to convert grams into amu by first converting grams to kilograms and then dividing the resulting kilogram value by 1.66 x 10^-27 which will give you the mass in amu, which you will then have to divide by 6.02 x 10^23 to find the mass of each individual atom in amu.

Edit: I believe either you or the person who originally came up with the problem meant to say 63.5 instead 6.5 since 6.02 x 10^23 atoms of copper is a mole which would weigh 63.5g not 6.5g.

CyphersumSep 23, 2013

+22

The link you posted isn't really working so I'm just going to assume that the function you're referring to is the standard formula for compounded interest, that is p(1+r)^x. In this case the principal amount is $1000 and x is 3. So it would look something like 1000(1+r)^3. Well in order to find the rate of annual interest if the balance after three years is B you simply have to set the formula equal to B and then isolate r.

1000(1+r)^3=B

First divide both sides by a 1000,

1000(1+r)^3=B (1+r)^3=B/1000

then cube root both sides,

(1+r)^3=B/1000 1+r=cuberoot(B)/cuberoot(1000) 1+r=cuberoot(B)/10

and then simply subtract 1 from both sides getting the final equation r=(cuberoot(B)/10) -1, which is the formula for finding the value of r given the value of B

CyphersumSep 17, 2013

+22

Well f(-1) is just the value of f(x) when x=-1, or the value of 4x²+5x+7 when x=-1 since f(x)=4x²+5x+7. So just substitute -1 for x in the quadratic and do the arithmetic.

4x²+5x+7 4(-1)²+5(-1)+7 4+-5+7=6

Therefore f(-1)=6. Hope that helps.

CyphersumSep 17, 2013

+22

37.5% can also be written as 375/1000. If we write it that way the equation becomes,

x/(10000+x)=375/1000

Then we cross multiply,

x/(10000+x)=375/1000 (1000)(x)=(375)(10000+x) 1000x=3750000+375x

Subtract 375x from both sides,

1000x=3750000+375x 625x=3750000

Then divide both sides by 625 to solve for x getting x=6000. Hope that helped.

CyphersumSep 14, 2013

+22

Since the roots of the polynomial are 1,2, and k, and the lead coefficient is -1 the factors of the polynomial are going to be (-x+1),(x-2), and (x-k).

Therefore f(x)=(-x+1)(x-2)(x-k)

(-x+1)(x-2)(x-k)=-x^3 + (-k+3)x^2 + (3k-2)x + 2k

Dividing this polynomial by (x-3) using synthetic division we get a remainder of 2k-6.

We know that f(x) divided by (x-3) has a remainder of 8. So, 2k-6=8 k=7

If k=7 then f(x)=-x^3+10x^2-23x+14. You can check by dividing this polynomial by (x-3) and seeing if you get a remainder of 8.

Hope that helps.

CyphersumSep 13, 2013

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