Need Math Help?

[Death]

Okay, thanks a lot Corpsecreate! Yea the ln 10 is equal to 10^1/e, I just found out today.

 

[Tee ay eye]

I was taking a test today, and a question was

Find the limit as X approaches 4:

√(5+x) - 3
4-x

I put the answer as no limit, but some other kids told me they got 1/6. Maybe there were different test forms....

 

[moogle]

Okay, thanks a lot Corpsecreate! Yea the ln 10 is equal to 10^1/e, I just found out today.

Google says:
ln(10) = 2.30258509
10^(1 / e) = 2.33281039

Alas, they're not equal.

I was taking a test today, and a question was

Find the limit as X approaches 4:

√(5+x) - 3
4-x

I put the answer as no limit, but some other kids told me they got 1/6. Maybe there were different test forms....

L'Hopital's rule... take the derivative of top and bottom!

lim x->4 of (√(5+x) -3)/(4-x)
= lim x->4 of [1/(2√(5+x))] / [-1]
= 1/(2√9) / -1
= -1/6

 

[Tee ay eye]

L'Hopital's rule... take the derivative of top and bottom!

lim x->4 of (√(5+x) -3)/(4-x)
= lim x->4 of [1/(2√(5+x))] / [-1]
= 1/(2√9) / -1
= -1/6

My teacher didn't teach us derivatives yet.

Would there be another way of solving it without a calculator?

 

[Super Touhey]

My teacher didn't teach us derivatives yet.

Would there be another way of solving it without a calculator?

multiply both sides by (√(5+x)+3)

You then get:
____5+x-9____
(4-x)*(√(5+x)+3)
which equals
_____x-4_____
(4-x)*(√(5+x)+3)
cancel out x-4...
___-1___
√(5+x)+3
substitute 4 in for x and you get -1/6

 

[Tee ay eye]

omfg, i feel so stupid

i thought of multiplying the top and bottom by the conjugate of the numerator, but i didn't think it all the way through.

****ckkkkk

 

[Arturito_Burrito]

A ball is thrown straight down from the top of a 225 foot building with an initial velocity of –29 feet per second. Use the position function for free-falling objects given below.
s(t) = –16t^2 + v0t + s0
(a) What is the velocity of the ball after 3 seconds?
-125 ft/sec

(b) What is the velocity of the ball after falling 45 feet?


Ok I can't figure out how to get B could someone tell me what i'm supposed to do next? Hopefully in the next 25 minutes cause thats when my HW is due =\

edit: supposed to be s(t) = –16t^2 + v0t + s0 had it as -16t2

edit2 : times up =\ I'm pretty sure it was -61 in the end but just as i got the answer the time changed for everybody don't procrastinate

 

[POKE40]

Since you did it already I'll do it anyway:

Vo= -25
s0 = 225

plug that in
find the derivative. Then plug in 3

(something interesting:
s(t) is the position
s'(t) is the velocity
s''(t) is acceleration

oh wait you finished already.

 

[Sinz]

Alright, Dryu just sent me this over a text. so, here it goes. I am just going to copy what he sent me, and maybe you guys know what it is.
Circle lies in the first quadrant, tangents to both the x and y axis. The radius is 5.

Thats all he sent me. :/ He told me he was working on "mid points and end point stuff."
Anyone wanna help him out?

 

[POKE40]

Alright, Dryu just sent me this over a text. so, here it goes. I am just going to copy what he sent me, and maybe you guys know what it is.
Circle lies in the first quadrant, tangents to both the x and y axis. The radius is 5.

Thats all he sent me. :/ He told me he was working on "mid points and end point stuff."
Anyone wanna help him out?

Does he want to create an equation for the circle?

 

[moogle]

Alright, Dryu just sent me this over a text. so, here it goes. I am just going to copy what he sent me, and maybe you guys know what it is.
Circle lies in the first quadrant, tangents to both the x and y axis. The radius is 5.

Thats all he sent me. :/ He told me he was working on "mid points and end point stuff."
Anyone wanna help him out?

an equation for the circle would be (x-5)² + (y-5)² = 25
center is at (5,5)
it's tangent to the x-axis at (5,0), tangent to the y-axis at (0,5)

I can't think of anything else that's very relevant...

 

[Arturito_Burrito]

Ok I'm a little confused on this problem and it doesn't seem hard so i'm probably just over looking something simple but both my ideas where wrong.

Consider the following function.
f(x) = (x+6)/(x-1)
(a) Find f '(x).

-7/(x-1)^2

(b) Find f '(9).

I tried plugging in 9 to the original function and to the derivative but both where wrong.

 

[Sinz]

So you take the derivative with regards to x. A is the top, b is the bottom.
(b'a-a'b)/b^2
A=(x+6)
A'=1
B=x-1
B'=1
(1(x+6)-(x-1)1)/(x^2-2x+1)
(X+6)-(x-1)/(x^2-2x+1)
x-x+6+1=7
7/(x^2-2x+1) = f'(x)
F'(9)
7/(9)^2-2(9)+1)
7/(81-18+1)
7/(64)

I think I did it right.

 

[Arturito_Burrito]

yah you did except the 7 is supposed to be a negative. Thanks for the help.

 

[Sinz]

So you take the derivative with regards to x. A is the top, b is the bottom.
(b'a-a'b)/b^2
A=(x+6)
A'=1
B=x-1
B'=1
(1(x+6)-(x-1)1)/(x^2-2x+1)
(X+6)-(x-1)/(x^2-2x+1)
x-x+6+1=7
7/(x^2-2x+1) = f'(x)
F'(9)
7/(9)^2-2(9)+1)
7/(81-18+1)
7/(64)

I think I did it right.

I figured what I did wrong.
((x-1)-(x+6))/(x^2-2x+1)
-7/(x^2-2x+1)
-7/64

 

[Ocho(*8*)]

Should I be using a trig substitution to integrate (8 - x^2)^.5 ? (Thats the square root of 8 minus x squared) It seems like there should be an easier way.

Also, the Integral of (sinx)^3 isn't just -(1/4)(cosx)^4, is it?

Am I wrong in thinking that sin^3(x) = (sin(X))^3 : I remember something like that but I can't wuite recall it...

One more thing - how do you know how much you have to change the bounds of your integral when you integrate and substitute a trig function for X. ( If you don't know what I'm talking about I'll try to give an example)

I also might need help with polynomial long division shortly...

 

[Corpsecreate]

Trig substitution would be needed for the (8 - x^2)^.5, square roots involving addition and subtraction are always really annoying to integrate.

(SinX)^3 = Sin^3X yes. The integral of Sin^3X is NOT what you have there though, if you have trouble solving it i'll show you the answer, Hint: use a substitution.

I think I know what you mean for the 3rd question. Lets say you want to integrate Sinx*Cosx from X = 2 to X = 5. Integral of Sinx*Cosx is the integral of 0.5*Sin(2x) which is -1/4Cos(2x). Evaluate that from X = 2 and X = 5 and you get (Cos4-Cos10)/4 which is roughly 0.046.

Now if you use a substitution... --->> Sinx*Cosx, let u = Sinx and so dx = du/Cosx ---> So you get the integral of u evaluated between A and B, im guessing you want to know how to find the values of A and B? Simple. We know when X is the variable its between 2 and 5. We also know that u = Sinx. This means that the values of A and B are the values of u evaluated when X = 2 and X = 5. In other words, the lower and upper bounds are Sin2 and Sin5 respectively.

The integral of u is 0.5u^2. Evaluate this between Sin2 and Sin5 and you get ( (Sin5)^2 - (Sin2)^2 ) / 2 --->> = 0.046, the same as before. Hope that answers your question.

 

[Ocho(*8*)]

Trig substitution would be needed for the (8 - x^2)^.5, square roots involving addition and subtraction are always really annoying to integrate.

(SinX)^3 = Sin^3X yes. The integral of Sin^3X is NOT what you have there though, if you have trouble solving it i'll show you the answer, Hint: use a substitution.

Dont know what you mean for the 3rd part

For the third part I meant what if I want the area from -2 to 6 of ( 16 - (x - 2)^2)^.5. I say: x - 2 = 4sin(z). That way I get a nice subtitution with 1 - sin^2(z). ( I used z instead of theta). Don't you have to change the bounds of the definite integral now.

My instinct is to set it up like: -2 = 4sin(z), and then solve for z which would be 4sin^-1(-2) = z and z ahould become the new lower boundary. The problem is sin^-1(-2) doesn't exist so I'm stuck. Same with 6 as the other bound.

Edit:
Looks like you edited your post as I made this post. I think that will help thank you...

 

[_KuyaSombreo_]

how do you factor the sums and differences of cubes?

 

[_KuyaSombreo_]

for example:

(x^3-8)

 

[T-block]

use a³-b³ = (a-b)(a²+ab+b²)

so (x³-8) = (x-2)(x²+2x+4)

 

[Corpsecreate]

If I want a 99% chance of winning the lotto OVER A PERIOD OF TIME where there are 45 numbers and you have to choose 6 and winning is considered you getting all 6 numbers. You choose 1 group of 6 numbers per week, How many weeks do you need to play?

 

[Sinz]

edit: i need to learn how to read

 

[moogle]

If I want a 99% chance of winning the lotto OVER A PERIOD OF TIME where there are 45 numbers and you have to choose 6 and winning is considered you getting all 6 numbers. You choose 1 group of 6 numbers per week, How many weeks do you need to play?

There are (45 choose 6) = 45*44*43*42*41*40/6! = 8145060 different combinations of 6 numbers chosen from a pool of 45 numbers. So the chance to win in one week is 1/8145060. We'll set this value equal to p.

The chance that you don't win in a given week is 1-p = 8145059/8145060. The chance you don't win 2 weeks in a row is (1-p)^2 = (8145059/8145060)^2. The chance you don't win k weeks in a row is (1-p)^k = (8145059/8145060)^k.

Now, the chance that you win at least once in a span of k weeks is one minus the chance that you win 0 times: 1 - (1-p)^k. Everything is in place now. We need to solve for k: 0.99 <= 1 - (8145059/8145060)^k. You can solve that beast of an inequality however you like. I get k=37550213 as the fewest number of weeks to have at least a 99% chance to win.

 

[Death]

A rabbit is moving along a straight path at a constant speed of 25 m/s. He passes a tortoise, who immediately goes after the rabbit, with a constant acceleration of 0.0030 m/s^2. How long will it take the tortoise to catch up with the rabbit (in h)?

I have no idea where to start. I guess you could calculate when the tortoise will reach a speed of 25 m/s, but it would still be behind the rabbit then. How would I even set up this problem, as there are very few givens and so many unknowns?

 

[_KuyaSombreo_]

A rabbit is moving along a straight path at a constant speed of 25 m/s. He passes a tortoise, who immediately goes after the rabbit, with a constant acceleration of 0.0030 m/s^2. How long will it take the tortoise to catch up with the rabbit (in h)?

I have no idea where to start. I guess you could calculate when the tortoise will reach a speed of 25 m/s, but it would still be behind the rabbit then. How would I even set up this problem, as there are very few givens and so many unknowns?

Im actually studying problems like this in physics too.
I imagine just using one of the kinematics equations will solve for the time.

 

[Death]

Yes, I would suppose that would be the way to solve it, but there really are only two givens:

We know the turtle's acceleration and we know that his initial speed/velocity was 0 m/s as he was at rest when the rabbit passed (might've forgotten this in OP). I don't see how we could solve for time interval unless we try trial and error?

For example, see how far the rabbit would be in 1 h and compare that to the turtle?

 

[moogle]

A rabbit is moving along a straight path at a constant speed of 25 m/s. He passes a tortoise, who immediately goes after the rabbit, with a constant acceleration of 0.0030 m/s^2. How long will it take the tortoise to catch up with the rabbit (in h)?

I have no idea where to start. I guess you could calculate when the tortoise will reach a speed of 25 m/s, but it would still be behind the rabbit then. How would I even set up this problem, as there are very few givens and so many unknowns?

rabbit: initial velocity = 25m/s, accel = 0 m/s^2
tortoise: initial velocity = 0m/s, accel = 0.0030 m/s^2

There's a nice little formula, d = v*t + 0.5a*t^2.
(d is distance, v is initial velocity, a is acceleration.)

You want to find the time, t, when the rabbit's distance equals the tortoise's distance.

25t + 0 = 0 + 0.5*0.0030*t^2

Solve for t: t=0 and t=16666.6667.

After 16666.6667 seconds, or 4.62962964 hours, the tortoise will pass the rabbit. (I didn't deal with sig figs... your teacher might care though.)

 

[2001]

nvm .

 

[Death]

Thanks so much moogle! I have some more question which, right now, seem impossible

Ben Johnson ran 100 m in 9.79 s. Assume he accelerated unifromly for the first 1.60 s, then finished the race at constant speed. What was Ben's acceleration for the first 1.60 seconds?

Okay, so he ran 8.19 s at a constant speed. And we can find his average speed to be about 10.2 m/s. Would finding the displacement as a result of his acceleration help in any way???

The question is whether a driver was exceeding the speed limit of 50 km/h before he made an emergency stop, with brakes locked and wheels sliding. The length of the skid marks on the road was 5.85 m. A police officer made the reasonable assumption that the maximum deceleration would not exceed that of gravity. On the basis of the evidence, was the driver exceeding the speed limit before the brakes were applied?

ANY HELP?

 

[SilverDrgn85]

Thanks so much moogle! I have some more question which, right now, seem impossible

Ben Johnson ran 100 m in 9.79 s. Assume he accelerated unifromly for the first 1.60 s, then finished the race at constant speed. What was Ben's acceleration for the first 1.60 seconds?

Okay, so he ran 8.19 s at a constant speed. And we can find his average speed to be about 10.2 m/s. Would finding the displacement as a result of his acceleration help in any way???

The question is whether a driver was exceeding the speed limit of 50 km/h before he made an emergency stop, with brakes locked and wheels sliding. The length of the skid marks on the road was 5.85 m. A police officer made the reasonable assumption that the maximum deceleration would not exceed that of gravity. On the basis of the evidence, was the driver exceeding the speed limit before the brakes were applied?

ANY HELP?

d = 1/2*a*t^2 + vo*t+d0 ------------------(1)
v = a*t + vo ----------------------------------(2)

For the first question, these are the two equations you need. Split the problem into two parts, the first 1.6 seconds and the last 8.19. The initial velocity and displacement for the second part are the velocity and displacement you achieved in the first part, which you should be able to get in terms of your initial acceleration.

For the second question, solve equation (1) for time using the quadratic formula and subtitute it into equation (2) to get the equation you need.

 

[Corpsecreate]

There are (45 choose 6) = 45*44*43*42*41*40/6! = 8145060 different combinations of 6 numbers chosen from a pool of 45 numbers. So the chance to win in one week is 1/8145060. We'll set this value equal to p.

The chance that you don't win in a given week is 1-p = 8145059/8145060. The chance you don't win 2 weeks in a row is (1-p)^2 = (8145059/8145060)^2. The chance you don't win k weeks in a row is (1-p)^k = (8145059/8145060)^k.

Now, the chance that you win at least once in a span of k weeks is one minus the chance that you win 0 times: 1 - (1-p)^k. Everything is in place now. We need to solve for k: 0.99 <= 1 - (8145059/8145060)^k. You can solve that beast of an inequality however you like. I get k=37550213 as the fewest number of weeks to have at least a 99% chance to win.

I Completely understand your working and I do believe your answer is correct. The thing I dont understand is why my answer is incorrect. I used the binomial formula NCX * (P)^X * (1-P)^(N-X) and solved for X and I got 52,721,139. Any idea why this didn't work?

 

[Death]

SilverDrgn, how would I find the velocity and displacement of the first part?

a = v/t but we only know t.

 

[_KuyaSombreo_]

plz help me with this calculus problem if you have the time:
Find the equation of the line that is tangent to the graph of "f" and parallel to the given line.
f(x) =x^3 ; 3x-y+1=0

To save time, I have calculated that the derivative is x^2 (though it may need verification) and the slope of the given line is obviously 3. But how do I go about finding the equation of the tangent line to graph of "f"?

 

[POKE40]

plz help me with this calculus problem if you have the time:
Find the equation of the line that is tangent to the graph of "f" and parallel to the given line.
f(x) =x^3 ; 3x-y+1=0

To save time, I have calculated that the derivative is x^2 (though it may need verification) and the slope of the given line is obviously 3. But how do I go about finding the equation of the tangent line to graph of "f"?

You got the wrong derivative there.

If you did the power rule correctly you should get 3x^2 as the derivative.
Let me see what you can get from there <3

 

[_KuyaSombreo_]

O_O
oops well thanks, yeah that does get me the right answer

*slaps hand against forehead*
i forgot to apply pascal's triangle, man i am soo stupid

thnx again for helping me with this

 

[SilverDrgn85]

SilverDrgn, how would I find the velocity and displacement of the first part?

a = v/t but we only know t.

You need to use equation (1) twice, once for the first 1.6 seconds and once for the last 8.19 seconds. You'll have three equations and three unknowns. You can just get the displacement and velocity of the first part in terms of your unknown acceleration and substitute those into your displacement equation for the last part.

 

[Frown]

Okay, this is my first math question in 4 months, so I haven't really warmed up yet. I suspect that this is really easy, but I still need help.

7/4(x-4)+6 = 7/4x-1

Why?

 

[cutter]

Okay, this is my first math question in 4 months, so I haven't really warmed up yet. I suspect that this is really easy, but I still need help.

7/4(x-4)+6 = 7/4x-1

Why?

Distributive property.

Multiply the 7/4 through each term in the parentheses (x-4).

So we get on the front:

7/4x-7+6 = 7/4x-1

Then just combine like terms:

7/4x-1 = 7/4x-1

 

[Fuelbi]

Oh god these equations make me fear when Ill have more advanced algebra >_<