hemtae
Member
combine like terms, so you have
7y/12 = 6/5
then multiply each side by 12/7 to cancel out the (7/12) coefficient on the left so you have
y = 72/35
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The Math Help Thread
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combine like terms, so you have
7y/12 = 6/5
then multiply each side by 12/7 to cancel out the (7/12) coefficient on the left so you have
y = 72/35
ahhh cool thanks man. was unsure about what to do with the fractions since the both had variables on topz.
Calc 1 (got a test next friday, need help remembering)
4.2 Q0039 Use any method to find relative extrema of the function
f(x)=16x^(3)(x+1)^(2)
4.2 Q040 f(x)=9x^(2)(x+1)^(3)
f has a relative min of ______ at x =
f has a relative max of ______ at x=
Could really use the help
4.2 Q0039 Use any method to find relative extrema of the function
f(x)=16x^(3)(x+1)^(2)
4.2 Q040 f(x)=9x^(2)(x+1)^(3)
f has a relative min of ______ at x =
f has a relative max of ______ at x=
Could really use the help
hemtae
Member
Calc 1 (got a test next friday, need help remembering)
4.2 Q0039 Use any method to find relative extrema of the function
f(x)=16x^(3)(x+1)^(2)
4.2 Q040 f(x)=9x^(2)(x+1)^(3)
f has a relative min of ______ at x =
f has a relative max of ______ at x=
Could really use the help
If the first derivative is 0 and the second derivative is negative then its a relative max
If the first derivative is 0 and the second derivative is positive then its a relative min
I'm not good enough at mental math to actually do the derivatives and I don't have any paper around right now so if you need help with those parts someone else will have to assist you.
youngwerther
Banned
Related rates problem
At noon, ship A is 150 km west of Ship B. Ship A is sailing east at 35 km/h and ship B is sailing north at 25 km/h. How fast is the distance between the ships changing at 4:00 PM?
Not sure how to relate all that information.
nvm I got it.
At noon, ship A is 150 km west of Ship B. Ship A is sailing east at 35 km/h and ship B is sailing north at 25 km/h. How fast is the distance between the ships changing at 4:00 PM?
Not sure how to relate all that information.
nvm I got it.
youngwerther
Banned
Ok this one I don't know.
A spotlight on the ground shines on a wall 12 m away. If a man 2 m tall walks from the spotlight toward the building at a speed of 1.6 m/s, how fast is the length of his shadow on the building decreasing when he is 4 m from the building?
Will I have two triangles?
A spotlight on the ground shines on a wall 12 m away. If a man 2 m tall walks from the spotlight toward the building at a speed of 1.6 m/s, how fast is the length of his shadow on the building decreasing when he is 4 m from the building?
Will I have two triangles?
I don't know if I got it all correct but here's an attempt.
Where x is equal to 1.6t
x = 12-4 = 8 => t = 8/1.6 = 5
tan(a) = 2/x = h/12 => h = (12*2)/x = 24/x = 24 / (1.6t) = 15*t^-1
dh/dt = -15*t^-2 = [t = 5] = -15*5^-2 = -15*0.04 = -15/25 = -0.6
So the height of the shadow should be decreasing by 0.6 m/s
thequickandthedead
Member
Thnks for your clarification MikeDip and Leezard.
Can anyone check my answer for this mechanics question?
"At time t=0 a ball is projectected vertically upwards from a point O and rises to a max height of 40m above O."
The first part of the question is to show that speed of projection is 28ms^-1 which i did pretty easily. But the second part i'm having doubts about: "find time in seconds when the ball is 33.6m above O."
I substituted s=33.6, a=9.8, and u=0 into
S=ut+1/2at^2
to find that t=2.62
Can anyone check what i've done wrong?
Can anyone check my answer for this mechanics question?
"At time t=0 a ball is projectected vertically upwards from a point O and rises to a max height of 40m above O."
The first part of the question is to show that speed of projection is 28ms^-1 which i did pretty easily. But the second part i'm having doubts about: "find time in seconds when the ball is 33.6m above O."
I substituted s=33.6, a=9.8, and u=0 into
S=ut+1/2at^2
to find that t=2.62
Can anyone check what i've done wrong?
CoffeeJanitor
Member
Velocity is not zero at 33.6 m.
thequickandthedead
Member
The initial velocity is zero.
Hey, does anyone know any resources I can hit up to learn stochastic calculus and stuff?
No, the initial velocity is 28 ms^-1. That's what you showed in the first question.
No, the initial velocity is 28 ms^-1. That's what you showed in the first question.
The position of the ball is the integral of its velocity. Since we start at t=0 we get:
The velocity can be written as:
Using this in the integral gives:
Assuming your previous answer for v_0 is correct, we then get:
I assume you can solve the quadratic equation yourself.
It's been a while since I solved a problem like this so there might be some errors here.
The position of the ball is the integral of its velocity. Since we start at t=0 we get:
The velocity can be written as:
Using this in the integral gives:
Assuming your previous answer for v_0 is correct, we then get:
I assume you can solve the quadratic equation yourself.
It's been a while since I solved a problem like this so there might be some errors here.
He's doing M1, I sat the paper he's practicing on, so, its a bit hardcore what you did for his examination. His methodology is correct, he's just using incorrect values that's all.
thequickandthedead
Member
Thanks, i found the answer. Out of curiosity, what exam board are you doing?
I'm done
I was edexcel maths. The paper that question is from was the paper I sat in june during year 12.
Ah. As I live in Sweden M1 doesn't tell me anything and it's always a bit difficult to know at what level these courses are. Anyway, great that he managed to solve the problem
thequickandthedead
Member
I'm done
I was edexcel maths. The paper that question is from was the paper I sat in june during year 12.
Ah ok. I'm doing OCR. Did you do any further pure or decision units?
Can anyone help me with this one? (Calculus)
If the equation of motion of a particle is given by s = A cos(ωt + δ
, the particle is said to undergo simple harmonic motion.
(a) Find the velocity of the particle at time t.
(b) When is the velocity 0? (Use n as the arbitrary integer.)
Can someone help me with an explanation/work and not only the answer? Thanks! It's for bonus and I don't even have the slightest clue.
If the equation of motion of a particle is given by s = A cos(ωt + δ
, the particle is said to undergo simple harmonic motion.(a) Find the velocity of the particle at time t.
(b) When is the velocity 0? (Use n as the arbitrary integer.)
Can someone help me with an explanation/work and not only the answer? Thanks! It's for bonus and I don't even have the slightest clue.
opticalmace
Member
You know the position of the particle as a function of time (given by the equation). How is velocity related to position?Can anyone help me with this one? (Calculus)
If the equation of motion of a particle is given by s = A cos(ωt + δ
(a) Find the velocity of the particle at time t.
(b) When is the velocity 0? (Use n as the arbitrary integer.)
Can someone help me with an explanation/work and not only the answer? Thanks! It's for bonus and I don't even have the slightest clue.
Hi need help with this one. (calc 1)
Use a graphing utility to estimate the maximum and minimum values of f, if any, on the stated interval and then use calculus methods to find the exact values.
f(x)=10ln(x^(2)+1)-8x;[0,3]
f'(x)=(10/x^(2)+1)(2x)-8
f'(x)=(20x/x^(2)+1)-8
then I set it equal to zero and get stuck
f'(x)=(20x/x^(2)+1)-8=0
Use a graphing utility to estimate the maximum and minimum values of f, if any, on the stated interval and then use calculus methods to find the exact values.
f(x)=10ln(x^(2)+1)-8x;[0,3]
f'(x)=(10/x^(2)+1)(2x)-8
f'(x)=(20x/x^(2)+1)-8
then I set it equal to zero and get stuck
f'(x)=(20x/x^(2)+1)-8=0
HollovVpo1nt
Banned
Hey guys, question.
Does any of you have a easy way to calculate i^(n!)?
For example, i^2! = i^(2*1) = i² = -1
i^3!= i^(3*2*1) = i^6 = (i^2)^3 = -1^3 = -1
Does it work this way? I have to calculate i^7!
Can I use this trick -> a^bc = ( a^b)^c
i^7! = i^(7*6*5*4*3*2*1) = (i^4)^(7*6*5*3*2*4) = 1^(7*6*5*3*2*1) = 1?
Does any of you have a easy way to calculate i^(n!)?
For example, i^2! = i^(2*1) = i² = -1
i^3!= i^(3*2*1) = i^6 = (i^2)^3 = -1^3 = -1
Does it work this way? I have to calculate i^7!
Can I use this trick -> a^bc = ( a^b)^c
i^7! = i^(7*6*5*4*3*2*1) = (i^4)^(7*6*5*3*2*4) = 1^(7*6*5*3*2*1) = 1?
HollovVpo1nt
Banned
Any idea how I can prove this:
?
cpp_is_king
Member
Any idea how I can prove this:
?
If it didnt, then would the series on the left converge?
kidtamagotchi
Member
I am having trouble with math logic and valid/invalid arguments. Here are the questions (I have to show work):
Determine if the statement is true or false:
If all frogs can dance, then I am a millionaire.
Determine whether the argument is valid or invalid.
My plant is fertilized or it turns yellow. My plant is turning yellow. Therefore, my plant is not fertilized. (Use standard forms)
If Jim likes to ski, then he will like to vacation in the mountains. Jim does not like to vacation in the mountains. Therefore, he does not like to ski. (Use standard forms)
Any help would be appreciated!
Determine if the statement is true or false:
If all frogs can dance, then I am a millionaire.
Determine whether the argument is valid or invalid.
My plant is fertilized or it turns yellow. My plant is turning yellow. Therefore, my plant is not fertilized. (Use standard forms)
If Jim likes to ski, then he will like to vacation in the mountains. Jim does not like to vacation in the mountains. Therefore, he does not like to ski. (Use standard forms)
Any help would be appreciated!
Not sure what to say about this one, are you given any hypotheses? Anything? Or just this statement? Because I've seen logic textbooks have ridiculous stuff like this be true before. In the real world? This is false. EDIT: Or, I guess the problem is assuming real-world conditions, meaning 1) not all frogs can dance (that we know) and 2) you are not a millionaire (I'm assuming). In that case, you have a false statement implies a false statement, which is a true statement.
Say F=my plant is fertilized and Y=my plant turns yellow.
Given: b) F [or] Y is true a) Y is true
Argument: a) and b) => F is false
Valid/Invalid: Invalid. In mathematical reasoning, "or" is understood to be inclusive by default. Meaning, F [or] Y is true when 1) F is true and Y is false 2) F is false and Y is true 3) both are true. Thus given Y is true and (F [or] Y) is true, F is indeterminate because both case 2 and case 3 are possible.
Say S=Jim likes to ski, V=Jim likes to vacation in the mountains.
Given: a) S=>V is true b) V is false
Argument: a) and b) => S is false
Valid/Invalid: Valid. S=>V is false only when S is true and V is false. In every other case it is true. Given that V is false, then, S must be false.
Another way to prove this, if you've reached this point already in your course, is the law of contraposition. The law of contraposition states:
(A=>B)=>(~B=>~A)
So if S=>V is true, then ~V=>~S is true. If V is false, then ~V is true. For ~V=>~S to be true when ~V is true, ~S must be true. Therefore S is false.
kidtamagotchi
Member
Thanks for the help! The teacher just glossed over this stuff in class and gave us tons of homework and a take home test. I am stressed out right now!
SniperHunter
Banned
pretty basic physics question: we are give times for an orange falling off the table, it's position is given every .25 seconds. I drew a position time graph for it's motion - basic stuff.
Now the question get's vague, I have to draw tangents on the graph and create a time velocity data table. My question is what is the most precise method of get slope of tangets
Now the question get's vague, I have to draw tangents on the graph and create a time velocity data table. My question is what is the most precise method of get slope of tangets
cpp_is_king
Member
Is this calculus based physics?
SniperHunter
Banned
to be honest it's badly organized, it's most trig based with some basic calculus thrown in for confusion. I know there was a graphing program that gave precise slopes of tangents but I forgot it's name
cpp_is_king
Member
Well the position formula for a falling object is y(t) = y0 - g*t^2/2 where g = 9.8 m/s^2
If you can use calculus then you can just take the derivative to get velocity.
v(t) = -g*t
and plug in values of t to get the exact value at various values of t. I never took non-calc based physics so I don't know what they do instead of using derivative, but I think they just have you memorize the formula for velocity. So, velocity is given by v(t) = -g*t
If none of this sounds familiar, then you might have to resort to something else, like estimating the tangent with a diagonal.
SniperHunter
Banned
all right thnx for the help, I will try doing it your way
opticalmace
Member
If you have to just draw them on the graph, perhaps try something like this:
http://en.wikipedia.org/wiki/File:Heun%27s_Method_Diagram.jpg
(you red lines here would be straight lines between neighbouring data points)
Otherwise you could fit your data etc.
edit: the only danger in cpp_is_king's method is that it assumes the initial velocity is zero (there is a v_initial*t term he has dropped). The experimental data might not reflect that. You're better off fitting your data with the quadratic to get the parameters to get x(t) and then taking its derivative to get v(t). Though from how you worded it, that's probably not what they want.
Thanks
Got another one for you guys. Let s(t)=5t^(2)-17t be the position of a particle moving on a coordinate line, where s is in feet and t is in seconds. Find the maximum speed of the particle during the time interval 1≤t≤2
EDIT: nevermind figured it out
Hey GAF, right now I'm in grade 12 Calculus and Vectors. Currently we're doing stuff with the derivatives of exponential functions and it's screwing with my brain. The question that I'm stumped on is this:
Find the derivative of:
e^(2t) / [1 + e^(2t)]
The answer is supposed to be 2e^(2t) / [1 + e^(2t)]^2, but I cannot for the life of me figure out how to get the numerator. Right now I have:
(2e^(2t) * [1 + e^(2t)]) - (e^(2t) * [2e^(2t)]) / [1 + e^(2t)]
I'm stumped. :/
Find the derivative of:
e^(2t) / [1 + e^(2t)]
The answer is supposed to be 2e^(2t) / [1 + e^(2t)]^2, but I cannot for the life of me figure out how to get the numerator. Right now I have:
(2e^(2t) * [1 + e^(2t)]) - (e^(2t) * [2e^(2t)]) / [1 + e^(2t)]
I'm stumped. :/
cpp_is_king
Member
Looks good so far, you've used the quotient rule. You messed up two things though. First, you didn't square the denominator (double check the formula for quotient rule). Second, you didn't put the numerator in parentheses. Everything left of the / sign is the numerator, so you have to make sure you parenthesize it.
So anyway, expand out the top and collect terms. The numerator, after expanding, becomes:
2e^(2t) + 2e^(4t) - 2e^(4t)
The last 2 vanish and you're left with a numerator of only 2e^(2t)
That divided by the bottom (which you forgot to square) gives you the answer.
Whoopsie, I actually did square the denominator, just forgot to type that in. And thanks, I didn't know I had to expand. I'm not so great with this stuff (my mark is a 65.5, and I need it to be in the high 70s for uni, fml), so I'm not sure when to expand or factor out common terms. Got it now, thanks!
cpp_is_king
Member
You factor / expand any time factoring / expanding leads to the answer
Really though, there's not a rule. You should always look for ways to manipulate expressions into different forms. Stuff works just because it does, not because there's any rule that tells you when / why it does.If you've got an expression that seems too complicated and/or doesn't look like it's supposed to look, then you your first instinct should be "maybe I need to find something to factor" or "maybe if I expand some stuff out thigns will cancel".
systemfehler
Member
Any idea how I can prove this:
?
Via L'Hôpital's rule?
You factor / expand any time factoring / expanding leads to the answer
Heh, I'm not that mathematically inclined [my interests are more science/medicine based (don't remind me that I need math D
]. The only way I know the answer to something for sure is when I look in the back of my textbook :/ Screws me over on tests sometimes.
A lot of the time.
Is there any way to become good at math? :/
Heh, I'm not that mathematically inclined [my interests are more science/medicine based (don't remind me that I need math DA lot of the time.
Is there any way to become good at math? :/
I found most solutions at your sort of level are to be gotten simply; if its become hideous, backtrack son, this isn't the path.
Also, stop focusing on finding the answer, and just, manipulate. Manipulate the expression in any way you can spot. If you can expand, expand. If you can factorise, factorise. I found that helped too.
youngwerther
Banned
Homework time!
We're doing linear approximations and I missed class, so I'm teaching myself out of the book and want to verify that I'm doing this right. Appreciate anyone who checks this for me
Find the linearization L(x) of the function at a.
f(x) = sinx, a=pi/6
So what I did was gather the following information..
f'(x) = cosx
f(pi/6) = 1/2
f'(pi/6) = sqrt(3)/2
Then did this
L(x) = 1/2 + sqrt(3)/2 (x - pi/6)
Is that how you do these?
We're doing linear approximations and I missed class, so I'm teaching myself out of the book and want to verify that I'm doing this right. Appreciate anyone who checks this for me
Find the linearization L(x) of the function at a.
f(x) = sinx, a=pi/6
So what I did was gather the following information..
f'(x) = cosx
f(pi/6) = 1/2
f'(pi/6) = sqrt(3)/2
Then did this
L(x) = 1/2 + sqrt(3)/2 (x - pi/6)
Is that how you do these?
thequickandthedead
Member
Need some help with two questions:
1. The cubic equation x^3+Px^2+10x+Q=0 has roots α+1, β+1, and γ+1.
Find the value of P and Q.
2. The roots of equation: x^3-9x^2+27x-29=0 are denoted by α, β, and γ, where α is real and β and γ are complex.
i)it's given that β=P+iQ, where Q>0. Find the value of P in terms of α.
ii)Find the value of Q, in terms of α only.
1. The cubic equation x^3+Px^2+10x+Q=0 has roots α+1, β+1, and γ+1.
Find the value of P and Q.
2. The roots of equation: x^3-9x^2+27x-29=0 are denoted by α, β, and γ, where α is real and β and γ are complex.
i)it's given that β=P+iQ, where Q>0. Find the value of P in terms of α.
ii)Find the value of Q, in terms of α only.
For the second problem, are you allowed to use complex roots of unity? You can figure out what the roots are explicitly by rewriting the polynomial as (x-3)^3 - 2. Since all three roots satisfy (x - 3)^3 = 2, You'll get that α - 3 = 2^1/3, β - 3 = 2^1/3 * W_3, and γ - 3 = 2^1/3 * W_3^2, where W_3 = e^i*2pi/3 = cos(2pi/3) + isin(2pi/3). So you can write the real and imaginary parts of β in terms of α by replacing 2^1/3 with α - 3.
smokeandmirrors
Banned
Uh really really really stupid question that I cannot figure out why I'm stuck...
*log base 2 = lgn..
the power of (n / lg n) is 1 right?
(n / lg n) ^ 1
or is it (n ^ 1 / lg n)?
I literally have no idea why this is stumping me so. I've been working with recurrences so I think my brain is shot.
*log base 2 = lgn..
the power of (n / lg n) is 1 right?
(n / lg n) ^ 1
or is it (n ^ 1 / lg n)?
I literally have no idea why this is stumping me so. I've been working with recurrences so I think my brain is shot.
opticalmace
Member
I'm not really sure what you're asking... but I will say that (a/b)^1 = (a^1/b) = (a/b^1) = (a/b). Because x^1 = x.
??
smokeandmirrors
Banned
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