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[KaminaSquirtle]

My first thought with that problem would be to find the function of his distance to 3rd base with respect to how far away is his from 1st base when he is running from home to first base.  Then take the derivative with respect to how far away is his from 1st base of the function found earlier, and plug 30 feet into that.  Maybe I'm completely wrong, but hopefully that should help until I have time to actually solve the problem.

[eerr]

I could do this but,

Really you need to define S and X

solve for ds using dx.

hint: dx=16
hint2: you need trig functions for this. They really can't be removed.

[penguify]

Is the answer

Spoiler (click to show/hide)

16(cos(tan-1((90)/(90-30)))=(32√13)/13=8.87 ft/s?

Because if that's correct, it can be done without trig functions. I used similar triangles and the pythagorian theorem to get it, and trig functions to get it again. But I haven't taken calculus, so it might be wrong.

Spoiler: explanation (click to show/hide)

I drew it out as a right triangle ABC with 60 and 90 ft legs, then drew a line BD passing through the the right angle and perpendicular to AC. AD in ADB is proportional to AB in ABC, and so is the kid's speed in that direction. So I set it up as ((60^2 + 90^2)^.5)/60=16/x and solved for x. Is this a valid way of solving the problem, and is that answer correct?

[eerr]

It might not be precise enough. I really couldn't say.

Actually that looks perfectly valid.
eh I dunno.

I just leapt at knowing trig functions.

[Blargityblarg]

I have my first Year Eleven Maths Methods exam tomorrow (the one with no calculator or notes.) I, not being one for revision, am currently reading the summaries of every chapter we've done in the past six months. This includes 'Advanced Functions and Relations', 'Probability and Simulation', 'Calculus', 'Circular Functions', 'Exponential and Logarithmic Functions' and 'Probability Applications'.

I'm probably alright on most of this, except for Probability Applications, which I seem to remember mostly deal with ⁿP_r and ⁿC_r stuff. Can I get a summary of when each is required and/or used?

[Heron TSG]

solve for ds using dx.

Yes, this is what I'm having trouble with. How?

I know how to take derivatives pretty well, I just don't know how to apply it to this type of problem. (Growing piles of sand and filling balloons are good, though.)

[eerr]

Start by finding the formulas for X and S.

[Vector]

Can I get a summary of when each is required and/or used?

Permutations: number of choices possible when order matters
Combinations: number of choices possible when order doesn't matter

[lordnincompoop]

I breezed through combinations and permutations when I did it. It was mainly because they're very closely linked with factorials which are familiar to me, and because the questions posed were unusually easy.

Also, I learned it as _nP_r and _nC_r.

[MaximumZero]

Today I found out that I was the only one in my class that remembered "Soh Cah Toa." Thanks, guys. ^_^

[Vector]

Today I found out that I was the only one in my class that remembered "Soh Cah Toa." Thanks, guys. ^_^

*cheers*


Today I was beaten in the face by the Axiom of Choice =/  On the other hand, now I know what it is...

[Blargityblarg]

Exam went fairly well. Only question I had no idea for was something like:

A leaky bottle has water in it; the amount of water in cm³ is modelled by V=-t²(t²+2)+642, find when the bottle will be empty, give answer in an exact form.

I'm not sure if those were the exact figures used, though.

[Soadreqm]

When the bottle is empty, V is zero. Solve for t.

[MaximumZero]

Today I found out that I was the only one in my class that remembered "Soh Cah Toa." Thanks, guys. ^_^

*cheers*


Today I was beaten in the face by the Axiom of Choice =/  On the other hand, now I know what it is...

*looks it up on wikipedia*
...
*head asplode*

[lordnincompoop]

How do I find the angle between two intersecting lines, knowing only the length and slope of each line?