Recent content by Shawn Garsed

Homework Statement Show that ##\sum_{k=2}^\infty d_k## converges to ##\lim_{n\to\infty} s_{nn}##. Homework Equations I've included some relevant information below: The Attempt at a Solution So far I've managed to show that ##\sum_{k=2}^\infty |d_k|## converges, but I don't know how to move...

Nevermind, I solved it.

Homework Statement Homework EquationsThe Attempt at a Solution I've got a feeling that the problem is either incomplete or unclear, because so far I've come up with nothing but vague ideas. If it is clear, then please let me know so this thread can be closed/deleted.

They are real numbers.

How did I not see that, I feel so stupid. ##1 = b* b^{-1}## ##a = a *(b* b^{-1})## ##a = (a*b^{-1})*b## ##ac = ((a*b^{-1})*b)*c## ##ac = (a*b^{-1})*(bc)## ##(ac)*(bc)^{-1} = (a*b^{-1})*((bc)*(bc)^{-1})## ##(ac)/(bc) = a/b## I think this is it.

Homework Statement Prove the following: ##a / b = ac / bc##, if ##b, c \neq 0##. Homework Equations P1-12 The Attempt at a Solution ##a/b = a*b^{-1}## ##1 = c*c^{-1}## ##a/b*1 = (a*b^{-1})(c*c^{-1})## ##a/b = (a*c)(b^{-1}*c^{-1})## Now, if ##b^{-1}c^{-1} = (bc)^{-1}##, then the problem is...

@Curious3141 Once again you're right. I really need to get some sleep. Thanks for the help guys.

I see what you mean, R then equals Hh/r which eliminates the need for the angle θ. I kept getting confused because there are two values for both the radius and the height, one is a constant and the other is a variable.

@Curious3141 How would you relate r to h without using trig, cause I see no other way, though I could be missing something. @ehild You're right I forgot some parentheses. Fixed it.

Here's my (attempted) solution given the information I have. r=htanθ, θ is the angle between h and the slant height. V=5t=tan2θh3∏/3, therefore h=(15t/∏tan2θ)1/3 and h'=(5/∏tan2θ)*(∏tan2θ/15t)2/3. When the cup is half full t=tan2h3∏/30 and h'=5*41/3/(∏tan2θh2).

How can I do that if I don't know the angle between h and the slant height.

That's what I was thinking too. Here's the question in it's entirety: "A cup in the form of a right circular cone with radius r and height h is being filled with water at the rate of 5 cu in./sec. How fast is the level of the water rising when the volume of the water is equal to one half the...

Homework Statement A right circular cone with radius r and height h is being filled with water at the rate of 5 cu in./sec. How fast is the level of the water rising when the cone is half full.Homework Equations V=r2h∏/3The Attempt at a Solution V=5t. The level of the water is determined by h...

Thanks HallsofIvy, I got it now. It's x/(4(4-x2)1/2).

I've used 4-x2, (4-x2)-1/2 and (4-x2) 1/2 as a substitution.