
Older Activity

Today, 00:16
Yes, now it makes sense to me the think of the "worst case scenario" for $n$ cards (let's call this $W_n$) to be:
...
9 replies  153 view(s)

Yesterday, 21:09
Only when the roots of the characteristic equation are imaginary do you typically express the homogeneous solution as a sinusoid. For example, if the...
4 replies  78 view(s)

Yesterday, 19:59
What I used to like to do as a student, when presented with a batch of similar problems, is to generalize to get a formula I could use. Suppose we...
4 replies  78 view(s)

Yesterday, 19:01
This problem is almost identical to the previous. What is your homogeneous solution $y_h$?
4 replies  78 view(s)

Yesterday, 16:22
Hello and welcome to MHB! (Wave)
Using a thread title of "probability and statistics" in our forum titled "Basic Probability and Statistics" is...
1 replies  33 view(s)

Yesterday, 16:01
I didn't notice before, but your characteristic roots are incorrect...we actually have:
r\in\{2,0\}
And so the general solution is:
...
7 replies  114 view(s)

Yesterday, 13:29
The dimensions are length $\ell$, width $w$ and height $h$. Suppose we know $\ell$ and $w$ to be 6 and 2 respectively. A rectangular prism (cuboid)...
3 replies  58 view(s)

Yesterday, 12:32
I also thought that might be the intended problem. :D
6 replies  114 view(s)

Yesterday, 12:26
Interesting...I also thought 60 would be the maximum number too. (Thinking)
9 replies  153 view(s)

April 21st, 2017, 22:24
I've moved the thread, and will wait until someone more proficient at probability to chime in. :D
6 replies  114 view(s)

April 21st, 2017, 22:15
I think to begin, I would imagine that Randi has the cards arranged in the same order she will seek them...for example suppose she will seek them in...
9 replies  153 view(s)

April 21st, 2017, 21:25
Suppose $x\ne0$ and you divide both sides by $x^6$...what do you get?
6 replies  114 view(s)

April 21st, 2017, 19:33
I was getting ready to reply that you need another initial condition, but you've fixed that. Also, I moved the thread to "Differential Equations" as...
7 replies  114 view(s)

April 21st, 2017, 18:55
Okay, that was the next thing to do! Why? You found and solved the "characteristic equation". Where did you learn that? Didn't you, at the time...
7 replies  114 view(s)

April 21st, 2017, 00:15
Yes...that's good. :D
5 replies  79 view(s)

April 20th, 2017, 23:42
Well, think of it this way:
Consider first only from $x=0$ to $x=\pi$. The area $A_1$ under the curve is equal to the area of the rectangle with...
5 replies  79 view(s)

April 20th, 2017, 22:37
Let's look at the region over which we are to integrate:
If we use horizontal strips, we see they are bounded on the left by $x=\sqrt{4y^2}$...
4 replies  72 view(s)

April 20th, 2017, 21:50
Let's first look at the region $D$ over which we are directed to integrate:
Now if we use horizontal strips, then we see they are bound on the...
5 replies  72 view(s)

April 20th, 2017, 15:55
The average value $M$ of a function $f(x)$ over some interval $$ where $a<b$ is given by:
M=\frac{1}{ba}\int_a^b f(x)\,dx
Suppose we use a...
5 replies  79 view(s)

April 20th, 2017, 10:35
From the region $D$...in this case it is a rectangular region bounded by the lines x=\pi,\,x=\pi,\,y=0,\,y=\frac{\pi}{2}.
6 replies  82 view(s)

April 20th, 2017, 10:31
That's where the sketch of the region $D$ comes in...for example when using horizontal strips, we see they are bounded on the left by the line $x=0$...
4 replies  61 view(s)

April 20th, 2017, 10:26
I've given the limits in the definite double integrals. :D
6 replies  82 view(s)

April 20th, 2017, 10:07
Since we are given the vertex, let's use the vertex form of a parabola:
y=a(xh)^2+k
Since the vertex (turning point) is given as $(1,6)$, we...
4 replies  60 view(s)

April 20th, 2017, 02:20
To decide, do a sketch of your region, and draw in both horizontal and vertical strips. If one way can be done without the lower and upper boundaries...
8 replies  100 view(s)

April 20th, 2017, 02:18
We should first note that the two boundary functions intersect at $\displaystyle \begin{align*} (2, 0) \end{align*}$ and $\displaystyle...
4 replies  72 view(s)

April 20th, 2017, 02:17
First we should note that the functions intersect at (0, 0), so if we use vertical strips we see that they will go from x = 0 to x = 4. The bottom of...
5 replies  72 view(s)

April 20th, 2017, 01:11
If we use horizontal strips, then we have:
I=\int_0^4 e^y\int_0^{4y} x\,dx\,dy
And if we use vertical strips, we have:
I=\int_0^4...
4 replies  61 view(s)
 Date of Birth
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 BS Mathematics, East Tennessee State University
BS Computer Science, East Tennessee State University
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