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• October 15th, 2017, 22:29
MarkFL replied to a thread Show AB = BC in Pre-Calculus
It tells you the three points are collinear...now, is point $B$ the midpoint of $\overline{AC}$ ?
9 replies | 92 view(s)
• October 15th, 2017, 22:00
MarkFL replied to a thread Show AB = BC in Pre-Calculus
Please attach the images inline...otherwise they won't show up in the "Topic Review" and having them show up there can be helpful when replying to a...
9 replies | 92 view(s)
• October 15th, 2017, 21:51
MarkFL replied to a thread Show AB = BC in Pre-Calculus
In order for three points to be collinear, we can pick any two distinct sets of two points from the set of three to form two line segments, and those...
9 replies | 92 view(s)
• October 15th, 2017, 16:11
Hello, MHB Community! (Wave) Those of you active in this forum have likely noticed some new thread prefixes associated with a few of the threads...
2 replies | 1870 view(s)
• October 15th, 2017, 04:16
Unsolved Challenge
Evaluate ∠APR in Challenge Questions and Puzzles
As soon as you know that $x = 1/\sqrt2$, it follows (by looking at the triangle $PNA$) that $\overline{AP} = 1$. So $Q,P,R$ all lie on a circle...
3 replies | 113 view(s)
• October 14th, 2017, 19:42
MarkFL replied to a thread Isosceles Triangle in Pre-Calculus
Yes, the distance formula would be a good way to proceed, but recall, an equilateral triangle is a special case of an isosceles triangle...so, you...
2 replies | 48 view(s)
• October 14th, 2017, 19:39
MarkFL replied to a thread Show AB + BC = AC in Pre-Calculus
Yes, and if this is true, then what must be true of the 3 points?
2 replies | 45 view(s)
• October 14th, 2017, 19:36
When doing synthetic division, the actual root $r$ or zero of the polynomial is put out to the left. Thus we know: f(r)=0 And the polynomial...
1 replies | 43 view(s)
• October 14th, 2017, 19:26
I am assuming the volume is the cubic polynomial: V(x)=2x^3+9x^2+4x-15 We are told the depth is $x-1$, so we know $1$ is a zero of the...
1 replies | 40 view(s)
• October 14th, 2017, 19:18
MarkFL replied to a thread Show AB = BC in Pre-Calculus
Yes, the distance formula would work, or if you can show the 3 points are collinear, then you could use the mid-point formula. :)
9 replies | 92 view(s)
• October 14th, 2017, 19:14
When I plug in the numbers, I get choice C). W|A - 40000(0.11/12)/(1-(1+0.11/12)^(-30*12))
2 replies | 58 view(s)
• October 14th, 2017, 16:09
Unsolved Challenge
Evaluate ∠APR in Challenge Questions and Puzzles
\coordinate (Q) at (-5,0) ; \coordinate (P) at (-3.5,3.5) ; \coordinate (R) at (5,0) ; \coordinate (A) at (0,0) ; \coordinate (N) at...
3 replies | 113 view(s)
• October 14th, 2017, 06:05
Unsolved Challenge
Prove ∠A≤60°. in Challenge Questions and Puzzles
Start with a bit of calculus. If $0<b\leqslant c$ and $f(x) = x(b+c-x)$, then $f(x) \geqslant bc$ whenever $b\leqslant x\leqslant c.$ The reason for...
2 replies | 116 view(s)
• October 13th, 2017, 07:04
If $z\in A\cap U^*$ (which is a nonempty set) then $z\notin A \cap U^*\cap V^*$ (because $A \cap U^*\cap V^*$ is empty). In particular, $z\notin... 2 replies | 52 view(s) • October 13th, 2017, 04:04 Starting from the fact that$e^t \to \infty$as$t\to\infty$, it follows that$\lim_{t\to\infty}e^{-t} = \lim_{t\to\infty}\dfrac1{e^t} =...
2 replies | 38 view(s)
• October 13th, 2017, 02:54
Let's let $D$ be the amount of the end of year deposits, and $i$ be the annual interest rate. So, the amount of the account at the end of year $n$...
2 replies | 46 view(s)
• October 12th, 2017, 09:29
MarkFL replied to a thread New here in Introductions
Hello and welcome to MHB, Johny! (Wave)
3 replies | 157 view(s)
• October 11th, 2017, 21:38
Okay, judging by your derivative, we are actually given: p(t)=10te^{-\frac{t}{8}} And so: p'(t)=-\frac{5}{4}e^{-\frac{t}{8}}(t-8) Do you...
2 replies | 53 view(s)
• October 11th, 2017, 12:06
You are correct on both counts. The definition of $\text{Arcsin}$ specifies that its domain is $$and its range is$$. If $x$ (in that domain) is...
2 replies | 92 view(s)
• October 11th, 2017, 12:01
Overview: This product is designed to allow you to designate forums in which sticky threads are visible even if users do not have permission via...
0 replies | 44 view(s)
• October 11th, 2017, 09:42
Congratulations, GJA, and welcome to the team! (Yes)
7 replies | 185 view(s)
• October 10th, 2017, 22:32
Let's look at your first equation: n^5+n^4=\left(n^5-n^3\right)(n-1)-(n-2) If we use $n=1$, we get: 2=1 So, it's not an identity...and we...
5 replies | 121 view(s)
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