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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 $\overline{AC}$ ?

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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...

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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...

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9 replies | 92 view(s)
October 15th, 2017, 16:11

MarkFL replied to a thread Guidelines for posting/answering a challenging problem or puzzle in Challenge Questions and Puzzles

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...

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2 replies | 1870 view(s)
October 15th, 2017, 04:16

Opalg replied to a thread
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...

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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...

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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?

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2 replies | 45 view(s)
October 14th, 2017, 19:36

MarkFL replied to a thread Question about roots/synthetic division in Pre-Algebra and Algebra

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...

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1 replies | 43 view(s)
October 14th, 2017, 19:26

MarkFL replied to a thread Help with an equation problem in Pre-Algebra and Algebra

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...

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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. :)

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9 replies | 92 view(s)
October 14th, 2017, 19:14

MarkFL replied to a thread [SOLVED] A family buys a house and has to pay monthly in Business Mathematics

When I plug in the numbers, I get choice C). W|A - 40000(0.11/12)/(1-(1+0.11/12)^(-30*12))

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2 replies | 58 view(s)
October 14th, 2017, 16:09

Opalg replied to a thread
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...

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3 replies | 113 view(s)
October 14th, 2017, 06:05

Opalg replied to a thread
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...

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2 replies | 116 view(s)
October 13th, 2017, 07:04

Opalg replied to a thread Disconnected Sets ... Palka, Lemma 3.1 ... in Analysis

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...

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2 replies | 52 view(s)
October 13th, 2017, 04:04

Opalg replied to a thread Limits of Complex Functions ... Final Remark from Palka in Section 2.2 ... in Analysis

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} =...

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2 replies | 38 view(s)
October 13th, 2017, 02:54

MarkFL replied to a thread [SOLVED] T 4–4 Deposits needed to accumulate a future sum in Business Mathematics

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 $n$...

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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)

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3 replies | 157 view(s)
October 11th, 2017, 21:38

MarkFL replied to a thread 6d After how many days is the percent of the population infected a maximum in Calculus

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...

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2 replies | 53 view(s)
October 11th, 2017, 12:06

Opalg replied to a thread Continuity of Complex Functions ... ... in Analysis

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...

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2 replies | 92 view(s)
October 11th, 2017, 12:01

MarkFL started a thread Visible Stickies in vBulletin Products

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...

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0 replies | 44 view(s)
October 11th, 2017, 09:42

MarkFL replied to a thread Welcome New MHB Math Helper GJA! in Announcements

Congratulations, GJA, and welcome to the team! (Yes)

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7 replies | 185 view(s)
October 10th, 2017, 22:32

MarkFL replied to a thread Powers...(again) in Pre-Algebra and Algebra

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...

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5 replies | 121 view(s)

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