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• Today, 12:24
Just to follow up, here is the completed table: Sum $S$ Probability of $S$: $P(S)$ Net Gain/Loss (in dollars) $G$ Product $G\cdot P(S)$
2 replies | 63 view(s)
• Today, 11:09
The function, $f$, is defined on the interval $$, and satisfies the following conditions: (a). f(0) = f(1) = 0. (b). For any a,b \in :... 0 replies | 17 view(s) • Yesterday, 22:32 MarkFL replied to a thread Radius of Circle in Pre-Calculus That is the radius of the circle after it has been increased by a units. If I tell you that my weight increased by 20 lbs., then you know my... 4 replies | 58 view(s) • Yesterday, 21:35 MarkFL replied to a thread Radius of Circle in Pre-Calculus Let's let 0<a be the number units the radius must be increased. And so the change in area we can write as: \Delta A=\pi(r+a)^2-\pi r^2=b Now... 4 replies | 58 view(s) • Yesterday, 20:41 Looks good. -Dan 2 replies | 32 view(s) • Yesterday, 15:14 I am so sorry, that I have posted a challenge, the solution of which, I am not certain. My problem is the use of the Rearrangement Inequality in the... 1 replies | 91 view(s) • Yesterday, 02:53 you can apply either way. but next steps become simpler if you apply difference of square x^6-y^6= (x^3+y^3)(x^3-y^3) 1st term is sum of cubes... 4 replies | 60 view(s) • March 25th, 2017, 21:53 MarkFL replied to a thread The Distance Across in Geometry \overline{MK}=\sqrt{(\sqrt{2}a)^2+(\sqrt{2}b)^2}=\sqrt{2\left(a^2+b^2\right)}=\sqrt{2(50)}=\sqrt{100}=10 :D 8 replies | 84 view(s) • March 25th, 2017, 21:31 At a guess you are forgetting about the cross term. (a + b)^2 \neq a^2 + b^2. It is (a + b)^2 = a^2 + 2ab + b^2. You are going to end up having to... 4 replies | 56 view(s) • March 25th, 2017, 21:07 MarkFL replied to a thread Lagrange Multipliers 2 in Calculus I arbitrarily chose another point on the constraint, so that we could do a comparison like I mentioned just now in the other thread. :D 9 replies | 84 view(s) • March 25th, 2017, 21:04 MarkFL replied to a thread Lagrange Multipliers in Calculus I chose the point as it is on the constraint. Using that point, we can determine if our one critical point is a maximum or a minimum. If the... 9 replies | 72 view(s) • March 25th, 2017, 20:52 Rewrite as \sqrt{2t+5}+\sqrt{2t+8}=\sqrt{8t+25}. What do you get when you square both sides? 4 replies | 56 view(s) • March 25th, 2017, 19:21 MarkFL replied to a thread Lagrange Multipliers 2 in Calculus I agree that the point (2,2), is the only one that meets all criteria. Now we need to compare the value of f at another point on the constraint,... 9 replies | 84 view(s) • March 25th, 2017, 19:08 MarkFL replied to a thread Lagrange Multipliers in Calculus I agree that of the 3 critical points, (1,1) is the only one in quadrant I. Now, we know this is either a maximum or a minimum, and to determine... 9 replies | 72 view(s) • March 25th, 2017, 11:15 MarkFL replied to a thread Factoring...6 in Pre-Calculus It might be more clear to state something like the following: The difference of cubes formula states: p^3-q^3=(p-q)\left(p^2+pq+q^2\right) ... 5 replies | 73 view(s) • March 25th, 2017, 10:47 MarkFL replied to a thread Lagrange Multipliers 2 in Calculus Consider: e^u=0 What do you get when solving for u? Okay, you correctly found x^2=y^2...what do you get when you substitute for... 9 replies | 84 view(s) • March 25th, 2017, 10:39 MarkFL replied to a thread Lagrange Multipliers in Calculus What I would do is use the constraint to determine y=2-x. Now substitute for y in both equations you mentioned, and solve for x, then your... 9 replies | 72 view(s) • March 25th, 2017, 02:30 This is a calculus question...please don't continue to post calculus questions in other forums. If given: ... 3 replies | 84 view(s) • March 24th, 2017, 23:17 greg1313 replied to a thread Factoring...8 in Pre-Calculus 1. Correct. 2. Correct. 3. Yes, apply the sum of cubes formula to 8a^3+27b^3. Be careful with your variable names. a does not necessarily... 2 replies | 39 view(s) • March 24th, 2017, 23:16 topsquark replied to a thread Factoring...7 in Pre-Calculus I mentioned this in another thread. Don't set the LHS of "a = a + b" It's too confusing. -Dan 3 replies | 48 view(s) • March 24th, 2017, 23:13 topsquark replied to a thread Factoring...6 in Pre-Calculus You need to clarify your variables. "b = (a - b)" isn't right. Pick a variable name, say, p... Anything but that b on the LHS.... Then you have p... 5 replies | 73 view(s) • March 24th, 2017, 23:12 MarkFL replied to a thread Lagrange Multipliers 2 in Calculus If you solve both equations for \lambda and then equate the results, you obtain: \frac{ye^{xy}}{2x}=\frac{xe^{xy}}{2y} Multiply through by 2:... 9 replies | 84 view(s) • March 24th, 2017, 22:57 greg1313 replied to a thread Factoring...7 in Pre-Calculus$$(a-b)^3=a^3-3a^2b+3ab^2-b^3$$Rearrange:$$\begin{align*}a^3-b^3&=(a-b)^3+3a^2b-3ab^2 \\ &=(a-b)^3+3ab(a-b) \\ &=(a-b) \\...
3 replies | 48 view(s)
• March 24th, 2017, 22:18
Yes. Then in case of doubt you after factoring can multiply and see the result
5 replies | 73 view(s)
• March 24th, 2017, 21:24
MarkFL replied to a thread Lagrange Multipliers in Calculus
Okay, so what this implies is: \frac{x}{\sqrt{6-x^2-y^2}}=\frac{y}{\sqrt{6-x^2-y^2}} Cross-multiply: x\sqrt{6-x^2-y^2}=y\sqrt{6-x^2-y^2} ...
9 replies | 72 view(s)
• March 24th, 2017, 21:05
topsquark replied to a thread Factoring...5 in Pre-Calculus
Yeppers! -Dan
2 replies | 33 view(s)
• March 24th, 2017, 16:18
MarkFL replied to a thread The Distance Across in Geometry
Using the Pythagorean theorem, we find: \overline{MK}=\sqrt{(\sqrt{2}a)^2+(\sqrt{2}b)^2}=\sqrt{2\left(a^2+b^2\right)} Now, we know that...
8 replies | 84 view(s)
• March 24th, 2017, 13:33
Is the angle contained by $a$ and $b$ equal to $90^\circ$? For that matter, what is the complete problem?
2 replies | 67 view(s)
• March 24th, 2017, 06:10
MarkFL replied to a thread [SOLVED] Minimum of function under constraint in Calculus
I would use W|A: W|A - optimize 2x+y subject to xy=18
8 replies | 254 view(s)
• March 24th, 2017, 04:29
The objective function is linear, so it describes a plane, and so I don't believe there will be any saddle points, or in fact any critical points...
4 replies | 62 view(s)
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