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Today, 21:53

MarkFL replied to a thread Quadratic Inequality...6 in Pre-Calculus

The solution is: \,\cup\, You missed an interval because -2 is not in the interval ... (an alarm should have gone off in your head when you saw...

6 replies | 47 view(s)

Today, 19:43

MarkFL replied to a thread Inequality & Calculator in Pre-Calculus

What you should have is: \frac{x^6-3x^3+1}{x^3}\ge0 Recall, you don't want to multiply an inequality by an expression having an unknown sign. ...

3 replies | 34 view(s)

Today, 16:16

MarkFL replied to a thread [SOLVED] 206.11.02.45 find the power series representation for g, Give interval of convergence in Calculus

The information regarding how $f$ and $g$ are related is missing...without that, we cannot help. :D

5 replies | 62 view(s)

Today, 14:28

MarkFL replied to a thread Quadratic Inequality...6 in Pre-Calculus

I stopped going to movie theaters several years ago because all the phones lit up like flashlights in my eyes during the entire show is just too...

6 replies | 47 view(s)

Today, 02:28

MarkFL replied to a thread Quadratic Inequality...6 in Pre-Calculus

Factor: (x^2-9)(x^2-16)\le0 Continue factoring...:D

6 replies | 47 view(s)

Today, 02:25

MarkFL replied to a thread Quadratic Inequality...5 in Pre-Calculus

You want to determine the roots of both the numerator and denominator as your critical numbers (i.e., values for which the expression can change...

2 replies | 30 view(s)

Today, 02:02

MarkFL replied to a thread Inequality & Calculator in Pre-Calculus

Move everything to the LHS, and then combine all terms into a rational expression...what do you then have?

3 replies | 34 view(s)

Yesterday, 22:03

MarkFL replied to a thread Two Pieces of Wire in Pre-Calculus

We require both: 0<x 0<12-x Combined, this gives us: 0<x<12

18 replies | 142 view(s)

Yesterday, 21:41

MarkFL replied to a thread Stanley A. Ellisen...Quotes in Chat Room

For better forum organization, I have merged the 4 threads pertaining to Stanley A. Ellisen quotes into one thread. This way they can all be...

4 replies | 57 view(s)

Yesterday, 21:12

MarkFL replied to a thread Two Pieces of Wire in Pre-Calculus

x and x - 12 represent lengths (assumed to be in cm)...and so must be positive. Lengths cannot be negative, and if we are to actually have two pieces...

18 replies | 142 view(s)

Yesterday, 19:13

MarkFL replied to a thread Two Pieces of Wire in Pre-Calculus

At this point you can multiply through by 8 to get: x^2-12x+32>0 Then factor: (x-4)(x-8)>0 Now solve this inequality, subject to:

18 replies | 142 view(s)

Yesterday, 11:04

MarkFL replied to a thread Find Perimeter of Rectangle in Pre-Calculus

When I was a student, I found one of the best ways to understand things is to look at them in general terms. For example, in this problem, rather...

21 replies | 182 view(s)

Yesterday, 10:49

MarkFL replied to a thread Find Perimeter of Rectangle in Pre-Calculus

What we see is that we must have: L=W And so, what we have found is that for a rectangle of a given area, the perimeter is the smallest it can...

21 replies | 182 view(s)

Yesterday, 10:34

MarkFL replied to a thread Find Perimeter of Rectangle in Pre-Calculus

Your next step should be: (L-W)^2=0 So, how must L and W be related in order for this to be true?

21 replies | 182 view(s)

Yesterday, 10:28

MarkFL replied to a thread Two Pieces of Wire in Pre-Calculus

No, what we want is: A\left(W_1\right)+A\left(W_2\right)>5 A(x)+A(12-x)>5 Now, the arguments for the area function represent wire lengths,...

18 replies | 142 view(s)

Yesterday, 10:10

MarkFL replied to a thread Two Pieces of Wire in Pre-Calculus

Yes, now we need to answer the question: For which values of x will the combined areas of the squares exceed 5 cm^2? We have two pieces of wire...

18 replies | 142 view(s)

Yesterday, 10:00

MarkFL replied to a thread Two Pieces of Wire in Pre-Calculus

Okay, you have a piece of wire whose length is let's say W...you bend it into a square...what is the perimeter of the square? Then using your formula...

18 replies | 142 view(s)

Yesterday, 09:55

MarkFL replied to a thread Find Perimeter of Rectangle in Pre-Calculus

Yes, once you simplify, you will find the implication. :D

21 replies | 182 view(s)

Yesterday, 09:53

MarkFL replied to a thread Quadratic Inequality...4 in Pre-Calculus

Yes, now combine terms on the LHS...:D

5 replies | 49 view(s)

Yesterday, 09:44

MarkFL replied to a thread Two Pieces of Wire in Pre-Calculus

Let's use x for the length of the sides of the square, so we have: P=4x A=x^2 Now, we want to replace x in the formula for the area with an...

18 replies | 142 view(s)

Yesterday, 09:39

MarkFL replied to a thread Find Perimeter of Rectangle in Pre-Calculus

You're just seeing what the equation implies about the relationship between L and W. :D

21 replies | 182 view(s)

June 23rd, 2017, 22:50

MarkFL replied to a thread Find Perimeter of Rectangle in Pre-Calculus

We have: \sqrt{LW}\le\frac{L+W}{2} When I ask "when does equality occur," I am essentially asking you to solve: \sqrt{LW}=\frac{L+W}{2} ...

21 replies | 182 view(s)

June 23rd, 2017, 21:56

MarkFL replied to a thread 206.07.05.88 partial fractions??? in Calculus

I would look at a substitution like: u=\sqrt{x^2+4x+3}\implies dx=\frac{u}{x+2}\,du And the integral then becomes: I=\int\frac{1}{u^2+1}\,du

1 replies | 32 view(s)

June 23rd, 2017, 19:33

MarkFL replied to a thread Two Pieces of Wire in Pre-Calculus

What is the area $A$ of a square whose perimeter is $P$?

18 replies | 142 view(s)

June 23rd, 2017, 19:25

MarkFL replied to a thread Quadratic Inequality...4 in Pre-Calculus

You don't want to multiply an inequality by an expression whose sign is unknown...arrange everything to one side and then get your critical values...

5 replies | 49 view(s)

June 23rd, 2017, 19:21

MarkFL replied to a thread Quadratic Inequality...3 in Pre-Calculus

You are assuming x is positive when you do that. A better step is to subtract x/2 from both sides: \frac{2}{x}-\frac{x}{2}<0 Combine terms: ...

2 replies | 40 view(s)

June 23rd, 2017, 15:00

MarkFL replied to a thread Quadratic Inequality in Pre-Calculus

Yes, we have a parabola opening upwards, and given that it has two real roots, we should expect to find it to be negative in between its roots. :D

7 replies | 75 view(s)

June 23rd, 2017, 14:44

MarkFL replied to a thread I have mathematics problems for solving but i can not understand how to solve these mathematics? in Pre-Calculus

Okay, I have several issues here: 1.) We ask that you post no more than 2 questions per thread: 2.) You've shown no effort:

1 replies | 71 view(s)

June 23rd, 2017, 13:38

MarkFL replied to a thread Quadratic Inequality...2 in Pre-Calculus

In this problem, you have a function representing a parabola that opens upwards. We should then expect, given that it has two real roots, that the...

7 replies | 80 view(s)

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