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[113  -  1] / 2  +  1 =57 terms

57 C 3 =29,260 - combinations, or number of totals.

The above total includes all duplicates, which number: 29,097   +  163 unique totals=29,260

(a) (x,y) = (-5,1)

(b) (x,y) = (7/2, -17/2)

The solutions are pi/20, pi/10, 3*pi/5

Transitive Property of Equality

Properties of addition, subtraction, multiplication, and division

Angles forming a linear pair sum to 180°

Definition of angle bisector

Definition of complementary angles

Definition of congruence

Definition of perpendicular lines

Definition of supplementary angles

Same with me, I've not seen this notation before, so this could be wrong.

I think that the e's are unit vectors and that we are being given the parametric equations of the line of integration.

\(x=u^{2},\quad y=2u, \quad z=u^3\)

from which

\(2xyz^{2}=2.u^{2}.2u.(u^{3})^{2}=4u^{9},\)

and

\(dr=e_{x}dx+e_{y}dy+e_{z}dz=e_{x}2u\, du+e_{y}2\, du+e_{z}3u^{2} du\)

So,

\(\displaystyle \int_{L}2xyz^{2}\, dr=e_{x}\int^{1}_{0}4u^{9}.2u\,du+e_{y}\int^{1}_{0}4u^{9}.2\, du+e_{z}\int^{1}_{0}4u^{9}.3u^{2}\,du \\ =(8/11)e_{x}+(4/5)e_{y}+e_{z}.\)

Apologies if that's a load of rubbish !

What is the value of b+c if x^2+bx+c>0 only when \( x\in (-\infty, 2)\cup(2,\infty)?\)?

\(x^2+bx+c>0 \)

this is a concave up parabola.

If this function is greater than zero for all values of x except for x=2  then the vertex is  (2,0)

And there will only be one root.

so

\(x^2+bx+c=(x-2)^2\\ b=-4,\;c=4\\ b+c=0 \)

ANSW = 0 with a domain x all -1,1 and y all 0 to infinity

The parabola and the circle should just touch.

The blue circle is your solution.  As you can see your circl does not touch the parabola.

So the parabola is always more than 3.14 units from the origin.

Your answer is not correct.

The green circle is guests solution.  As you can see, his/her cirlce does appear to be tangential to the parabola. 

So the green answer appears to be correct.

If Polya is never to visit the sixth floor after she begins, we know that her first stop is at the seventh floor. Moreover, her second stop must be at the eighth floor. She has three moves left, and the only way she can ever visit the 6th floor from the 8th floor in three remaining moves is to go down in both of the following two steps. The probability of getting to the eighth step in two moves is \(\dfrac{1}{2^2}=\dfrac{1}{4}\). By similar reasoning, Polya has a \(\dfrac{1}{4}\) probability of getting from the eighth floor to the sixth floor in the next two moves, so the probability of not going downward in the next two steps is \(1-\dfrac{1}{4}=\dfrac{3}{4}\). So the overall probability of never hitting the sixth floor after the beginning is \(\dfrac{1}{4}\cdot\dfrac{3}{4}=\boxed{\dfrac{3}{16}}.\)

There are \(10^3=1000\) possible codes without restrictions. There are \(3\cdot9=27\) codes that differ in only one spot from mine (three choices for the differing digit and nine choices for its value), 3 codes that result from transposing two digits (have three choices for the fixed digits), and Reckha also can't use my code itself. Thus Reckha has a total of \(1000-27-3-1=\boxed{969}\) available codes.

Interesting answer, isn't it?

Let u and v be the solutions to 3x^2 + 5x + 7 = 2x^2 - 4x - 11. Find u/v + v/u.  

Start with the given                                                   3x² + 5x + 7  =  2x² - 4x - 11 

Subtract 2x² – 4x – 11 from both sides to obtain       x² + 9x +18  =  0  

Factor that resultant equation                                  (x + 6)(x + 3)  =  0  

Therefore the two solutions to the quadratic are       x = –6  and  x = –3  

So one of them is "u" and the other is "v"  

We want the solution to                                               (–6 / –3) + (–3 / –6)   

What this equals is                                                       (2) + (1/2)  

So the answer is                                                           5/2  or  2.5  

_.

(a) c = 4/5

(b) c > 4/5

(c) c < 4/5

C = 50t + 300

The derivative is \(-\frac{3}{2} x^{-7/2} + \frac{7}{4} x - 3x^{3/2}\)

Melody, I think my answer is correct.

The second line in your post proves that.

\(x^2+y^2=3.14^2\)

The exact value is: \(3.14005494464\)

You switched colors. Not correct! See answer 7#.

  !