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Note that (n+2)! is greater than n! by (n+2)(n+1)......so using 398 = n, we have

(398+2)*(398 + 1) = 400*399 = 159,600

Line will be perpendicular if their slopes are negative reciprocal.

First, find the slope of  -2y + 4  =  6x + 8

                                      -2y  =  6x + 4

                                         y  =  -3x - 2

The slope of this line is  -3  so the slope of any line parallel to it will be  1/3.

Now, find the equation of the line that passes through  (2,-8)  with a slope of  1/3.

Since we know a point and a slope, let's use the point-slope form:  y - y1  =  m(x - x1)

--->   y - -8  =  (1/3)(x - 2)

--->   y  + 8  =  (1/3)(x - 2)

--->   3y + 24  =  x - 2

--->  -x + 3y  =  -26

--->   x - 3y  =  26     <---  This is the equation of the line perpendicular to  y  =  -3x - 2  at the point (2, -8)

To find the value of n of the point  (n, 40), replace y with 40:

        x - 3(40)  =  26

        x - 120  =  26

         x  =  146  =  n

I can just add 1 to yours...and I'd have you beat..of course, you could add 1 to mine and have me beat...and we could continue this indefinitely.....thus proving that there IS no "highest" number !!!

First let x = 0

So

3(0) - y = 5

-y = 5     so... y = -5      and there's one point.... (0, -5)

Next. let y = 0 and we have

3x- 0 = 5

3x = 5    divide both sides by 3  and x= 5/3

So the second point is (5/3, 0)

Now....just plot both points on a graph and draw a line through them !!!

Hyperbolic cosine.

x^-1 = 1/x

So we have

1/x > x

Note that there are NO positive integer values that make this true!!! These two functions intersect at x = 1 and that's the first positive integer. At all x's greater than this, 1/x < x  !!!!

We can convert the minutes to a decimal = 52/60 = .86666

So, sin(37.86666) = about .613

Because the function in the numerator is > 0 for all real numbers (thus, the graph never intersects the x axis), we only need to concern ourselves with the denominator.....!!!

This function will be undefined when the denominator = 0

So.....setting 2x^2 + x - 6 to 0 and factoring, we have

(2x -3)(x + 2) = 0       and setting each factor to 0, we have x = -2 and x = 3/2...so the graph is undefined at these two values (it has vertical asymptotes at these two values)....we just need to look at 3 intervals

When x < -2, the rational function > 0   (test -3 to see this is true)

And when x > -2 but < 3/2, the rational function < 0  (test 0)

And when x > 3/2 , the rational function > 0 (test 2)

So, the solution is

(-∞, -2) U (3/2, ∞)

it is$${\mathtt{6\,643}} = {\mathtt{6.643\times 10^{3}}}$$.

or maybe the ansewer is 14,000,000?

no, not really.

-Robert

or even that.

oh, thanks melody.

And the one two above this one.

Cphil;, please help me on this one too and the one above.

uh... do you mean 12?

6+6-9*9

6-6-9-9

thats it

First the number of possible sets = C(52,2) = 1326

a) Two spades.......there are 13 spades and we want to choose any set of 2 of them = C(13,2) = 78

So.... 78/1326 = 1/17 = about .059 = about 5.9%

b) Both are the same suite.....there are 13 cards in one suit.....so C(13,2) = 78. But there are 4 suites, so we have  ...

[4*C(13,2)] /1326 = 4/17 = about .235 or about 23.5%

c) Two kings .....   there are 4 kings and we want to choose 2 of them......so C(4,2) = 6

And..... 6/1326  = 1/221 = about .0045 = about .45%

c^3 + 4c > 5c^2      subtract 5c^2 from both sides

c^3 + 4c - 5c^2 > 0   rearrange

c^3 - 5c^2 + 4c > 0     set this = 0 and factor

c^3 - 5c^2 + 4c = 0

c(c^2 -5c + 4) = 0

c(c-4)(c-1) = 0

And setting each factor to 0 , we have that c =0, c = 4 and c =1

Now, adding back the inequality sign, we have

c(c-4)(c-1) > 0   

And if c < 0 ,   c(c-4)(c-1) < 0

And if c > 0 but < 1 ,  c(c-4)(c-1) is > 0

And if c > 1 but < 4,  c(c-4)(c-1) is < 0

And if c > 4, c(c-4)(c-1) > 0

OK...we can use

(-∞ < x < -11) U (3.5 < x < ∞)

Cphill please help me on this.

Please give a good explanation

how wouldyou write this in interval notation?

x(x+7.5) > 38.5        simplifying, we have

x^2 + 7.5x > 38.5    subtract 38.5 from both sides

x^2 + 7.5x - 38.5 > 0

Answer:  (-∞, -10.965)  ∪  (3465,+∞)

Because:

x(x + 7.5) > 38

x² + 7.5x - 38 > 0

First, find the solutions of  x² + 7.5x - 38 = 0

I used the quadratic formula and got  x =  3.465  and  x  =  -10.965

These two numbers divide the x-axis into three groups.

So, there are three groups  (x <  -10.965)        (-10.965 < x < 3.465)       (x > 3.465)

Try any number from the first group; I'll choose -20; and put it back into the original inequality:

       x(x + 7.5) > 38     ===>     -20(-20 + 7.5)  =  250 and that's > 38 go this section works.

Try any number from the second group; I'll choose 0; and put it back into the original inequality:

       x(x + 7.5) > 38     ===>     0(0 + 7.5)  =  0 and that's not > 38 go this section doesn't works.

Try any number from the third group; I'll choose 10; and put it back into the original inequality:

       x(x + 7.5) > 38     ===>     10(10 + 7.5)  =  175 and that's > 38 go this section works.

Since the first group and the third group both work, the answer is:  x < -10.965  or  x > 3.465.