Someone please help... ap calc summer work... and i've forgotten how to do most of it?

Question

6) For what values of k is 5x+ky=3 parallel to 2x-3y? For what values of k are the two lines perpendicular?

13) Remembering that for even functions f(-x)=f(x) and that for odd functions f(-x)=-f(x) show whether the following functions are even, odd or neither
a. y=x^4
b. y= x-x^4
c. y= 1/((x^2) -4)
d. y= -2(x^3) +4x

21) Simplify each of the following
a. ((2/3)x^(-3))(15x^7)
b. (x^3)((2yz^2)^3)
c. ((3(x^3))(4(x^5))) / ((x^2)^3)
d. ((2(y^4))((3(y^2))^2)) / ((y^3)^4)
e. (3(a^(-2))(b^3))^(-3)

22 )Simplify by removing all possible factors from the radical
a. sqroot (9(a^8)b)
b. cubed root (24(a^4)(b^8))
c. sqroot (75 / (a^6))

23) Factor each of the following completely
c. 4(x^16) -9(y^6)
d. 6(x^2) + 7x - 20
e. 3(x^2) -5x + 2
h. (x^2) +4x + 4 + 9(y^2)

Additional Details:
I'm not really just wanting answers.. as it says i just need someone to remind me how to do these... so i can do them.. i have already learned all this just forgotten how to do it

Answer 1

you seem to want all your homework done.....

6) For what values of k is 5x+ky=3 parallel to 2x-3y?
2x-3y=????
the slope is 2/3 so for the line 5x +ky =3 to be parallel it needs to have the same slope:
-5/k= 2/3
so k =(-5)(3)/2 = 15/2
For what values of k are the two lines perpendicular?
here the slope -5/k = -3/2
so k = 5(2)/3 = 10/3

13) Remembering that for even functions f(-x)=f(x) and that for odd functions f(-x)=-f(x) show whether the following functions are even, odd or neither
a. y=x^4 even
b. y= x-x^4 neither
c. y= 1/((x^2) -4) even
d. y= -2(x^3) +4x odd

21) Simplify each of the following
a. ((2/3)x^(-3))(15x^7)
b. (x^3)((2yz^2)^3)
c. ((3(x^3))(4(x^5))) / ((x^2)^3)
d. ((2(y^4))((3(y^2))^2)) / ((y^3)^4)
e. (3(a^(-2))(b^3))^(-3)
this is way too much work.....

22 )Simplify by removing all possible factors from the radical
a. sqroot (9(a^8)b)= 3 a^4 b^{1/2}
b. cubed root (24(a^4)(b^8))
c. sqroot (75 / (a^6)) = sqrt(75)/a^3

23) Factor each of the following completely
c. 4(x^16) -9(y^6)= (2x^8-3y^3) ( 2x^8 +3y^3)
d. 6(x^2) + 7x - 20
e. 3(x^2) -5x + 2
h. (x^2) +4x + 4 + 9(y^2)
again, too much work....

Answer 2

6) For what values of k is 5x+ky=3 parallel to 2x-3y?
the slope of 2x-3y = 1 is 2/3. the line 5x +ky =3 is parallel if they have the same slope:
-5/k= 2/3
so k =(-5)(3)/2 = 15/2
For what values of k are the two lines perpendicular?
here the slope -5/k = -3/2
so k = 5(2)/3 = 10/3

13) Remembering that for even functions f(-x)=f(x) and that for odd functions f(-x)=-f(x) show whether the following functions are even, odd or neither
a. y=x^4 even
b. y= x-x^4 neither
c. y= 1/((x^2) -4) even
d. y= -2(x^3) +4x odd


22 )Simplify by removing all possible factors from the radical
a. sqroot (9(a^8)b)= 3 a^4 b^{1/2}
c. sqroot (75 / (a^6)) = sqrt(75)/a^3

23) Factor each of the following completely
c. 4(x^16) -9(y^6)= (2x^8-3y^3) ( 2x^8 +3y^3)

Answer 3

6. Remember the slope-intercept form of a line? That is:
y = mx + b

Here you are interested in "m" which is the slope of the line. If two lines have the same slope then they are parallel. If ltwo lines are perpendicular then, if "m" is the slope of one the other will have a slope of "-1/m".

13. Just substitute in x and -x and see what happens with y. Take y = x^3, if you put in -x you get y = -x^3 so it is an odd function.

21. This just means to multiply numbers, combine terms, etc to make some equation simpler to read. I shall illustrate with the first:
((2/3)x^(-3))(15x^7)
[(2/3)(-3)(15)]x^(-3)(x^7) = -30x^4

22. Remove stuff from under the square root sign that is a perfect square. For example SQRT(81 x^5) = 9x^2SQRT(x) since 9 is the square root of 81 and x^5 = x*x^2*x^2

23. Not sure what to say other than factor them. I guess you could say it means turning expressions or parts of expressions into terms of the form (....)(.....). I will use the first as an example. Both terms are perfect squares and since it is a squared term minus a squared term it can be written as:
(2x^8 - 3y^3)(2x^8 + 3y^3)
Something of the form A^2 - B^2 can be written as (A - B)(A + B)
The second is a little tougher but it can be factored into something along the lines of (ax + b)(cx - d) where ac=6 and bd=20 and bc-ad = 7

Answer 4

(a million) Multiply by ability of x^2 / x^2 to get (9x^2 - a million) / x(3x+a million) the impressive is the version of two squares. i think of you are able to take it from right here. (2) Multiply by ability of (a million+?5) / (a million+?5) (3) ((2x / 4?) + (a million - x/2)) = 0 x / 2? + a million - x/2 = 0 Multiply the two factors by ability of 2?: x + 2? - ?x = 0 2? = ?x - x 2? = x(?-a million) 2? / (?-a million) = x