Question

Can someone private message me? I need a TON of algebra 2 help, and I'd really like to explain the problem in a more private manner.

Answer 1

what you need?

Answer 2

Pm me? Dx

Answer 3

Fan me so I can message you back.

Answer 4

k

Answer 5

The design of a digital box camera maximizes the volume while keeping the sum of the dimensions at 6 inches. If the length must be 1.5 times the height, what should each dimension be?

Hint: Let x represent one of the dimensions, and then define the other dimensions in terms of x. (2 points)

Answer 6

the lenght is \(1.5\) times the height so if the height is \(x\) the lenght is \(1.5x\)

Answer 7

Okay. Gotcha.

Answer 8

oh no it doesn't say that does it, scratch that
lets make the width \(y\) so
\[x+1.5x+y=6\] or
\[2.5x+y=6\]

Answer 9

L+w+h right?

Answer 10

yes

Answer 11

Okay I see that.

Answer 12

now we want to maximize the volume
\[V=LWH=x\times 1.5x\times y\] we need to solve for \(y\)

Answer 13

\[2.5x+y=6\] so
\[y=6-2.5x\]

Answer 14

now the volume is \[V(x)=1.5x^2(6-2.5x)\]

Answer 15

is this a calculus class?

Answer 16

Algebra 2..

Answer 17

hmm i am stuck without calculus because you have a cubic funcition
the answer is
H = 1.6
L = 2.4
W = 2.0

Answer 18

Okay. Thank you.. I've been stuck on that one for awhile. I'm working on another, if you give me a second I'll post the next.

Answer 19

ok really i have no idea how you do that without calc

Answer 20

I'm seriously at a loss of words, some of this is beyond me. I don't even take calc next, just pre calc.

Answer 21

ok lets do one more
them maybe some tomorrow
you have time tomorrow?

Answer 22

Use Pascal’s triangle to expand the binomial.

(d – 5y)6 (2 points)

Answer 23

almost all day tomorrow.

Answer 24

ok i see it says "two points" so perhaps we can just get the answer, is that good enough?

Answer 25

This one I have to work out. If you just explain it to me I will do all of the work.

Answer 26

yikes ok
first the answer, it is \[d^6-30 d^5 y+375 d^4 y^2-2500 d^3 y^3+9375 d^2 y^4-18750 d y^5+15625 y^6\]

Answer 27

now the working out
we need the sixth level of pascals triangle, the one that begins with 1 6

Answer 28

i don't know if you have a picture of pascal's triangle, you can google it, but the sixth level has the numbers
\[1,5,15,20,15,6,1\]

Answer 29

those are the coefficents we need
then
\[(a+b)^6=a^6+6a^5b+15a^4b^2+20a^3b^3+15a^2b^4+6ab^5+b^6\]

Answer 30

Okay. Ugh.

Answer 31

where you see an \(a\) put a \(d\)
where you see a \(b\) put \(-5d\)

Answer 32

you can see why the numbers at the end get so big

Answer 33

Okay.. So.. one sec.

Answer 34

in any case if you do it right you get \[d^6-30 d^5 y+375 d^4 y^2-2500 d^3 y^3+9375 d^2 y^4-18750 d y^5+15625 y^6\]

Answer 35

I'm going to have faith in you. Thank you..

Answer 36

actually i did not do it by hand, it is donkey work
i did it here
http://www.wolframalpha.com/input/?i=%28d-5y%29^6

Answer 37

x4 – 41x2 = –400 I have to find the real and complex solutions for this, I know it's not too hard.

Answer 38

let me refresh i got the dreaded quesiton marks

Answer 39

no this one i s going to be easy

Answer 40

Okay.

Answer 41

\[x^4-41 x^2+400 = 0\] is a start then this one actually factors as
\[(x^2-25)(x^2-16)=0\]

Answer 42

factor again , get
\[(x+5)(x-5)(x+4)(x-4)=0\] set each factor equal to zero and solve in your head, get
\[x=5,x=-5,x=4,x=-4\]

Answer 43

snappy
one more?`

Answer 44

That was easy, okay. One moment.

Answer 45

If 2 + square root 3 is a polynomial root, name another root of the polynomial, and explain how you know it must also be a root.

Answer 46

I know how to find roots, but when I already have one I don't know how to plug it in?

Answer 47

it is the "conjugate' \(2-\sqrt3\)

Answer 48

that is all, they come in conjugate pairs
if the coefficients are integers then it must be \(2-\sqrt3\) because
\[(2+\sqrt3)(2-\sqrt3)=4-3=1\] an integer

Answer 49

Okay! Just the opposite!

Answer 50

you don't have to "find" it because you are told that one is \(2+\sqrt3\) the other is the conjugate that is all
not "opposite" but "conjugate"

Answer 51

Conjugate, got it. (: Should probably sound smarter than I claim to be. Thank you so much.

Answer 52

yw
get some rest