Question

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Answer 1

@Vocaloid Gotta metric ton of math I could use assistance with if you can x.x

Answer 2

yeah sure

Answer 3

2. Give an example of each of the following:
(a) A function whose domain is \([2,\infty]\)
(b) An arithmetic sequence
(c) A system of equations with no solutions

Answer 4

well for the first one we could modify a square root function

sqrt(x) gives a domain of [0, infinity)
so if we change it to sqrt(x-2) we get a domain of [2,infinity)

Answer 5

for an arithmetic sequence we could imagine a scenario like a phone bill where there's a flat fee a1 = $50 for example, and d = 0.01 per minute n, giving us: an = a1 + d(n-1) = 50 + 0.01(n-1)

Answer 6

for the last one just write down two parallel lines (same slop, different intercept)

y = mx + b where m is the slope and b is the intercept

Answer 7

*same slope

Answer 8

Alright,
for \(f(x)=\frac{1}{x^2-3}\) find:
(a) f(3)
(b) f(2+h)

Answer 9

just plug in x = 3 for a and x = (2+h) for b

Answer 10

for \(f(x)=\frac{1}{x-5}\) and \(g(x)=2^2-2\), find:
(a) \(f\circ g\)
(b) \(g\circ f\)

Answer 11

so f dot g means take the result for g(x), and substitute for x in f(x)

Answer 12

g(x) = 2, so you would use x = 2 for f(x) and find f(x)

Answer 13

for part b, just do it the other way around, look at g(x) and substitute f(x) into it (since g(x) doesn't have x in it, then g dot f would also just be 2

Answer 14

Ok,

For sequence given by \(a_n=4n+5\),
(a) find the first five terms
(b) find the sum of the first 25 terms,
(c) Is this an arithmetic sequence? If so, how can you tell? If not, why not?

Answer 15

for part a:

start with n =1 and find 4n + 5. then do n = 2, n = 3, n = 4, and n = 5

Answer 16

for part b:

sum = n(a1+an)/2 where a1 = the term when n = 1 and an = the term when n = 25

Answer 17

for part c: observe your sequence for part a and see if there's a common difference (the terms should increase/decrease by the same amount each time)

Answer 18

what does it mean by "area bounded by"?

Answer 19

graph all the inequalities and shade in the area that would satisfy all the inequalities

Answer 20

it will help to consider them one at a time (for example, for y < 1/2 x + 6 you would just graph y = (1/2)x + 6 with a dotted line and then shade underneath)

Answer 21

repeat this process with all of the inequalities, and then emphasize the area where all of the shaded regions overlap

Answer 22

Ok,

For the function defined by: \(f(x)=\left\{\begin{matrix}x^2,x\le1 \\ 2x+1,x\gt1,\end{matrix}\right\}\)
Evaluate Graph

I suck at sine functions

Answer 23

does it just say "evaluate graph"? that's odd

Answer 24

No, evaluate and graph, sorry about that

Answer 25

2 different parts

Answer 26

I would just use software to do this tbh

Answer 27

Oh, ok then, I was trying to avoid desmos x'D

Answer 28

you would just graph x^2 and then 2x + 1, and then just erase the parts of the graph that go outside the inequality

Answer 29

so for x^2 x≤1, just graph x^2 and then erase all the parts where x is greater than 1

Answer 30

^should be more like that since it crosses the origin

Answer 31

Ah, Ok...

the first part of this one is easy enough, but idk about the second part

Answer 32

if graphing is easier for you just graph and check if the intersection point is the same as the algebraic solution

Answer 33

if you know how to do row-reduction, then that will work to if you reduce to:

\[\left[\begin{matrix}1 & 0 \\ 0 & 1\end{matrix}\right]\]

Answer 34

that will give you the solution matrix on the right hand side

Answer 35

Ok,

Given matrices A, B, and C below, perform the indicated operations if possible. If the operation is not possible, explain why.
\(A=\left[\begin{matrix}2&-1&0\\0&5&0.3\\1&4&10\end{matrix}\right],B=\left[\begin{matrix}5&0&2\\1&-3&9\\2&0&4\end{matrix}\right],C=\left[\begin{matrix}1 & 3&5\end{matrix}\right]\)

(a) 3A + B
(b) 2B + C
(c) CA

Answer 36

since A and B have the same dimensions you can add/subtract them

for example: for a) 3A + B you would multiply every term in A by 3, and then add the corresponding entries in the matrices

Answer 37

for CA since C has dimensions 1 x 3 and A has dimensions 3 * 3 you can multiply them to get a 1 * 3 matrix

Answer 38

this is hard to explain but if you're in a hurry just use a matrix calculator

Answer 39

Ok, I'm not even typing this one

Answer 40

a) isn't too bad, just find f(1) and g(1) from the table and then do 3f + 2g

Answer 41

for b) find g(-1) = "some value"
then find f at that value (not -1) to get your answer

Answer 42

Express the following function, as a composition of two functions f and g.
\(h(x)=\frac{x^2}{(x^2+4)}\)

Answer 43

idk how to explain this but you could use g(x) = x^2 and f(x) = x/(x+4) since f dot g will give you h(x)

Answer 44

basically it's working backwards to find the composition instead of evaluating the composition

Answer 45

Finally is this massive question

Answer 46

a) f(x) is just x minus the coupon so
f(x) = x - 25

Answer 47

b)

g(x) is (1-0.2)x this is a 20% reduction in x

Answer 48

c) and d) f dot g is the price when you apply the sale discount first and g dot f is the price when you apply the coupon first

Answer 49

for e) you can calculate f dot g and g dot f yourself and you will see that they're not the same function, thus order matters

Answer 50

Ok, thank you.
(also if I have any troubles with these when I go back over them and try based off of what you told me, then I'll probably ask for more help ¯\_(ツ)_/¯)

Answer 51

np

I'm kind of in zombie mode right now so my explanations might not be that great today ;_;