Question

Help please

Answer 1

it says nothing about whether a or b have to be positive/negative/integers/whatever

you only know that b is an exponent and that means b is the number that says how many times to multiply a by itself

so A+D

Answer 2

just start off with the a terms

use rule 1 + 2 to simplify (a^2 * a^3)/(a^5)

Answer 3

gonna go to sleep tag me again when you're awake

Answer 4

@Vocaloid I'm back

Answer 5

\(\color{#0cbb34}{\text{Originally Posted by}}\) @Vocaloid
just start off with the a terms

use rule 1 + 2 to simplify (a^2 * a^3)/(a^5)
\(\color{#0cbb34}{\text{End of Quote}}\)

have you made any progress on this?

Answer 6

well this simplified would be a^5

Answer 7

the numerator becomes a^5

so (a^5)/(a^5) = ?

Answer 8

1

Answer 9

good, now we move on to the b terms

b * b^2 = ?

Answer 10

b^3

Answer 11

good, now we move on to the c terms

c/(c^2 * c^4) = ?

Answer 12

1/c^5

Answer 13

good so putting everything together --> b^3/c^5 --> your answer

Answer 14

thank you

Answer 15

\[\log (\frac{ (x+y)^3(x-y)^2 }{ x^2+y^2 })\]

Answer 16

is this the right answer for this

Answer 17

yup good

Answer 18

it's basically just the reverse of what you just did, separate the components of the log then drop the exponent down as coefficients

Answer 19

2log(x+3)... then continue with the rest of the log

Answer 20

the website is trying to expand the logarithm all the way even though it's probably not needed

2log(x+3) - log(x-2) - 4log(x^2+5) is what they are looking for

Answer 21

rewrite as an exponential equation

\[\ln (x+y)=5\]

Answer 22

raise both sides to the power of e

Answer 23

e^5=x+y

Answer 24

good but you might want to re-write that as y = e^5 - x so it looks like an equation of y in terms of x

Answer 25

rewrite as an logarithmic equation

2^4=(a-b)

Answer 26

y = (a - b), b is the base 2 and x is the exponent 4

re-write in the log form

Answer 27

log2(a-b)=4

Answer 28

good

Answer 29

I'm sorry not this one

Answer 30

a. 5
b. -4
c. -3
d. 0

Answer 31

well done

Answer 32

I dont know how to solve this for t

Answer 33

divide both sides by 500 first

then take the natural log of each side

then dividing by 0.06 will isolate t

Answer 34

4.709

Answer 35

check your calculations again

let's just take it one step at a time, divide both sides by 500 and lmk what you get

Answer 36

5=e^0.06t

Answer 37

good, now take the natural log of each side

Answer 38

wait is it 26....?

Answer 39

good but it wants 3 decimal places so your answer would be...?

Answer 40

26.824

Answer 41

good, that's it

Answer 42

since ln(0) is undefined which two choices can you eliminate right off the bat?

Answer 43

um c

Answer 44

what value of x will make ln(x-5) = ln(0)?

Answer 45

oh a and b

Answer 46

good, a and b are out

the actual behavior of ln(x-5) show that it increases quickly before crossing (6,0) so D is the best choice

Answer 47

for 13 if we plug in x = 0 we get 6, making A and B possible candidates

since the exponent is -x it will keep decreasing as x ---> infinity so B

Answer 48

=)

Answer 49

14 - what is the common ratio?

Answer 50

x3

Answer 51

good (just 3)

so r = 3

a1 = first term = 2

use nth term = a1 * r ^ (n-1) to find the nth term

Answer 52

2 * 3 ^ (n-1)

Answer 53

good

try to remember what n stands for

Answer 54

21

Answer 55

good, n = 12 so evaluate 2 * 3 ^ (n-1)

Answer 56

69735

Answer 57

you left off some digits, it's a very big #

Answer 58

6973568802

Answer 59

good

Answer 60

for 15 figure out the common ratio by dividing a3/a2

Answer 61

0.7

Answer 62

good, now we need to figure out what a1 is

if a1 * r = a2 then what is a1?

Answer 63

a1 * r = 0.7

Answer 64

would r be 6?

Answer 65

we calculated r earlier

Answer 66

0.7

Answer 67

a1 * 0.7= 0.7
a1=1

Answer 68

awesome now you have everything you need

evaluate sum

Answer 69

so
sn=1(1-0.7^n/1-0.7)

Answer 70

yes, keep going

Answer 71

remember what n stands for

also don't enter sn into the formula, it will treat sn as s*n

Answer 72

just enter this part 1(1-0.7^n/1-0.7)

and replace n w/ the appropriate value

Answer 73

n is 0.7?

Answer 74

n is the number of terms

r is 0.7.

Answer 75

6?

Answer 76

good, now evaluate the expression

Answer 77

0.74

Answer 78

check your calculations again, the answer is much bigger than that

Answer 79

(1-0.7^6)/(1-0.7) = ?

Answer 80

2.94

Answer 81

good but let's try to leave as many digits as possible so 2.94117

Answer 82

okay rewrite using radicals\[(a^\frac{ 3 }{ 4 })^5\]

Answer 83

i got\[(4 \sqrt{a^3})^5\]

Answer 84

yeah, that's right (just make sure the 4 is sitting on the radical sign not out in front)

also I"m not sure if they'd want you to multiply that 5 through the exponent but let's go with your answer

Answer 85

rewrite using radical exponents\[\sqrt[5]{x^2}\]

Answer 86

basically it's the reverse of the earlier problem, the exponent becomes the numerator of the fraction-exponent and the radical becomes the denominator

Answer 87

\[x^\frac{ 2 }{ 5 }\]

Answer 88

good

Answer 89

If you deposit $1,000 into an account that pays 4% interest compounded continuously, how long will it take the account to grow to $2,000?

Answer 90

A = Pe^rt solve for t

Answer 91

A = Pe^rt
we are given A, P and r:
2000 = 1000e^0.04t
divide both sides by 1000:
2 = e^0.04t
take Napierian log of both sides:
ln2 = 0.04t
divide both sides by 0.04:
t = ln2/0.04 ~ 17.33 years or 17years 4 months

Answer 92

is this right

Answer 93

yeah that's good

Answer 94

we want to know when Q(t) = 0.10Q_0

so plug in 0.10Q_0 for Q(t) and solve for t, you're given everything else and Q_0 should cancel out on both sides

Answer 95

0.1

Answer 96

check your calculations again, it should be much bigger than that

0.10Q_0 = Q_0 * e^(-0.07t) solve for t

Answer 97

0.10= * e^(-0.07t)

Answer 98

um what would e be?

Answer 99

e is euler's number and always has this value

Answer 100

the software you are using should have e automatically programmed into it, look for an italicized e

Answer 101

32.89

Answer 102

http://www.wolframalpha.com/input/?i=0.10+%3D+e%5E(-0.06x)

Answer 103

this gives me 38 seconds (since they want it rounded up to the nearest second)

Answer 104

yeah its probably my mistake in calculations

Answer 105

for 21 they're probably looking for "exponential"
22 - "limited"
23 - probably 'carrying capacity"

Answer 106

Thank you so much