Mathematics, 28.03.2020 19:22 evere11605

Find n please help me i’m desperate

Answers: 2

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Answers

Answer from: sa9334

Step-by-step explanation:

First thing we need to do is to reconcile that r to the negative power. You do that by following the rules for exponents. If

$\frac{x^m}{x^n}$ then the rule is to subtract the lower exponent from the upper:

$x^{m-n}$

Doing that with our base of r:

$\frac{r^3}{r^{-4}}$ is $r^{3-(-4)}$ which is r^7

So it looks like what we have now is:

p^3q^2(p^4q^nr^7)=p^7q^5r^7

NOW we will follow the rules for multiplying like bases with exponents. The rule for that is if you have like bases and you are multiplying those like bases, you add the exponents. So I'm going to kind of break up that problem and put the like bases together:

p^3p^4q^2q^nr^7=p^7q^5r^7

Working on the left side, p to the 3rd times p to the 4 gives you p to the 7th, which is what we have on the right. The r to the 7 is also the same on the left and the right. Working on the q's now, if we have q to the 2nd and we are looking for n, then

$q^{2+n}=q^5$ so 2 + n = 5 and n = 3

Answer from: ReaLily

n = 3

Step-by-step explanation:

${p}^{3}. {q}^{2} \bigg(\frac{ {p}^{4}. {q}^{n} . {r}^{3} }{{r}^{ - 4} } \bigg) = {p}^{7} . {q}^{5} . {r}^{7} \\ \\ {p}^{4 + 3}. {q}^{n + 2} . {r}^{3 + 4} = {p}^{7} . {q}^{5} . {r}^{7} \\ \\ {p}^{7}. {q}^{n + 2} . {r}^{7} = {p}^{7} . {q}^{5} . {r}^{7} \\ \\ {q}^{n + 2} = \frac{{p}^{7} . {q}^{5} . {r}^{7}}{{p}^{7} . {r}^{7}} \\ \\ {q}^{n + 2} = {q}^{5} \\ \\ n + 2 = 5 \\ \\ n = 5 - 2 \\ \\ n = 3$

Answer from: Quest

/-/////////looks tough ‍♂️
Use the image below, find the y value for the point hat divides the line segment cd into a ratio of

Answer from: Quest

part a

answer: a reasonable domain is $0 \le n \le 10$ where n is a real number. so n can be between 0 and 10. both endpoints are included.

work shown:

n is the number of days after the experiment starts. the smallest n can be is n = 0 which means that 0 days have gone by, and we're at the start. to find out how large n should be, then replace f(n) with 16.13 and solve for n. use logarithms to isolate the exponent.

f(n) = 12*(1.03)^n

16.13 = 12*(1.03)^n

16.13/12 = (1.03)^n

1.34416666666667 = (1.03)^n

(1.03)^n = 1.34416666666667

log[ (1.03)^n ] = log[ 1.34416666666667 ]

n*log[ 1.03 ] = log[ 1.34416666666667 ]

n = log[ 1.34416666666667 ]/log[ 1.03 ]

n = 10.0062999823929

this rounds to n = 10 which is fairly close but not 100% perfect. so this is the largest n can be.

note: if you plug n = 10 into f(n), you'll get roughly 16.127 which rounds to 16.13 (this comes up again in part c)

=====================================

part b

answer: the y intercept is 12. it represents the starting height of the plant in cm.

work shown:

plug n = 0 into the f(n) function. simplify

f(n) = 12*(1.03)^n

f(0) = 12*(1.03)^0

f(0) = 12*(1)

f(0) = 12

on day n = 0, aka the starting point, the height f(n) is 12 cm

=====================================

part c

answer: the average rate of change is approximately 0.43061036458991 (round however you need to). this represents the average growth rate from day n = 3 to day n = 10. so the plant grew roughly 0.43 cm per day during this timespan, assuming you round to 2 decimal places.

work shown:

compute f(3)

f(n) = 12*(1.03)^n

f(3) = 12*(1.03)^3

f(3) = 13.112724 < we'll use this later

compute f(10)

f(n) = 12*(1.03)^n

f(10) = 12*(1.03)^10

f(10) = 16.1269965521294 < we'll use this later

now use the formula below with a = 3 and b = 10

aroc = average rate of change

aroc = [ f(b) - f(a) ]/[ b - a ]

aroc = [ f(10) - f(3) ]/[ 10 - 3 ]

aroc = (16.1269965521294 - 13.112724)/(10 - 3)

aroc = 3.0142725521294/7

aroc = 0.43061036458991

round this however you need to

note: the plant grew approximately 3.01 cm over 7 days, so roughly 0.43 cm per day is the average growth rate (if you were to round to 2 decimal places).