Mathematics, 21.07.2019 12:30 jessezarate7129

Divide the following polynomials. then place the answer in the proper location on the grid. write your answer in order of descending powers of x. write the quotient and remainder as a sum in this format: . do not include parentheses in your answer. ( x^3 + y^3) ÷( x- y )

Answers: 2

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Answers

The answer is x²-y² + xy²+x²y/x-y
Solution:
By polynomial grid division, we start by the divisor (x - y) placed on the row headings of the table and end with the quotient on the column headings.
We know that x² must be in the top left of the grid so that the row and column multiply to x³. We multiply x² by the terms of the row headings to fill in all of the first column:
x²
x x³
-y -x²y

We got -x²y though we want y³. The next quadratic entry must then be -y² to get y³. Multiplying -y² by the divisor, we fill in all of the second column:
x² -y²
x x³ -xy²
-y -x²y y³

We end up with a grid sum -x²y - xy² which tells us that we have a remainder of xy² + x²y that we write next to the grid:
x² -y²
x x³ -xy² remainder: + x²y + xy²
-y -x²y y³

We have to add the remaining fractional part to the quotient that we can read off the first row. Therefore,
x³+y³ / x-y = x²-y² + xy²+x²y/x-y

Answer from: Quest

step-by-step explanation:

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)

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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).