Divide correctly 016 by 8 072 by 8

slavikrds [6]

For the carpet:

Given:

Area = x^2 + x - 20 ft^2
Length = x+ 5 ft

As a carpet is rectangular, the area is defined as the product of the length and the width. To obtain an expression of the carpet's width, the area is to be divided by the length, which is shown below:

__x_-_4___x + 5|x^2 + x - 20 x^2 + 5x -------- -4x - 20 -4x - 20 -------- 0

Therefore, the expression of width = x - 4.

Applying the value of x = 20 to obtain the measurements of the carpet, we obtain the following:

Width = x - 4 = 20 - 4 = 16ft
Length = x+ 5 = 20 + 5 = 25ft.

Therefore, the carpet is 25ft x 16ft.

For the wall:

The same principles apply to the wall as it is also assumed to be rectangular.

Given:
Area = x^2 + 17x + 30 ft^2
Width = x + 2

To obtain the expression for the wall's length, Area is to be divided by the Width, which is shown below:

__x_+_15______x + 2|x^2 + 17x + 30 x^2 + 2x -------- 15x + 30 15x + 30 --------- 0

Therefore, the expression for the wall's length is x + 15.

Applying the value of x = 20 to obtain the wall's dimensions:

Length = x + 15 = 20 + 15 = 35ft.
Width = x + 2 = 20 + 2 = 22ft.

Therefore the wall has measurements of 35ft x 22ft.

8 0

2 years ago

The price (in dollars) p and the quantity demanded q are related by the equation: p^2+2q^2=1100.If R is revenue, dR/dt can be ex

bagirrra123 [75]

FOR THE FIRST PROBLEM:

Differentiating p^2 + 2q^2 = 1100 with respect to time => 2p(dp/dt) + 4q(dq/dt) = 0

dp/dt = -2q/p(dq/dt) 

R = pq 

dR/dt = p(dq/dt) + q(dp/dt) = -p²/2q(dp/dt) + q(dp/dt) = (2q² - 1100)/2q * (dp/dt) + q(dp/dt) 

A = (2q - 550/q)

I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!

3 0

2 years ago

Does anyone know the answer of all these questions if so I will be Very glad if you help

USPshnik [31]

Answer:

6) 22,408

7) 8,993

8) 68,701

Step-by-step explanation:

6) 122408 - 100000 = 22,408

7) 8993/999 = 9 2/999

8) 98,700 - 29,999 = 68,701

7 0

2 years ago

Power Series Differential equation

KatRina [158]

The next step is to solve the recurrence, but let's back up a bit. You should have found that the ODE in terms of the power series expansion for $y$

$\displaystyle\sum_{n\ge2}\bigg((n-3)(n-2)a_n+(n+3)(n+2)a_{n+3}\bigg)x^{n+1}+2a_2+(6a_0-6a_3)x+(6a_1-12a_4)x^2=0$

which indeed gives the recurrence you found,

$a_{n+3}=-\dfrac{n-3}{n+3}a_n$

but in order to get anywhere with this, you need at least three initial conditions. The constant term tells you that $a_2=0$ , and substituting this into the recurrence, you find that $a_2=a_5=a_8=\cdots=a_{3k-1}=0$ for all $k\ge1$ .

Next, the linear term tells you that $6a_0+6a_3=0$ , or $a_3=a_0$ .

Now, if $a_0$ is the first term in the sequence, then by the recurrence you have

$a_3=a_0$
$a_6=-\dfrac{3-3}{3+3}a_3=0$
$a_9=-\dfrac{6-3}{6+3}a_6=0$

and so on, such that $a_{3k}=0$ for all $k\ge2$ .

Finally, the quadratic term gives $6a_1-12a_4=0$ , or $a_4=\dfrac12a_1$ . Then by the recurrence,

$a_4=\dfrac12a_1$
$a_7=-\dfrac{4-3}{4+3}a_4=\dfrac{(-1)^1}2\dfrac17a_1$
$a_{10}=-\dfrac{7-3}{7+3}a_7=\dfrac{(-1)^2}2\dfrac4{10\times7}a_1$
$a_{13}=-\dfrac{10-3}{10+3}a_{10}=\dfrac{(-1)^3}2\dfrac{7\times4}{13\times10\times7}a_1$

and so on, such that

$a_{3k-2}=\dfrac{a_1}2\displaystyle\prod_{i=1}^{k-2}(-1)^{2i-1}\frac{3i-2}{3i+4}$

for all $k\ge2$ .

Now, the solution was proposed to be

$y=\displaystyle\sum_{n\ge0}a_nx^n$

so the general solution would be

$y=a_0+a_1x+a_2x^2+a_3x^3+a_4x^4+a_5x^5+a_6x^6+\cdots$
$y=a_0(1+x^3)+a_1\left(x+\dfrac12x^4-\dfrac1{14}x^7+\cdots\right)$
$y=a_0(1+x^3)+a_1\displaystyle\left(x+\sum_{n=2}^\infty\left(\prod_{i=1}^{n-2}(-1)^{2i-1}\frac{3i-2}{3i+4}\right)x^{3n-2}\right)$

4 0

2 years ago

I need help with this question it is on mathswatch btw.

navik [9.2K]

Answer:

x is less then or equal to -3

x<-3 (the < has to have a line underneath)

Step-by-step explanation:

4 0

2 years ago

Divide correctly 016 by 8072 by 8​

Divide correctly 016 by 8072 by 8