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3 years ago

7

Bertie Bee's Carpet Cleaners charge $1.22 per square foot to clean carpets. Millie Mott's Carpet Cleaners charge $9.50 per squar

e yard. Which company offers the better deal?

1 answer:

Crank3 years ago

6 0

Answer:

Bertie Bee's Carpet Cleaners

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Solve the following differential equation: y" + y' = 8x^2

PtichkaEL [24]

Answer:

$y=y_p+y_h = \frac{8}{3}x^3-8x^2+16x+ C_1 + C_2e^{-x}$

Step-by-step explanation:

Let's find a particular solution. We need a function of the form $y= ax^3+bx^2+cx+d$ such that

$y'= 3ax^2+2bx+c$ and

$y''= 6ax+2b$

$y'+y''= 3ax^2+2bx+c+6ax+2b = 3ax^2+x(2b+6a)+(c+2b) = 8x^2$

then, 3a= 8, 2b+6a =0 and c+2b = 0. With the first equation we obtain

a = 8/3 and replacing in the second equation 2b+6(8/3) = 2b + 16 = 0. Then, b = -8. Finally, c = -2(-8) = 16.

So, our particular solution is $y_p= \frac{8}{3}x^3-8x^2+16x$ .

Now, let's find the solution $y_p$ of the homogeneus equation $y''+y'=0$ with the method of constants coefficients. Let $y=e^{\lambda x}$

$y'=\lambda e^{\lambda x}$

$y''=\lambda^2e^{\lambda x}$

then $\lambda e^{\lambda x}+\lambda^2 e^{\lambda x} = 0$

$e^{\lambda x}(\lambda +\lambda^2)= 0$

$(\lambda +\lambda^2)= 0$

$\lambda (1+\lambda)= 0$

$\lambda =0$ and $\lambda)= -1$ .

So, $y_h = C_1 + C_2e^{-x}$ and the solution is

$y=y_p+y_h =\frac{8}{3}x^3-8x^2+16x+ C_1 + C_2e^{-x}$ .

5 0

3 years ago

Original price of a pen $1.99 tax:6%

egoroff_w [7]

Answer:

The final price would be 2.11$

5 0

3 years ago

The beginning balance of Keyshawn's savings account for the month of September was $3900, and it remained this way for the first

musickatia [10]

Simple or compound interest

8 0

3 years ago

Need Help Please!!!!!!!

marshall27 [118]

ANSWER

$1,413.81

EXPLANATION

The compound interest formula is given by:

$A=P(1+r\%)^t$

Where P=900 is the balance in the account, t=10 is the number of years and r=0.0462 is the rate.

We substitute the values in to the formula to get:

$A=900(1+4.62\%)^{10}$

$A=900(1.0462)^{10}$

This simplifies to:

$A=1413.81$

Therefore $1413.81 will be in the account after 10 years.

6 0

3 years ago

Read 2 more answers

19. Rick shared his bag of grapes withfriends. He gave /210of the bag to Melissaand /410 of the bag to Ryan. What fractionof the

kvv77 [185]

Rick started with 10/10 of the grapes because he had all of them at the start.

Then he gave 2/10 and 4/10 of the grapes away.

10/10 - 2/10 - 4/10 = 4/10 = 2/5 left

answer: Rick had 2/5 of the grapes left.

4 0

3 years ago