Bob is making a curtain to surround a table she bought 3 1/4 yards of fabric her total cost was $13 what was the cost per yard

Find the solution the each of the following first order linear differential equations:

Cerrena [4.2K]

Answer:

a. $y=\frac{2}{3}x^7+cx^4$

b. $y=2e^{7x}-ce^{5x}$

c. $y=e^{-2x}arctan(e^{2x})+ce^{-2x}$

d. $i=e^{-2t}\left(\frac{8\left(3e^{2t}\sin \left(3t\right)+2e^{2t}\cos \left(3t\right)\right)}{13}+C\right)$

Step-by-step explanation:

a) xy' -4y = 2 x^6

$xy'-4y=2x^6\\y'-\frac{4}{x}y=2x^5\\p(x)=\frac{-4}{x}\\Q(x)=2x^5\\\mu(x)=\int P(x)dx=\int \frac{-4}{x}dx=Ln|x|^{-4}\\y=e^{-\mu(x)}\int {e^{\mu(x)}Q(x)dx}\\y=x^4 \int {x^{-4}2x^6}dx\\y=\frac{2}{3}x^7+cx^4$

b) y' - 5y = 4e^7x

$y'-5y=4e^{7x}\\p(x)=-5\\Q(x)=4e^{7x}\\\mu(x)=\int P(x)dx=\int-5dx=-5x\\y=e^{-\mu(x)}\int {e^{\mu(x)}Q(x)dx}\\y=e^{5x}\int {e^{-5x}4e^{7x}}dx\\y=2e^{7x}-ce^{5x}$

c) dy/dx + 2y = 2/(1+e^4x)

$\frac{dy}{dx}+2y=\frac{2}{1+e^{4x}}\\p(x)=2\\Q(x)=\frac{2}{1+e^{4x}}\\\mu(x)=\int P(x)dx=\int 2dx=2x\\y=e^{-\mu(x)}\int {e^{\mu(x)}Q(x)dx}\\y=e^{-2x}\int {e^{2x}\frac{2}{1+e^{4x}}}dx\\y=e^{-2x}arctan(e^{2x})+ce^{-2x}$

d) 1/2 di/dt + i = 4cos(3t)

$\frac{1}{2}\frac{di}{dt}+i=4cos(3t)\\\frac{di}{dt}+2i=8cos(3t)\\p(t)=2\\Q(t)=8cos(3t)\\\mu(t)=\int P(t)dt=\int 2dt=2t\\i=e^{-\mu(t)}\int {e^{\mu(t)}Q(t)dt}\\i=e^{-2t}\int {e^{2t}8cos(3t}dt\\i=e^{-2t}\left(\frac{8\left(3e^{2t}\sin \left(3t\right)+2e^{2t}\cos \left(3t\right)\right)}{13}+C\right)$

3 0

3 years ago

1.

kodGreya [7K]

Answer: 1. All the numbers within the whole

number set {0,1,2,3,...) as well as

all of the opposites. Integers

2. The result of adding two or more

Numbers. Sum

3. The result of subtracting one

number from another. difference

4. A number that is multiplied by

another number factor

5. A number to be divided by

another number. dividend

6. A number by which another

number is to be divided. divisor

7. Two or more factors multiplied

together results in this. product

8. A dividend is divided by a divisor

and the result is this. quotient

9. Also called reducing means to

make the fraction as simple as possible. the simplest form

10. It is the largest number that

divides exactly into two or more numbers. Least Common Denominator

11. The smallest number that is a

multiple of two or more numbers

The LCM or Least Common Multiple

12. Using unit factors to convert measurements. Dimensional Analysis

Step-by-step explanation:

It took a while to sort all of the questions out. I hope this is a study guide, not a test

5 0

3 years ago

these 15 colored pencils make up 20% of jordon's colored pencil collection.how many colored pencils does jordon have in his coll

dmitriy555 [2]

Answer:

75 coloured pencils

Step-by-step explanation:

Let's say Jordon has x total pencils.

We know that 20% of these x pencils is 15, so we have:

20% * x = 15

Remember that % is just "out of 100", so 20% = 20/100 = 0.20. Then:

0.20x = 15

x = 15 / 0.20 = 75

Jordon has 75 coloured pencils.

6 0

3 years ago

Read 2 more answers

Determine the coordinates of the point shown. A coordinate grid shown. There are increments of 0.5 for each grid line on each of

Leni [432]

Grid lines to the right represent positive numbers for the first coordinate. 3 of them will put you on a grid line with a value of 3×0.5 = 1.5.

You now know enough to select the correct answer, ...

... (1.5, -2.5)

_____

You can confirm this is the correct answer by figuring the second coordinate. Down represents negative numbers, so down 5 units is -(5×0.5) = -2.5. This matches the second coordinate of the chosen answer.

3 0

3 years ago

Add using scientific notation.<br> (5.2 x 10') + (3.01 x 10^)

satela [25.4K]

Answer: What's the exponents?

Step-by-step explanation:

5.2+3.01=8.21

but then there's no exponents that you stated. So it would be 8.21x10^?

If the tens do have exponents above them, add them together.

I hope this answer helps you!

7 0

3 years ago

Bob is making a curtain to surround a table she bought 3 1/4 yards of fabric her total cost was $13 what was the cost per yard￼

Bob is making a curtain to surround a table she bought 3 1/4 yards of fabric her total cost was $13 what was the cost per yard