2 years ago

(01.04) Solve the following for y: 4x + 2y = −2 (6 points)

Mathematics

1 answer:

Marat540 [252]2 years ago

6 0

Factor out the common term 2

2(2x + y) = -2

Divide both sides by 2

2x + y = -1

Subtract 2x from both sides

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Consider the differential equation y'' − y' − 30y = 0. Verify that the functions e−5x and e6x form a fundamental set of solution

Alex Ar [27]

Answer:

Step-by-step explanation:

We have to take the derivatives for both functions and replace in the differential equation. Hence

for y=e^{-5x}:

$y(x)=e^{-5x}\\y'(x)=-5e^{-5x}\\y''(x)=25e^{-5x}\\$

for y=e^{6x}:

$y(x)=e^{6x}\\y'(x)=6e^{6x}\\y''(x)=36e^{6x}\\$

Now we replace in the differential equation y'' − y' − 30y = 0

for y=e^{-5x}:

$25e^{-5x}+5e^{-5x}-30e^{-5x}=0\\25+5-30=0$

for y=e^{6x}:

$36e^{6x}-6e^{6x}-30=0\\36-6+30=0$

Now, to know if both function are linearly independent we calculate the Wronskian

$W(f,g)=fg'-f'g$

$W(e^{-5x},e^{6x})=(e^{-5x})(6e^{6x})-(-5e^{-5x})(e^{6x})\neq 0$

I hope this is useful for you

Best regard

7 0

3 years ago

7/9 - 3/9 = ???????????????????????????????

Alexus [3.1K]

Answer:

your answer is : 4/9

~hope you have a great day/night :-) ~

Step-by-step explanation:

6 0

2 years ago

Read 2 more answers

<img src="https://tex.z-dn.net/?f=x%5E%7B2%7D%20-36%5Cfrax%2B5%2F%28x%2B6%29" id="TexFormula1" title="x^{2} -36\frax+5/(x+6)" al

zhannawk [14.2K]

the answer is

x^{2}-31x+5b

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1 year ago

How many cookies will Tina have if she bakes 7 more batches more than the maximum number of batches in the table

attashe74 [19]

Answer:

Step-by-step explanation:

8 0

2 years ago

Marjorie needs to calculate how much water a cylindrical tank will hold. The tank is 9 feet high and has a diameter of 5 feet. H

aniked [119]

Answer:

The volume of the cylindrical tank is 176.625 cubic feet.

Step-by-step explanation:

Given : The tank is 9 feet high and has a diameter of 5 feet.

To find : Marjorie needs to calculate how much water a cylindrical tank will hold ?

Solution :

The volume of a cylinder is $V=\pi r^2 h$

The diameter is d=5 feet

The radius is $r=\frac{d}{2}$

$r=\frac{5}{2}=2.5$ feet.

The height is h=9 feet.

Substitute the value in the formula,

$V=3.14\times (2.5)^2\times 9$

$V=3.14\times 6.25\times 9$

$V=176.625$

The volume of the cylindrical tank is 176.625 cubic feet.

8 0

2 years ago

Read 2 more answers