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Strike441 [17]
2 years ago
14

Solve the given differential equation by using an appropriate substitution. The DE is of the form dy/dx = f(Ax + By + C), which

is given in (5) of Section 2.5. dy/dx = 4 + (y − 4x + 6)^1/2
Mathematics
1 answer:
Mariana [72]2 years ago
7 0

d<em>y</em>/d<em>x</em> = 4 + √(<em>y</em> - 4<em>x</em> + 6)

Make a substitution of <em>v(x)</em> = <em>y(x)</em> - 4<em>x</em> + 6, so that d<em>v</em>/d<em>x</em> = d<em>y</em>/d<em>x</em> - 4. Then the DE becomes

d<em>v</em>/d<em>x</em> + 4 = 4 + √<em>v</em>

d<em>v</em>/d<em>x</em> = √<em>v</em>

which is separable as

d<em>v</em>/√<em>v</em> = d<em>x</em>

Integrating both sides gives

2√<em>v</em> = <em>x</em> + <em>C</em>

Get the solution back in terms of <em>y</em> :

2√(<em>y</em> - 4<em>x</em> + 6) = <em>x</em> + <em>C</em>

You can go on to solve for <em>y</em> explicitly if you want.

√(<em>y</em> - 4<em>x</em> + 6) = <em>x</em>/2 + <em>C</em>

<em>y</em> - 4<em>x</em> + 6 = (<em>x</em>/2 + <em>C </em>)²

<em>y</em> = 4<em>x</em> - 6 + (<em>x</em>/2 + <em>C </em>)²

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Answer:

<h2> The answer is X= -4 </h2>

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6 0
3 years ago
In a certain Algebra 2 class of 29 students, 7 of them play basketball and 14 of them
Mariulka [41]

Answer:

<em>Two possible answers below</em>

Step-by-step explanation:

<u>Probability and Sets</u>

We are given two sets: Students that play basketball and students that play baseball.

It's given there are 29 students in certain Algebra 2 class, 10 of which don't play any of the mentioned sports.

This leaves only 29-10=19 players of either baseball, basketball, or both sports. If one student is randomly selected, then the propability that they play basketball or baseball is:

\displaystyle P=\frac{19}{29}

P = 0.66

Note: if we are to calculate the probability to choose one student who plays only one of the sports, then we proceed as follows:

We also know 7 students play basketball and 14 play baseball. Since 14+7 =21, the difference of 21-19=2 students corresponds to those who play both sports.

Thus, there 19-2=17 students who play only one of the sports. The probability is:

\displaystyle P=\frac{17}{29}

P = 0.59

3 0
3 years ago
Given the equation 5x − 4 = –2(3x + 2), solve for the variable. Explain each step and justify your process.
blagie [28]
A.
5x-4=-2(3x+2) \ \ \ \ \ \ \ \ \ |\hbox{expand the bracket} \\&#10;5x-4=-2 \times 3x-2 \times 2 \\&#10;5x-4=-6x-4 \ \ \ \ \ \ \ \ \ \ \ \ \ |\hbox{add 6x to both sides} \\&#10;11x-4=-4 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ |\hbox{add 4 to both sides} \\&#10;11x=0 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ |\hbox{divide both sides by 11} \\&#10;x=0

B.
3(2x-4)=5x-1 \\&#10;6x-12=5x-1 \\&#10;\boxed{11x-12=-1} \Leftarrow \hbox{the first mistake} \\&#10;11x=11 \\&#10;\boxed{x=11} \Leftarrow \hbox{the second mistake}

Megan's solution isn't correct.
The first mistake: she subtracted 5x from the right-hand side of the equation, but added 5x to the left-hand side.
The second mistake: she divided the right-hand side of the equation by 11, but didn't divide the left-hand side.

The correct solution:
3(2x-4)=5x-1 \ \ \ \ \ \ \ \ \ \ \ |\hbox{expand the bracket} \\&#10;3 \times 2x+3 \times (-4)=5x-1 \\ 6x-12=5x-1 \ \ \ \ \ \ \ \ \ \ \ \ \ \ |\hbox{subtract 5x from both sides} \\&#10;x-12=-1 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \  |\hbox{add 12 to both sides} \\&#10;x=11
3 0
2 years ago
How did the temperature change if: At first it increased by 25% and then decreased by 40%
Roman55 [17]

Answer:

24.6 % decrease

Step-by-step explanation:

Let x be the original temperature

Increase by 25%

x + .25x

1.25x

Decrease by 40%

The amount decreased is

(1.25x) *.40

.496x

Subtract that from 1.25x

1.25x - .496x

.754x

We need to find the percent decrease

1 - .754 = .246

24.6 % decrease

7 0
3 years ago
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FrozenT [24]
(72/80)x90=81
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5 0
2 years ago
Read 2 more answers
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