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maw [93]
2 years ago
5

CALCULUS: Determine which function is a solution to the differential equation y ' − y = 0.

Mathematics
1 answer:
Montano1993 [528]2 years ago
8 0

C: none of these are solutions to the given equation.

• If<em> y(x)</em> = <em>e</em>², then <em>y</em> is constant and <em>y'</em> = 0. Then <em>y'</em> - <em>y</em> = -<em>e</em>² ≠ 0.

• If <em>y(x)</em> = <em>x</em>, then <em>y'</em> = 1, but <em>y'</em> - <em>y</em> = 1 - <em>x</em> ≠ 0.

The actual solution is easy to find, since this equation is separable.

<em>y'</em> - <em>y</em> = 0

d<em>y</em>/d<em>x</em> = <em>y</em>

d<em>y</em>/<em>y</em> = d<em>x</em>

∫ d<em>y</em>/<em>y</em> = ∫ d<em>x</em>

ln|<em>y</em>| = <em>x</em> + <em>C</em>

<em>y</em> = exp(<em>x</em> + <em>C </em>)

<em>y</em> = <em>C</em> exp(<em>x</em>) = <em>C</em> <em>eˣ</em>

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Naddika [18.5K]

Answer:

$1.25

Step-by-step explanation:

This can best be determined using a set of linear equations that are solved simultaneously.

This pair of linear equations may be solved simultaneously by using the elimination method. This will involve ensuring that the coefficient of one of the unknown variables is the same in both equations.

Let the cost of a cookie be c, cost of a doughnut be d and that of a box of doughnut hole be h then if cost of 4 cookies, 6 doughnuts, and 3 boxes of doughnut holes is $8.15, we have

4a + 6d + 3h = 8.15

and the cost of 2 cookies, 3 doughnuts, and 4 boxes of doughnuts holes is $7.20 then

2a + 3d + 4h = 7.20

Dividing the first by 2

2a + 3d + 1.5h = 4.075

subtracting from the second equation

2.5h = 3.125

h = 1.25

The cost of a box of doughnut holes is $1.25

5 0
2 years ago
Curtis lives 9 miles away from Jean. If Curtis can ride his bike at a constant rate of 12 miles per hour, how many minutes would
sasho [114]
It will take Curtis 45 minutes to ride his bike from his house to Jean's house.
4 0
3 years ago
Plz help me Thx so much
Degger [83]

Answer:

shipping and handling is <u>18.90</u> dollars

Step-by-step explanation:

percent means "per one hundred", so any percent can be written as a fraction over 100

30% = 30/100 = 0.30

Multiply 0.30 with the price 63 to get 0.30*63 = 18.90, which is the cost of shipping only. This result is added on top of the 63 dollars to get the total cost.

8 0
3 years ago
Read 2 more answers
Please Answer fast .......​
VashaNatasha [74]

Answer:

  3)  67/441

Step-by-step explanation:

Comparing the given equation to the expressions you need to evaluate, you find there might be a simplification.

  3x² +5x -7 = 0 . . . . . given equation

  3x² +5x = 7 . . . . . . . add 7

  x(3x +5) = 7 . . . . . . . factor

  3x +5 = 7/x . . . . . . . . divide by x

Now, we can substitute into the expression you are evaluating to get ...

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__

We know that when we divide the original quadratic by 3, we get

  x² +(5/3)x -7/3 = 0

and that (α+β) = -5/3, the opposite of the x coefficient, and that α·β = -7/3, the constant term. The sum of squares is ...

  α² +β² = (α+β)² -2αβ = (-5/3)² -2(-7/3) = 25/9 +14/3 = 67/9

Then the value of the desired expression is ...

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8 0
3 years ago
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Im working on a math sheet
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Answer:

b

Step-by-step explanation:

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