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3 years ago

Sandy bought a soft drink for 2 dollars and 6 candy bars. she spent a total of 20 dollars. how much did each candy bar cost

Mathematics

1 answer:

dezoksy [38]3 years ago

3 0

Each candy bar was $3.00.

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Set up but do not solve for the appropriate particular solution yp for the differential equation y′′+4y=5xcos(2x) using the Meth

taurus [48]

Answer:

So, solution of the differential equation is

$y(t)=-\frac{5x^2}{4}\cot 2x\cdot \cos 2x+c_1e^{-2it}+c_2e^{2it}\\$

Step-by-step explanation:

We have the given differential equation: y′′+4y=5xcos(2x)

We use the Method of Undetermined Coefficients.

We first solve the homogeneous differential equation y′′+4y=0.

$y''+4y=0\\\\r^2+4=0\\\\r=\pm2i\\\\$

It is a homogeneous solution:

$y_h(t)=c_1e^{-2i t}+c_2e^{2i t}$

Now, we finding a particular solution.

$y_p(t)=A5x\cos 2x\\\\y'_p(t)=A5\cos 2x-A10x\sin 2x\\\\y''_p(t)=-A20\sin 2x-A20x\cos 2x\\\\\\\implies y''+4y=5x\cos 2x\\\\-A20\sin 2x-A20x\cos 2x+4\cdot A5x\cos 2x=5x\cos 2x\\\\-A20\sin 2x=5x\cos 2x\\\\A=-\frac{x}{4} \cot 2x\\$

we get

$y_p(t)=A5\cos 2x\\\\y_p(t)=-\frac{5x^2}{4}\cot 2x\cdot \cos 2x\\\\\\y(t)=y_p(t)+y_h(t)\\\\y(t)=-\frac{5x^2}{4}\cot 2x\cdot \cos 2x+c_1e^{-2it}+c_2e^{2it}\\$

So, solution of the differential equation is

$y(t)=-\frac{5x^2}{4}\cot 2x\cdot \cos 2x+c_1e^{-2it}+c_2e^{2it}\\$

7 0

3 years ago

Serena has a summer job as a lifeguard at the neighborhood pool. She earns $240 a week. By rounding her weekly income to the nea

Nesterboy [21]

<h2>Answer: B </h2>

Step-by-step explanation:

If your rounding her weekly income you would go down to $200 then take that times 11 for each week, giving you $2,200 roughly

3 0

3 years ago

Help me, practice questions.

ioda

None of them match the answer is really (-2,2), (-4,2), and (-2,8).

8 0

2 years ago

One positive number is three more than twice another. If their product is 629, find the numbers.

sineoko [7]

Answer:

x = 17 and y = 37

Step-by-step explanation:

Let the numbers be x and y.

y = 3 + 2x

xy = 629

substituting y in the second equation we get

x(3+2x) = 629

3x + 2 $x^{2}$ = 629

2 $x^{2}$ + 3x - 629 = 0

Solving a quadratic equation by using its formula:

x = [-3 ±√(9-4(2)(-629)] / 4

x = [-3 ± √5041] / 4

x = [-3 ± 71] / 4

x = 17 and $\frac{-37}{2}$

Ignore the negative number in x and just use x = 17 in the first equation we get

y = 3 + 2(17) = 37

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3 years ago

What is the perimeter<br><br><br> This Pythagorean theorem

Elenna [48]

Answer:

a is 5 so the perinmeter is 30

6 0

2 years ago