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sineoko [7]
2 years ago
12

The length of a rectangle is 5 inches more than the width. the perimeter is 30 inches. find the length and the width

Mathematics
1 answer:
xeze [42]2 years ago
6 0

Answer:

Length = 10 inches

Width = 5 inches

Step-by-step explanation:

p = 2w + 2l

l = w + 5

30 = (2w + 2(w + 5))

30 = 4w + 10

20 = 4w

w = 5

l = w + 5

= 5 + 5

= 10

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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
The solution set to 6 + 2n > 12 is n > 3. Which are the correct representations of this solution? Select two options.
Alina [70]

The correct representation of 6 + 2n > 12 (n > 3) is  (3, ∞) and a number line with an open circle at +3 and being shaded from +3 to +5.

<h3>What is an equation?</h3>

An equation is an expression that shows the relationship between two or more numbers and variables.

Given the equation::

6 + 2n > 12

Subtracting 6 from both sides:

6 + 2n - 6 > 12 - 6

2n > 6

Dividing by 2:

n > 3

The correct representation of 6 + 2n > 12 (n > 3) is  (3, ∞) and a number line with an open circle at +3 and being shaded from +3 to +5.

Find out more on equation at: brainly.com/question/2972832

#SPJ1

3 0
2 years ago
Math problem 6 divided by 10/12
Darina [25.2K]
The answer to your problem would be 0.05
3 0
3 years ago
Read 2 more answers
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