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2 years ago

If f(x) = 2x - 3 and g(x) = (x + 3)/2, show that f(g(x)) = g(f(x)) = x.

Mathematics

1 answer:

3241004551 [841]2 years ago

4 0

See attached photo……………..

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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

A shirt is on sale for 45% off the price. The cost of the shirt is $14.95. What is the price of the shirt now?

Pavlova-9 [17]

Answer:

$8.2225

Step-by-step explanation:

100% - 45% = 55%

then divide 55 by 100 to get .55

lastly multiply .55 to 14.95 to get 8.2225

3 0

3 years ago

Which choice is the solution to the inequality below?<br> 2x < 20

sergey [27]

X less than 10 is the answer I think

7 0

3 years ago

Just need the answer. it was "Check all that apply." at the end.

lianna [129]

Billy, let's recall what a linear pair of angles is:

• They are formed when two lines intersect.

• Two angles are said to be linear if they are adjacent angles formed by two intersecting lines.

• The measure of a straight angle is 180 degrees, so a linear pair of angles must add up to 180 degrees.

Upon saying that we have that:

• CAD and DAE are linear pairs

• CAD and CAB are linear pairs

• DAE and BAE are linear pairs

• DAE and DAC are linear pairs

Now, you are ready to select all the options that actually apply.

3 0

1 year ago

Plz help theses are exponents

ohaa [14]

For number 30 its 3
10

for 34 its 2
1/3

3 0

3 years ago