classify the pair of angles. (supplementary, adjacent, vertical, or complementary) then find the value of x.

Mathematics

1 answer:

earnstyle [38]3 years ago

8 0

Answer:

Supplementary angles; 148°

Step-by-step explanation:

180° - 32° = 148° (supplementary angles)

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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 telescope is discounted 30%. Sales price is $126. Find the original price.

Gemiola [76]

Answer:

180 dollars

Step-by-step explanation:

if it was discounted by 30 percent, that means 126 is 70 percent of the orin=inal price. If you divide 126 by 70, you get 1.8 is the money worth 1 percent. Multiply 1.8 by 100 to get the original price, and you end up with 180 dollars.

5 0

3 years ago

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Can someone please help me here! Tell me the answer I’ll give a brainliest to the one who is right!

Anton [14]

Answer:

False

Step-by-step explanation:

The equation is equal to -24 = -19. That's not true

3 0

3 years ago

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