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2 years ago

HELP ME PLEASE :D :D

Mathematics

1 answer:

Talja [164]2 years ago

3 0

Make proportions and reduce them.
6/9=2/3
10/15=2/3
The two rectangles are similar proportionally with a ratio of 2:3.

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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

2 years ago

Each week, Ms.Jones goes to the grocery store and estimates that she will spend $120. This week, she actually spent $90. What is

horsena [70]

I think there is a 25% percent error.

4 0

2 years ago

Read 2 more answers

A lighthouse has a shadow that is 36 feet long. Zara is 4 feet tall, and she is standing next to the lighthouse. Zara has a shad

pychu [463]

Answer:

48 feet

Step-by-step explanation:

At a particular time, objects and their shadows are proportionate.

Therefore, in figure,

AB/FD = BC/DE --- (1)

where AB is the height of the lighthouse, BC, its shadow and FD is the height of Zara and DE is her shadow.

From the given information,

BC = 36 feet

FD = 4 feet and DE = 3 feet

(1) becomes

AB/4 = 36/3

AB = 12

AB = 48

Hence, the height of the lighthouse is 48 feet.

7 0

2 years ago

Mr. Jones's prescription calls for 1.04 tablets per day. Based on this information, how many tablets should Mr. Jones take per d

katrin2010 [14]

Answer:

c) 1

Step-by-step explanation:

4 0

2 years ago

Suppose your car averages 38 miles per gallon on the high-

Stella [2.4K]

Answer:

a. around 36.36 hours; around 28.57 hours

b. $134.21; $159.38

Step-by-step explanation:

4 0

2 years ago