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Alecsey [184]
1 year ago
12

Please help these are review questions for my test tomorrow and i cannot figure them out on my own

Mathematics
1 answer:
igomit [66]1 year ago
7 0

Answer:

17.A 18.A

Step-by-step explanation:

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The sine of the complimentary angle of 34°
tester [92]

Answer: 0.559192903....

Step-by-step explanation:

4 0
3 years ago
Solve the nonhomogeneous differential equation y′′+25y=cos(5x)+sin(5x). Find the most general solution to the associated homogen
Marrrta [24]

Answer:

y(x)=c_1cos(5x)+c_2sin(5x)+0.1xsin(5x)-0.1xcos(5x)

Step-by-step explanation:

The general solution will be the sum of the complementary solution and the particular solution:

y(x)=y_c(x)+y_p(x)

In order to find the complementary solution you need to solve:

y''+25y=0

Using the characteristic equation, we may have three cases:

Real roots:

y(x)=c_1e^{r_1x} +c_2e^{r_2x}

Repeated roots:

y(x)=c_1e^{rx} +c_2xe^{rx}

Complex roots:

y(x)=c_1e^{\lambda x}cos(\mu x) +c_2e^{\lambda x}sin(\mu x)\\\\Where:\\\\r_1_,_2=\lambda \pm \mu i

Hence:

r^{2} +25=0

Solving for r :

r=\pm5i

Since we got complex roots, the complementary solution will be given by:

y_c(x)=c_1cos(5x)+c_2sin(5x)

Now using undetermined coefficients, the particular solution is of the form:

y_p=x(a_1cos(5x)+a_2sin(5x) )

Note: y_p was multiplied by x to account for cos(5x) and sin(5x) in the complementary solution.

Find the second derivative of y_p in order to find the constants a_1 and a_2 :  

y_p''(x)=10a_2cos(5x)-25a_1xcos(5x)-10a_1sin(5x)-25a_2xsin(5x)

Substitute the particular solution into the differential equation:

10a_2cos(5x)-25a_1xcos(5x)-10a_1sin(5x)-25a_2xsin(5x)+25(a_1xcos(5x)+a_2xsin(5x))=cos(5x)+sin(5x)

Simplifying:

10a_2cos(5x)-10a_1sin(5x)=cos(5x)+sin(5x)

Equate the coefficients of cos(5x) and sin(5x) on both sides of the equation:

10a_2=1\\\\-10a_1=1

So:

a_2=\frac{1}{10} =0.1\\\\a_1=-\frac{1}{10} =-0.1

Substitute the value of the constants into the particular equation:

y_p(x)=-0.1xa_1cos(5x)+0.1xsin(5x)

Therefore, the general solution is:

y(x)=y_c(x)+y_p(x)

y(x)=c_1cos(5x)+c_2sin(5x)+0.1xsin(5x)-0.1xcos(5x)

6 0
3 years ago
Total cost to stay one night at sleepyhead Motel is $119 without breakfast and $142 with breakfast included what is the differen
BartSMP [9]
<h2>Answer:</h2>

The  difference in the cost for a one-night stay with and without breakfast is:

                             $ 23

<h2>Step-by-step explanation:</h2>

Total cost to stay one night at sleepyhead Motel without breakfast is: $119.

and cost to stay one night at sleepyhead Motel with breakfast is: $142.

Hence, the difference in the cost for a one-night stay with and without breakfast is calculated by:

               $ (142-119)

                 =   $ 23

Hence, the answer is: $ 23

4 0
3 years ago
A hexagon has two congruent sides that
dem82 [27]

Answer:

9

Step-by-step explanation:

2(10) + 4(x-3) = 44

4(x-3) = 24

x-3 = 6

x = 9

4 0
3 years ago
How many dimensions can a polygon grow from?
skelet666 [1.2K]
It can go up to four dimensional.
4 0
3 years ago
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