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earnstyle [38]
3 years ago
10

4 - (-18) = 4 - (-18) =

Mathematics
1 answer:
VashaNatasha [74]3 years ago
8 0

Answer: 22

Step-by-step explanation:

4 - (-18) = 4 + (+ 18) = 22

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Assume that a student attends a four-year college with tuition costs of $20,000 per year, room and board costs of $5,000 per yea
Kamila [148]

Answer:

$180,000.

Step-by-step explanation:

We have been given that a student attends a four-year college with tuition costs of $20,000 per year, room and board costs of $5,000 per year, and books/entertainment costs of $1,000 per year. If the student did not go to college, she would work at a job that pays $25,000 per year but still face the same room and board and entertainment expenses.

We know that opportunity cost is the profit lost, when one alternative is selected over another.

Opportunity cost of attending college for 4 years would be amount lost from job in 4 years plus amount spent on studies because the student lost $25,000 for four years for not doing the job and spent $20,000 for 4 years on studies.

4(\$25000+\$20,000)=4(\$45,000)=\$180,000

Therefore, the opportunity cost of attending college for this student for four years is $180,000.

7 0
3 years ago
Can someone help me with these questions please and thank you. I WILL MARK BRANLIEST!
Korvikt [17]

Answer:35 1  32

Step-by-step explanation:

5 0
3 years ago
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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
Which matrix represents the solution to the system of equations below?
boyakko [2]

Answer:

The one that's include a rows 2 1 1 2

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3 years ago
What are the intercepts of this function f(x)=-8x+4
Sidana [21]

Answer:

Step-by-step explanation:

to find the x-intercept:

Make y=0

0=-8x+4

8x =4

x=4/8

x=1/2

to find y-intercept:

Make x=0

y=-8(0) +4

y=4

Hope this helps!

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3 0
3 years ago
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