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levacccp [35]
2 years ago
11

A class has 4 boys and 10 girls. What is the ratio in simplest form that compares number of boys to total number of students? (4

points)
Mathematics
1 answer:
Black_prince [1.1K]2 years ago
6 0
2:7

Because you have to add all the students.

4+ 10 = 14

Boys to students = 4:14

Simplest form: 2:7 because two can go into 4 two times and can go into 14 seven times.
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Consider the following differential equation to be solved by undetermined coefficients. y(4) − 2y''' + y'' = ex + 1 Write the gi
kompoz [17]

Answer:

The general solution is

y= (C_{1}+C_{1}x) e^0x+(C_{3}+C_{4}x) e^x +\frac{1}{2} (e^x(x^2-2x+2)-e^x(2(x-1)+e^x(2))

     + \frac{x^2}{2}

Step-by-step explanation:

Step :1:-

Given differential equation  y(4) − 2y''' + y'' = e^x + 1

The differential operator form of the given differential equation

(D^4 -2D^3+D^2)y = e^x+1

comparing f(D)y = e^ x+1

The auxiliary equation (A.E) f(m) = 0

                         m^4 -2m^3+m^2 = 0

                         m^2(m^2 -2m+1) = 0

(m^2 -2m+1) this is the expansion of (a-b)^2

                        m^2 =0 and (m-1)^2 =0

The roots are m=0,0 and m =1,1

complementary function is y_{c} = (C_{1}+C_{1}x) e^0x+(C_{3}+C_{4}x) e^x

<u>Step 2</u>:-

The particular equation is    \frac{1}{f(D)} Q

P.I = \frac{1}{D^2(D-1)^2} e^x+1

P.I = \frac{1}{D^2(D-1)^2} e^x+\frac{1}{D^2(D-1)^2}e^{0x}

P.I = I_{1} +I_{2}

\frac{1}{D^2} (\frac{x^2}{2!} )e^x + \frac{1}{D^{2} } e^{0x}

\frac{1}{D} means integration

\frac{1}{D^2} (\frac{x^2}{2!} )e^x = \frac{1}{2D} \int\limits {x^2e^x} \, dx

applying in integration u v formula

\int\limits {uv} \, dx = u\int\limits {v} \, dx - \int\limits ({u^{l}\int\limits{v} \, dx  } )\, dx

I_{1} = \frac{1}{D^2(D-1)^2} e^x

\frac{1}{2D} (e^x(x^2)-e^x(2x)+e^x(2))

\frac{1}{2} (e^x(x^2-2x+2)-e^x(2(x-1)+e^x(2))

I_{2}= \frac{1}{D^2(D-1)^2}e^{0x}

\frac{1}{D} \int\limits {1} \, dx= \frac{1}{D} x

again integration  \frac{1}{D} x = \frac{x^2}{2!}

The general solution is y = y_{C} +y_{P}

         y= (C_{1}+C_{1}x) e^0x+(C_{3}+C_{4}x) e^x +\frac{1}{2} (e^x(x^2-2x+2)-e^x(2(x-1)+e^x(2))

      + \frac{x^2}{2!}

3 0
3 years ago
Trevor ran a race in 1 4/5 hours. He ran a total of 8 1/3 miles. How far did he run in one hour?
gulaghasi [49]

Answer:

4.63

Step-by-step explanation:

4/5 of an hour is 48 minutes

1 4/5 hour is 60 + 48

which is

108 minutes

he ran 8 1/3 miles in 108 minutes

so

(8 1/3 times 60 ) ÷ 108

which =

4.6296296296 miles in one hour

6 0
2 years ago
Read 2 more answers
(10 Points) Tanya is visiting New Orleans, and she wants to bring back T-shirts for all her friends. She’s
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I’m on the way home I can see if I could have a good time at your house and I’ll
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2 years ago
HELP PICTURE IS SHOWNN
Gnom [1K]
Angle TVU = 1/2 (120 - 12) = 108/2 = 56°

Therefore, the correct answer is D.
7 0
3 years ago
Find the area. Will mark brainliest
chubhunter [2.5K]

Answer:

80.64

Step-by-step explanation:

12.6*6.4=80.64

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