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NikAS [45]
2 years ago
8

Complete the table. Round to the nearest cent if necessary.

Mathematics
1 answer:
murzikaleks [220]2 years ago
6 0
Answer: 99.07$
Steps: First turn 32% into a decimal by moving the decimal right 2 places. You get 0.32. Then multiply 75.05$ by your decimal. You get 24.016. Add that to 75.05 and round your cent up, getting 99.07$ Sorry if i am incorrect this is my first answer. Hope I helped :)
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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
No irrational numbers are whole numbers. True or false and why?
Luda [366]
Hi!

Irrational numbers cannot be whole numbers. In order to be a whole number, you cannot have any decimals or fractions. Irrational numbers possess these properties.

Hopefully, this helps! =)
4 0
3 years ago
Read 2 more answers
Triangle ABC is similar to triangle DEF. The length of BC is 21cm. The length of DE is 10 cm. The length of EF is 14 cm. What is
Anarel [89]
It's a similar triangle so the ratios of corresponding sides should be equal which means

BC/EF = AB/DE
21/14 = AB/10
AB = 21/14 * 10 = 15 cm
8 0
3 years ago
Read 2 more answers
A miners' cage of mass 420 kg contains 3 miners of total mass 280 kg. The cage
svp [43]

Answer:

5817 Newtons.

Step-by-step explanation:

Total mass of the cage + the miners = 700 Kg which is a downward force of  700g N.

The net downward force = 700g - T where T is the tension (force) in the cable. The g = acceleration due to gravity = 9.81 m s-2.

We  calculate the  acceleration of the cage by using an equation of motion:

Distance = ut + 1/2 a t^2     where u = initial velocity , t = time and a = acceleration:

75 = 0(t) + 1/2 a (10^2)

50a =  75

a = 1.5 m s-2.

So using Newtons second law of motion

Force = mass * acceleration:

700*9.81 - T = 700 * 1.5

T = 700 * 9.81 - 700*1.5

= 5817 N.

8 0
3 years ago
The 5 in 6.052 has 1/10 the value of the 5 in _____? a)0.815 b)53.2 c)4.45 d)7.5
olasank [31]
Would it be a correct me if im wrong
3 0
3 years ago
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