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hjlf
3 years ago
12

The problems in the leilatu Tigil-dilu Culum.-19-12​

Mathematics
1 answer:
Elan Coil [88]3 years ago
7 0
I could be 7- or it could be just 7
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Solve the problem.
yarga [219]

Answer:

39%

Step-by-step explanation:

Let's find the answer by using the following formula:

selling price=(paid price)+((paid price)*(percent markup)) which can be written as:

percent markup=((selling price)-(paid price))/(paid price)

percent markup=(27.80-20)/20

percent markup=0.39=39%

In conclusion, the percent markup is 39%.

4 0
3 years ago
Solve differential equation:<br><br> y'''+4y''-16y'-64y=0 y(0)=0, y'(0)=26, y''(0)=-16
Ipatiy [6.2K]

Answer:  The required solution of the given differential equation is

y(x)=3e^{4x}-3e^{-4x}+2xe^{-4x}.

Step-by-step explanation:  We are given to solve the following differential equation :

y^{\prime\prime\prime}+4y^{\prime\prime}-16y^\prime-64y=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\\y(0)=0,~y^\prime(0)=26,~y^{\prim\prime}(0)=-16.

Let, y=e^{mx} be an auxiliary solution of equation (i).

Then, y^\prime=me^{mx},~~y^{\prime\prime}=m^2e^{mx},~~y^{\prime\prime\prime}=m^3e^{mx}.

Substituting these values in equation (i), we get

m^3e^{mx}+4m^2e^{mx}-16me^{mx}-64e^{mx}=0\\\\\Rightarrow (m^3+4m^2-16m-64)e^{mx}=0\\\\\Rightarrow m^3+4m^2-16m-64=0,~~~~~~~~~[\textup{since }e^{mx}\neq 0]\\\\\Rightarrow m^2(m-4)+8m(m-4)+16(m-4)=0\\\\\Rightarrow (m-4)(m^2+8m+16)=0\\\\\Rightarrow (m-4)(m+4)^2=0\\\\\Rightarrow m-4=0,~~(m+4)^2=0\\\\\Rightarrow m=4,~m=-4,~-4.

So, the general solution is given by

y(x)=Ae^{4x}+Be^{-4x}+Cxe^{-4x}.

Then, we have

y^\prime=4Ae^{4x}-4Be^{-4x}-4Cxe^{-4x}+Ce^{-4x},\\\\y^{\prime\prime}=16Ae^{4x}+16Be^{4x}+16Cxe^{-4x}-4Ce^{-4x}-4Ce^{-4x}\\\\\Rightarrow y^{\prime\prime}=16Ae^{4x}+16Be^{4x}+16Cxe^{-4x}-8Ce^{-4x}.

With the conditions given, we get

y(0)=A+B+C\times 0\\\\\Rightarrow A+B=0\\\\\Rightarrow A=-B~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)

y^\prime(0)=4A-4B+C\\\\\Rightarrow 4A-4B+C=26\\\\\Rightarrow 4(A+A)+C=26~~~~~~~~~~~~~~~~[\textup{using equation (i)}]\\\\\Rightarrow C=26-8A~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)

and

y^{\prime\prime}(0)=16A+16B-8C\\\\\Rightarrow 16A-16A-8C=-16~~~~~~~~~~~~[\textup{using equation (ii)}]\\\\\Rightarrow -8C=-16\\\\\Rightarrow C=2.

From equation (iii), we get

C=26-8A\\\\\Rightarrow 2=26-8A\\\\\Rightarrow 8A=24\\\\\Rightarrow A=3.

From equation (ii), we get

B=-3.

Therefore, the required solution of the given differential equation is

y(x)=3e^{4x}-3e^{-4x}+2xe^{-4x}.

4 0
3 years ago
Problem Emily convinced her mom to buy a giant box of her favorite cereal. Her mom doesn't think the box will fit on their shelf
Doss [256]
The height of the box should be 40cm
3 0
2 years ago
Explain please thanks
Paladinen [302]
All the angles inside a triangle add up to 180°.

(2x + 15) + (5x + 5) + x = 180
8x + 20 = 180
8x = 180 - 20
8x = 160
x = 160/8
x = 20
the question is asking what angle B is,
B = 2(20) + 15
B = 40 + 15
B = 55°
7 0
3 years ago
Can anyone tell me what is 2/5 x 3/2 ?
Mars2501 [29]

Answer:

6/10

Step-by-step explanation:

2 × 3 = 6

5 × 2 = 10

OR

6/10 = 3/5

4 0
2 years ago
Read 2 more answers
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