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kramer
3 years ago
10

Pls help me with this

Mathematics
1 answer:
ValentinkaMS [17]3 years ago
6 0
I don’t see anything
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.05×+.25=1.0 idk how to do this
Ede4ka [16]
.05 x 1.5 + .25 = 1.0
3 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
The perimeter of an isosceles triangle is 1 m, and the length of the base is equal to 0.4 m. Find the length of a leg.​
ExtremeBDS [4]

Answer:

0.22m

Step-by-step explanation:

0.22361m

7 0
2 years ago
At the bank of a river, by measurement, a = 9 ft., b = 15 ft., c = 12 ft., and d = 7 ft.How long is x?
Orlov [11]

Answer: x is 20

Step-by-step explanation:

This is ratio

a : c = b : x and d : unknown

a : c = 9 : 12 = 3 : 4 which is 9/12

b : x = 15 : x which is 15 / x

So the proportion will be :

3/4 = 15/x

So Cross multiplying

3x = 90

Divide both side by 3

x = 90/3

x = 20

7 0
3 years ago
150 centimeters is equivalent to
Elina [12.6K]
<span>150 centimeters is equivalent to 1 1/2 meters </span>
6 0
3 years ago
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