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son4ous [18]
3 years ago
11

Find the value of kk for which the constant function x(t)=kx(t)=k is a solution of the differential equation 5t3dxdt+2x−2=05t3dx

dt+2x−2=0
Mathematics
1 answer:
uranmaximum [27]3 years ago
3 0
Given the differential equation

5t^3 \frac{dx}{dt} +2x-2=0

The solution is as follows:

5t^3 \frac{dx}{dt} +2x-2=0 \\  \\ \Rightarrow5t^3 \frac{dx}{dt} =2-2x \\  \\ \Rightarrow \frac{5}{2-2x} dx= \frac{1}{t^3} dt \\  \\ \Rightarrow \int {\frac{5}{2-2x} } \, dx = \int {\frac{1}{t^3}} \, dt \\  \\ \Rightarrow- \frac{5}{2} \ln(2-2x)=- \frac{1}{2t^2} +A \\  \\ \Rightarrow\ln(2-2x)= \frac{1}{5t^2} +B\\  \\ \Rightarrow2-2x=Ce^{\frac{1}{5t^2}} \\  \\ \Rightarrow 2x=Ce^{\frac{1}{5t^2}}+2 \\  \\ \Rightarrow x=De^{\frac{1}{5t^2}}+1
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Y = −3x <br> x + y = −4<br> Solution system
Verizon [17]

Answer:

Step-by-step explanation:

Y = - 3x. Equation 1

x + y = - 4 equation 2

Putting value of y

x + (-3x) = - 4

x - 3x = - 4

-2x = - 4

x = - 4/-2 = 2

Putting value of x in the equation 1

Y = - 3(2)

Y = - 6

7 0
3 years ago
Please help! ill mark you as brain if your right!!!!
yulyashka [42]

Answer:

SA = 1099 square inches.

Step-by-step explanation:

Just plug into the formula

SA = 2pir^2 + 2pi r h where pi = 3.14, r = 5 and h = 30

SA = 2 (3.14) (5^2) + 2 (3.14)(5)(30)

SA = 157 + 942

SA = 1099 square inches.

6 0
3 years ago
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ehidna [41]
To find slope subtract the two points in the coordinate (y). We have 8 and 4 so subtract those two. You get 8-4=4. Now start from the same coordinate expect this time subtract (x). Which is 9-3=6. You have 4/6 simplify and you get 2/3. Your slope is 2/3. Hope this helps
5 0
2 years ago
Help ^^^ use picture above
aalyn [17]
The question reminds you of all the tools you need:

It says ...

"Opposite angles are equal."
So the upper right angle is x+40 just like the bottom left,
and the bottom right angle is 3x+20 just like the upper left.

And it says ...

"The sum of all angles is 360°."
You know what each of the four angles is, so you can addum all up,
set the sum equal to 360, find out what number ' x ' is, and then
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8 0
3 years ago
Read 2 more answers
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N76 [4]

Answer:

12

Step-by-step explanation:

These are similar triangles, so the ratio of their sides is the same for each side.

AB = 8  and  BD = 10

So, the ratio is 8:10   or   4:5

Because the triangles are similar....

The ratio of AC:CE  is also  4:5

12:15 = 4:5

So, 12 is the answer!

8 0
3 years ago
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