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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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The table represents a function.
Elenna [48]

f(5) is -8 ⇒ 1st answer

Step-by-step explanation:

Function is a relation between set of of ordered pairs (x , y),and every x has only one y

Examples:

  • {(-1 , 2) , (2 , 4) , (5 , -3)} is a function because x = -1 has only y = 2, x = 2 has only y = 4 and x = 5 has only y = -3
  • {(-2 , 4) , (0 , -1) , (-2 , 5)} is not a function because x = -2 has y = 4 and 5

The notation of the function is f(x) = y

The table:

→    x     :    f(x)

→    -4    :    -2

→    -1     :    5

→     3    :    4

→     5    :   -8

From the table

∵ x = -4

- The corresponding value of y to x = -4 is -2

∴ f(-4) = -2

∵ x = -1

- The corresponding value of y to x = -1 is 5

∴ f(-1) = 5

∵ x = 3

- The corresponding value of y to x = 3 is 4

∴ f(3) = 4

∵ x = 5

- The corresponding value of y to x = 5 is -8

∴ f(5) =-8

f(5) is -8

Learn more:

You can learn more about the functions in brainly.com/question/10879401

#LearnwithBrainly

3 0
3 years ago
Solve x/-5=-15 and i will give brainliest if right answers are
san4es73 [151]

Answer:

if x divided by negative 5 equals negative 15, you multiply both sides by negative 5, leaving x = 75, which should be your answer

Step-by-step explanation:

8 0
3 years ago
-1/3 + 7/4. in simplest form plzz
Goryan [66]
Greatest Common Factor: 12-1/3 = -4/12, 7/4 = 21/12-4/12 + 21/12 = 17/12
Answer in simplest form: 17/12
7 0
3 years ago
Read 2 more answers
Find the distance between each pair if points
sukhopar [10]

Answer:

point a is positive but point b is negative

6 0
3 years ago
A line m is perpendicular to an angle bisector of ∠A. The sides of ∠A intersect this line m at points M and N. Prove that △AMN i
Ray Of Light [21]

Answer:


Step-by-step explanation:

<em><u>Given</u></em><u>:</u>       A line m is perpendicular to the angle bisector of ∠A. We call this  

                 intersecting point as D. Hence, in figure ∠ADM=∠ADN =90°.

                 AD is angle bisector of ∠A. Hence, ∠MAD=∠NAD.

<u><em>To Prove</em></u>:   <em><u>ΔAMN is an isosceles triangle. i.e any two sides in ΔAMN are</u></em>

<em>                    </em><em><u>equal. </u></em>

<em><u>Solution</u></em>:  Now, In ΔADM and ΔADN

                 ∠MAD=∠NAD     ...(1) (∵Given)

                  AD=AD                ...(2) (∵common side)

                  ∠ADM=∠ADN     ...(3) (∵Given)

                  <u><em> Hence, from equation (1),(2),(3) ΔADM ≅ ΔADN</em></u>

                                                         ( ∵ ASA  congruence rule)

                  ⇒<u><em> AM=AN</em></u>

                  Now, In Δ AMN

                 AM=AN (∵ Proved)

                  Hence, ΔAMN is an isosceles  triangle.


7 0
3 years ago
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