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Mrac [35]
3 years ago
11

Determine the longest interval in which the given initialvalue problemis certainto have a unique twicedifferentiable solution. D

o not attempt to find the solutionty'' + 3y = t, y(1) = 1, y'(1) = 9
Mathematics
1 answer:
AlekseyPX3 years ago
6 0

Answer:

t_o = 3, so solution exists on (0,4).  

Step-by-step explanation:

Use Theorem

Divide equation with t(t — 4).

y''+[3/(t-4)]*y'+ [4/t(t-4)]*y=2/t(t-4)

p(t)=3/t-4—> continuous on (-∞, 4) and (4,∞)

q(t) = 4/t(t-4) —> continuous on (-∞,0), (0,4) and (4, ∞)

g(t) = 2/t(t-4)—> continuous on (-∞, 0), (0,4) and (4,∞)

t_o = 3, so solution exists on (0,4).  

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Please help <br> I will mark brainlist
Naya [18.7K]

Answer:

B x = sqrt(48)

Step-by-step explanation:

Half of the bottom side measures 4.

4^2 + x^2 = 8^2

16 + x^2 = 64

x^2 = 48

x = sqrt(48)

Answer: B x = sqrt(48)

4 0
3 years ago
Please include work!
geniusboy [140]

Answer:

x = ± 4

y = - 2

Step-by-step explanation:

y = 0.5x² - 10 ------------------------(I)

y = -x² + 14   ------------------------(II)

Substitute the y value in equation (II)

    0.5x² - 10  = -x² + 14           {Add x² to both sides}            

0.5x² + x² -10 = 14                  {combine like terms}

       1.5x² - 10 = 14                   {Add 10 to both sides}

               1.5x² = 14 + 10

                1.5x² = 24         {Divide both sides by 1.5}

               1.5x²/1.5 = 24/1.5

                       x² = 16

                      x = ±4

Substitute x = 4 in (I)

y = 0.5 * 4² - 10

 = 0.5*16 - 10

 = 8- 10

y = -2

Substitute x = -4 in (I)

y = 0.5 * (-4)² - 10

 = 0.5*16 - 10

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y = -2

5 0
3 years ago
I need help again.lol
Monica [59]

Answer:

13\ units

Step-by-step explanation:

One is asked to find the distance between two points on a coordinate plane. The easiest way to do so is to use the distance formula, this formula is the following:

D=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2

Where ((x_1,y_1)) and ((x_2,y_2)) are the points which one needs to find the distance between. In this case, these points are as follows:

k\ (-3,5)

j\ (-8, -7)

Substitute these points into the formula and solve for the distance between these points,

D=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2

D=\sqrt{((-3)-(-8))^2+((5)-(-7))^2

Simplify,

D=\sqrt{((-3)-(-8))^2+((5)-(-7))^2

D=\sqrt{(-3+8)^2+(5+7)^2

D=\sqrt{(5)^2+(12)^2

D=\sqrt{25+144}

D=\sqrt{169}

D=13

8 0
2 years ago
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7 0
3 years ago
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10th term of an= 20-2n
Dmitry [639]

Answer:

We have that a_{n} = 20-2n

Step-by-step explanation:

We have just to replace n=10 on the general equation

a_{10} = 20-2×10

Therefore:

a_{10} = 0

8 0
3 years ago
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