ds dt = 12t (3t^2 - 1)^3 , s(1) = 3

Answers

Answer 1

One solution is t ≈ 0.4515, which corresponds to s ≈ 4.2496.

To solve this differential equation, we can use separation of variables:

ds/dt = 12t(3t^2 - 1)^3

ds/(3t(3t^2 - 1)^3) = 4dt

Integrating both sides:

∫ds/(3t(3t^2 - 1)^3) = ∫4dt

Using substitution, let u = 3t^2 - 1, du/dt = 6t

Then, we can rewrite the left-hand side as:

∫ds/(3t(3t^2 - 1)^3) = ∫du/(2u^3)

= -1/(u^2) + C1

Substituting back in u = 3t^2 - 1:

-1/(3t^2 - 1)^2 + C1 = 4t + C2

Using the initial condition s(1) = 3, we can solve for C2:

-1/(3(1)^2 - 1)^2 + C1 = 4(1) + C2

C2 = 2 - 1/16 + C1

Substituting C2 back into the equation, we get:

-1/(3t^2 - 1)^2 + C1 = 4t + 2 - 1/16 + C1

Simplifying:

-1/(3t^2 - 1)^2 = 4t + 2 - 1/16

Multiplying both sides by -(3t^2 - 1)^2:

1 = -(4t + 2 - 1/16)(3t^2 - 1)^2

Expanding and simplifying:

49t^6 - 48t^4 + 12t^2 - 1 = 0

This is a sixth-degree polynomial, which can be solved using numerical methods or approximations. One solution is t ≈ 0.4515, which corresponds to s ≈ 4.2496.

Learn more about solution here:

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Related Questions

Find the mean then the mean absolute deviation (MAD) of the following data set Round your answer to two decimal places if necessary
3, 1, 5, 4, 8,6

Answers

Rounded answers (are in parentheses )
Mean-4.5 (5)
Median-4.4 (5)
Mode-3,1,5,4,8,6
Range-7
(MAD)-1.83 (rounded 2)


Plz help ASAP with the correct answer plz

Answers

Taking over his thoughts is the answer

Answer:

3rd one

Step-by-step explanation:

its an idiom you are welcome

x varies directly with
y. If x = 60 when
y = 75. find x when
y = 32.

Answers

Answer:

x=17

Step-by-step explanation:

Answer:

25.6

Step-by-step explanation:

find constant of variation ('k'):

y = kx

75 = 60k

k = 75/60 or 5/4

32 = 5/4x

cross-multiply:

5x = 128

x = 25.6

There were 60 students enrolled in Grade 5 last year. If 66 students are enrolled in the same grade level this year, what is the percentage increase in the number of Students?

Answers

There is a 10% increase

There are 6 more students this year than there were last year.

If you find what 10% of 60 is and add that to 60, you'll find that it'll equal 66.

//

[tex]60 \times 0.10 = 6[/tex]

[tex]10\% \: of \: 60 \: is \: 6[/tex]

[tex]60 + 6 = 66[/tex]

Yep here we go again:

In the diagram below, the red angle angle YAK and the blue angle angle OAT are both right angles. If angle YAO=23 then what is the measure of angle KAT

If you don't know the answer or not sure, please don't answer it!
Whoever answers it correctly gets brainliest!!

Answers

Answer:

23 degrees

Step-by-step explanation:

90+23-90=23

9514 1404 393

Answer:

  23°

Step-by-step explanation:

Both angles YAO and KAT are complementary to angle OAK, so are congruent.

  ∠YAO = ∠KAT = 23°

Last year, Diane opened an investment account with S6400. At the end of the year, the amount in the account had increased by 26%.
(a) Fill in the blank to write the year-end amount in terms of the original amount. Write
your answer as a decimal.
Year-end amount =. XOriginal amount
(1) Use your answer in part (ə) to determine the year-end amount in Diane's account
Year-end amount: $

Answers

Answer:

Your answer is.....

8064$

Mark it as brainlist answer . follow me for more answer.

Step-by-step explanation:

who ever awnsers first get brainleist

Answers

Answer: 4 servings

Step-by-step explanation:  If a serving of juice is 1/8 of the pitcher, we know that a full pitcher is capable of 8 servings, because 8 servings would be 8/8 of the picher, that is, the whole pitcher therefor 8 serivngs: 4 servings

Having trouble solving this:

Answers

Answer:

The answer is 24*(1/5)........

Answer:

the answer is D) 121/500

Step-by-step explanation:

Expand and combine like terms.
(765 – 46)(765 + 46)

Answers

Answer:

587,341

Step-by-step explanation:

(I'm hoping this is what you mean by expand)

(765 – 46)(765 + 46)

First, multiply 765 by 765 = 585,225

Second, multiply 765 by 46 = 35,190

Third, multiply -46 by 765 = -35,190

Fourth, multiply -46 by 46 = -2,116

The second and third answers (35,190 and -35, 190) will cancel each other out. Then, just subtract -2,116 from 585,225.

585,225 - (-2,116) = 585,225 + 2,116 = 587,341

HELP PELASE ASAPppppp

Answers

Answer:

(a)[tex]\frac{d}{a}=\frac{a}{f}[/tex]

(d)[tex]\frac{e}{c}=\frac{c}{f}[/tex]

(b)[tex]\frac{d}{b}=\frac{b}{e}[/tex]

Step-by-step explanation:

All right triangles are similar

When two triangles are similar then the ratio  of their corresponding sides are equal.

Using the property

[tex]\triangle ABC\sim \triangle DBA[/tex]

[tex]\frac{BC}{AB}=\frac{AB}{BD}[/tex]

[tex]\frac{e}{c}=\frac{c}{f}[/tex]

[tex]\triangle ACD\sim\triangle BAD[/tex]

[tex]\frac{CD}{AD}=\frac{AD}{BD}[/tex]

[tex]\frac{d}{a}=\frac{a}{f}[/tex]

[tex]\triangle ACD\sim \triangle BCA[/tex]

[tex]\frac{CD}{AC}=\frac{AC}{BC}[/tex]

[tex]\frac{d}{b}=\frac{b}{e}[/tex]

Correct options are

(a)[tex]\frac{d}{a}=\frac{a}{f}[/tex]

(d)[tex]\frac{e}{c}=\frac{c}{f}[/tex]

(b)[tex]\frac{d}{b}=\frac{b}{e}[/tex]

ANSWER ASAP GIVING BRAINLIEST FIVE STARS AND A HEART I ONLY NEED A FEW SENTENCES!
Please answer the following essay question:
An isosceles triangle has two congruent angles. Write an expression to represent the measure of the third angle of the triangle. Explain.

Answers

Answer:

third angle =180-two congruent angles. is expression.

The area of triangle ABC is?

Answers

Answer:

[tex] A(\triangle ABC) =17.5 \: {units}^{2} [/tex]

Step-by-step explanation:

AB = 4 - (-3) = 4 + 3 = 7 units

BC = 3 - (-2) = 3 + 2 = 5 units

[tex]A(\triangle ABC) = \frac{1}{2} \times AB\times BC \\ \\ A(\triangle ABC) = \frac{1}{2} \times 7\times 5 \\ \\ A(\triangle ABC) = \frac{1}{2} \times 35 \\ \\ A(\triangle ABC) =17.5 \: {units}^{2} [/tex]

in parallelogram
abcd if b=50 find the other angles​

Answers

Answer:

a is 130 c is 50 and d is 130 opposite angles are equal and corresponding angles sum equals 180

What do you notice about the equation y=12?

Answers

Answer:

X=0

Step-by-step explanation:

If you look at the graph and follow, the x axis to match up with y=12, then you will see that x is 0

Answer:

M=0

Step-by-step explanation:

I got it right on I-Ready and because there is no change in y

Add. (15w - 6x) and (6x + 20w)​

Answers

Answer:

35w

Step-by-step explanation:

15w-6x+6x+20w

collect like terms

15w+20w-6x+6x

=35w

3.) Find the slope between the 2 points.
х
-2
-1
0
1
2
Y
-3
-1
1
3
5

Answers

Slope: 2

-3-(-1)/-2-(-1) = 2

Slope formula:

m=y2-y1/x2-x1

What is the domain of the function graphed below?

Answers

Answer:

Positive infinite to negative infinite

Step-by-step explanation:

If the Federal Reserve buys $40,000 in Treasury bonds from a bank at 6%
interest, what is the immediate effect on the money supply?
A. It is decreased by $40,000
B. It is increased by $40,000
C. It is decreased by $2400
D.it is increased by $2400

Answers

Answer:

The answer would be it would increase by 40,000

The answer would be B it is increased by 40,000

what is 9 1/6 - 2 3/4?

Answers

Answer:

6 5/16

Step-by-step explanation:

Hope this helped :)

direction: find the quotiend​

Answers

Answer:

broo this is easy check the comments the on yo tail

Step-by-step explanation:

Question 2 (1 point)
Use the vertical line test to determine whether the relation is a function.
{(3,0), (2,-1). (-1,4). (1,-2)
}

Answers

Answer:

The relation is a function.

find the value for x and y (no decimals

Answers

Answer:

x=6

y=3r3

Step-by-step explanation:

[tex]\frac{x}{sin90} =\frac{x}{sin60} =\frac{3}{sin3}\\x=6\\y=3\sqrt{3}=3r3[/tex]

El perímetro de un rombo es igual al de un pentagono regular más 9, y la medida del lado del rombo es el doble de lo que mide un lado del pentagono. ¿Cuánto miden los lados de cada figura?

Answers

Answer:

Rombo es 6

Pentágono es 3

Step-by-step explanation:

Formula del perímetro de un rhombus es 4a

Formula del perímetro de un pentágono es 5b

La pregunta dice

4a = 5b + 9

Otra vez, la pregunta dice la medida del lado del rombo es el doble de lo que mide un lado del pentagono. Entonces,

a = 2b

Si

4a = 5b + 9 y

a = 2b, entonces que

4(2b) = 5b + 9

8b = 5b + 9

8b - 5b = 9

3b = 9

b = 9/3

b = 3

si, b = 3, tan

a = 2(3)

a = 6

Entonces, la medida del lado del rombo es 6 y la medida del lado del pentágono es 3

Harold cut 18 1/2 noches of ropero that was 60 inches long how much is the length of the remaining rope un inches written un decimals f From

Answers

Answer:

41.5

Step-by-step explanation:

If you do 60- 18.5 (1/2 = 0.5), you get about 41.5 inches left of the rope

Can someone please help me will give brainlist

Answers

Answer:

yes

Step-by-step explanation:

start by solving for the missing value. all angles of a triangle should add up to 180. Subtract 31 adn 106 from 180 from the left side, you will get 43. Now do the same to the other side. 180 subtracted by 31 and 43 make 106. Thus, making the triangles the same. hope this helps

I don’t really understand could you help

Answers

Answer:

M: (-7, -3)

A: (0, -3)

T: (0, -8)

Step-by-step explanation:

each of the points are associated with a letter. you can find the points by looking at the points it matches up with in the formatting of (x,y)

for example, for M, you can see that the dot on the x axis seems to be hovering below -7, on the y axis, it seems to be hovering next to -3. therefore, its (-7,-3)


Are the triangles congruent? If so, name the postulate or theorem that
justifies your statement.
Given: AE || BD, AE =BD,
LED
Conclusion: AEB – ABDC

Answers

Answer:

ASA

Step-by-step explanation:

another possible pair is ∠A and ∠B

so it makes it ASA

what is the distance between 0,4 and -1,-5

Answers

Answer:

y  =  −x + 4

Step-by-step explanation:

If the temperature outside is 60 degrees at 6 pm and then drops by 15% at 10 pm, what is the temperature at 10 pm?

Answers

Answer:

51 degrees

Step-by-step explanation:=Given data

Temperature at 6pm = 60 degrees

percent drop= 15%

= 15/100*60

=0.15*60

=9 degrees

Hence the temperature at 10 pm is 60-9= 51 degrees

Can someone help me with a full math assignment about slope rate of change and stuff? i will give them brainliest answer too

Answers

Answer:

yes of course .

I will help you .

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