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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find the value for x and y (no decimals
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]
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
HELP PELASE ASAPppppp
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.
Answer:
third angle =180-two congruent angles. is expression.
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
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 help me with a full math assignment about slope rate of change and stuff? i will give them brainliest answer too
Answer:
yes of course .
I will help you .
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)
}
Answer:
The relation is a function.
what is 9 1/6 - 2 3/4?
Answer:
6 5/16
Step-by-step explanation:
Hope this helped :)
Expand and combine like terms.
(765 – 46)(765 + 46)
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
Having trouble solving this:
Answer:
The answer is 24*(1/5)........
Answer:
the answer is D) 121/500
Step-by-step explanation:
I don’t really understand could you help
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
Answer:
ASA
Step-by-step explanation:
another possible pair is ∠A and ∠B
so it makes it ASA
What do you notice about the equation y=12?
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
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: $
Answer:
Your answer is.....
8064$
Mark it as brainlist answer . follow me for more answer.
Step-by-step explanation:
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?
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
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?
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]
Add. (15w - 6x) and (6x + 20w)
Answer:
35w
Step-by-step explanation:
15w-6x+6x+20w
collect like terms
15w+20w-6x+6x
=35w
what is the distance between 0,4 and -1,-5
Answer:
y = −x + 4
Step-by-step explanation:
What is the domain of the function graphed below?
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
Answer:
The answer would be it would increase by 40,000
direction: find the quotiend
Answer:
broo this is easy check the comments the on yo tail
Step-by-step explanation:
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!!
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°
The area of triangle ABC is?
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
Answer:
a is 130 c is 50 and d is 130 opposite angles are equal and corresponding angles sum equals 180
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?
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
who ever awnsers first get brainleist
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
3.) Find the slope between the 2 points.
х
-2
-1
0
1
2
Y
-3
-1
1
3
5
Plz help ASAP with the correct answer plz
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.
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
Can someone please help me will give brainlist
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