Find the particular solution of the differential equation?
/=5^3+9^2, when =1, =8
Answers
Answer:
[tex]\displaystyle s = \frac{5t^4}{4} + \frac{9}{t} - \frac{9}{4}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to RightEquality Properties
Multiplication Property of EqualityDivision Property of EqualityAddition Property of EqualitySubtraction Property of EqualityAlgebra I
Exponential Rule [Rewrite]: [tex]\displaystyle b^{-m} = \frac{1}{b^m}[/tex]Calculus
Derivatives
Derivative Notation
Solving Differentials - Integrals
Integration Constant C
Integration Rule [Reverse Power Rule]: [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]
Integration Property [Multiplied Constant]: [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
Integration Property [Addition/Subtraction]: [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]
Step-by-step explanation:
*Note:
Ignore the Integration Constant C on the left hand side of the differential equation when integrating.
Step 1: Define
[tex]\displaystyle \frac{ds}{dt} = 5t^3 + \frac{9}{t^2}[/tex]
t = 1
s = 8
Step 2: Integrate
[Derivative] Rewrite [Leibniz's Notation]: [tex]\displaystyle ds = (5t^3 + \frac{9}{t^2})dt[/tex][Equality Property] Integrate both sides: [tex]\displaystyle \int {} \, ds = \int {(5t^3 + \frac{9}{t^2})} \, dt[/tex][Left Integral] Reverse Power Rule: [tex]\displaystyle s = \int {(5t^3 + \frac{9}{t^2})} \, dt[/tex][Right Integral] Rewrite [Integration Property - Addition]: [tex]\displaystyle s = \int {5t^3} \, dt + \int {\frac{9}{t^2}} \, dt[/tex][Right Integrals] Rewrite [Integration Property - Multiplied Constant]: [tex]\displaystyle s = 5\int {t^3} \, dt + 9\int {\frac{1}{t^2}} \, dt[/tex][Right Integrals] Rewrite [Exponential Rule - Rewrite]: [tex]\displaystyle s = 5\int {t^3} \, dt + 9\int {t^{-2}} \, dt[/tex][Right Integrals] Reverse Power Rule: [tex]\displaystyle s = 5(\frac{t^4}{4}) + 9(\frac{t^{-1}}{-1}) + C[/tex][Right Integrals] Rewrite [Exponential Rule - Rewrite]: [tex]\displaystyle s = 5(\frac{t^4}{4}) + 9(\frac{1}{t}) + C[/tex]Multiply: [tex]\displaystyle s = \frac{5t^4}{4} + \frac{9}{t} + C[/tex]Step 3: Solve
Substitute in variables: [tex]\displaystyle 8 = \frac{5(1)^4}{4} + \frac{9}{1} + C[/tex]Evaluate exponents: [tex]\displaystyle 8 = \frac{5}{4} + \frac{9}{1} + C[/tex]Divide: [tex]\displaystyle 8 = \frac{5}{4} + 9 + C[/tex]Add: [tex]\displaystyle 8 = \frac{41}{4} + C[/tex][Subtraction Property of Equality] Isolate C: [tex]\displaystyle \frac{-9}{4} = C[/tex]Rewrite: [tex]\displaystyle C = \frac{-9}{4}[/tex]Particular Solution: [tex]\displaystyle s = \frac{5t^4}{4} + \frac{9}{t} - \frac{9}{4}[/tex]
Topic: AP Calculus AB/BC (Calculus I/II)
Unit: Differentials Equations and Slope Fields
Book: College Calculus 10e
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Answers
Answer:
Step-by-step explanation:
It depends on whether the 30 cm side is the hypotenuse, or one of the legs.
If the 30 cm side is the hypotenuse, then the third side is √(30^2-10^2) = √800 = 20√2 cm
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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Step-by-step explanation:
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Step-by-step explanation:
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Answers
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Answers
Answer:
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Step-by-step explanation:
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Answers
Answer:
2
Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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Answers
Answer:
Step-by-step explanation:
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b=6
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Answers
Answer:
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If we go upwards N units, then we add N.
If we go downwards N units, then we subtract N.
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Answers
Answer:
the answer is 10832
Step-by-step explanation:
you can use a calculator
Answer:
10832
Step-by-step explanation:
Add one digit at the time (from right to left):
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Answers
Answer:
x=16, have a great day
Step-by-step explanation:
Answer:
x = 16
Step-by-step explanation:
13x + 7 = 215
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Answers
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Answers
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Step-by-step explanation:
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Answers
Answer:
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Answers
Answer:
Step-by-step explanation:
5(m-3)≥7m-2.4
5m-15≥7m-2.4
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Answer:
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Step-by-step explanation:
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Answers
Answer:
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Step-by-step explanation:
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Suppose that we have a rectangle with length L and width W.
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Step-by-step explanation:
Answer:
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Answer:
Step-by-step explanation:
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-2x-3y=-7
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Answers
Answer:
x = 2
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Step-by-step explanation:
-2x-3y=-7, y=6x-11
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x = 2
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Answer:
x = 2, y = 1
Step-by-step explanation:
We have a system of equations:
-2x - 3y = -7
y = 6x - 11
Substitute the given value of y into the equation -2x - 3y = -7
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17 miles in 2 minutes;
60 miles in 8 minutes;
26 miles in 4 minutes;
33 miles in 6 minutes
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The hypotenuse of a triangle is one foot more than
twice the length of the shorter leg. The longer leg IS
seven feet longer than the shorter leg. Find the
dimensions of the triangle.
Answers
Answer:
y uwu
Step-by-step explanation: i think
plzzz helppp!!!!! Marking most Brainly!!!!!
Answers
Answer:
c
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
there are less people to answer so it wouldn't be enough
30 POINTS PLUS BRAINLIEST PLEASE ANSWER THESE MATH QUESTIONS.ALL TROLL ANSWERS WILL BE REPORTED MUST HE DONE IN 1HR OR.LESS.
Answers
Answer:
4) wall = 114 ft^2
$118.56 to paint
5) 77 cm^2
Step-by-step explanation:
4) (15 x 8)-(2 x 3)=120-6=114 ft^2
114 x $1.04 = $118.56
5) (14 x 3.5) + (8 x 3.5) = 49 + 28 = 77 cm^2
Answer:
4:
114,$118.56
5. 77
Step-by-step explanation:
To find the area of the wall, you multiply 15 x 8, then subtract (2 x 3) from that answer.
15 x 8 = 120
120 - (3 x 2) =
120 - 6 = 114ft^2
To find the cost, multiply the area by the cost:
1.04 x 114 = $118.56
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8 x 3.5 = 28 cm^2
14 x 3.5 = 49cm^2
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49 + 28 = 77 cm^2
Find four consecutive odd integers if the sun of the first and fourth is 3 less than 3 times the second
Answers
Answer:
5
Step-by-step explanation:
Solve this system using the substitution method: 2a-4b=9; 2b-4a=-3
Answers
Answer:
1 ) 1,4.5 2)1,-5/4
Step-by-step explanation:
we have to solve both by :
let a be (1) in first case
now solve like this 2(1)-4b=9
