Answer:
[tex]\displaystyle f(t) = \frac{t^5}{5} + 91t - 3ln|t| - \frac{1819}{20}[/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
FunctionsFunction NotationCalculus
Derivatives
Derivative Notation
Antiderivatives - 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 [Addition/Subtraction]: [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]
Integration Property [Multiplied Constant]: [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle f'(t) = t^4 + 91 - \frac{3}{t}[/tex]
[tex]\displaystyle f(1) = \frac{1}{4}[/tex]
Step 2: Integration
Integrate the derivative to find function.
[Derivative] Integrate: [tex]\displaystyle \int {f'(t)} \, dt = \int {t^4 + 91 - \frac{3}{t}} \, dt[/tex]Simplify: [tex]\displaystyle f(t) = \int {t^4 + 91 - \frac{3}{t}} \, dt[/tex]Rewrite [Integration Property - Addition/Subtraction]: [tex]\displaystyle f(t) = \int {t^4} \, dt + \int {91} \, dt - \int {\frac{3}{t}} \, dt[/tex][1st Integral] Integrate [Integral Rule - Reverse Power Rule]: [tex]\displaystyle f(t) = \frac{t^5}{5} + \int {91} \, dt - \int {\frac{3}{t}} \, dt[/tex][2nd Integral] Integrate [Integral Rule - Reverse Power Rule]: [tex]\displaystyle f(t) = \frac{t^5}{5} + 91t - \int {\frac{3}{t}} \, dt[/tex][3rd Integral] Rewrite [Integral Property - Multiplied Constant]: [tex]\displaystyle f(t) = \frac{t^5}{5} + 91t - 3\int {\frac{1}{t}} \, dt[/tex][3rd Integral] Integrate: [tex]\displaystyle f(t) = \frac{t^5}{5} + 91t - 3ln|t| + C[/tex]Our general solution is [tex]\displaystyle f(t) = \frac{t^5}{5} + 91t - 3ln|t| + C[/tex].
Step 3: Find Particular Solution
Find Integration Constant C for function using given condition.
Substitute in condition [Function]: [tex]\displaystyle f(1) = \frac{1^5}{5} + 91(1) - 3ln|1| + C[/tex]Substitute in function value: [tex]\displaystyle \frac{1}{4} = \frac{1^5}{5} + 91(1) - 3ln|1| + C[/tex]Evaluate exponents: [tex]\displaystyle \frac{1}{4} = \frac{1}{5} + 91(1) - 3ln|1| + C[/tex]Evaluate natural log: [tex]\displaystyle \frac{1}{4} = \frac{1}{5} + 91(1) - 3(0) + C[/tex]Multiply: [tex]\displaystyle \frac{1}{4} = \frac{1}{5} + 91 - 0 + C[/tex]Add: [tex]\displaystyle \frac{1}{4} = \frac{456}{5} - 0 + C[/tex]Simplify: [tex]\displaystyle \frac{1}{4} = \frac{456}{5} + C[/tex][Subtraction Property of Equality] Isolate C: [tex]\displaystyle -\frac{1819}{20} = C[/tex]Rewrite: [tex]\displaystyle C = -\frac{1819}{20}[/tex]Substitute in C [Function]: [tex]\displaystyle f(t) = \frac{t^5}{5} + 91t - 3ln|t| - \frac{1819}{20}[/tex]∴ Our particular solution to the differential equation is [tex]\displaystyle f(t) = \frac{t^5}{5} + 91t - 3ln|t| - \frac{1819}{20}[/tex].
Topic: AP Calculus AB/BC (Calculus I/II)
Unit: Integration
Book: College Calculus 10e
pls i need help i’ll give brainliest!
9514 1404 393
Answer:
x = 12
Step-by-step explanation:
The rule here is that the product of the lengths from the external point of intersection (angle vertex) to the intersections with the circle is the same for both secants. The tangent counts as intersecting the circle twice. So, we have ...
(6)(6) = (3)(x)
x = 36/3 = 12 . . . . . divide by the coefficient of x
How many square feet is the world's largest pizza, including the crust?
(Be sure to show and/or explain your work, make your final answer clear, and include units)
The worlds largest pizza, including the crust, has a length of 131 feet
Answer:
The largest pizza has a total surface area of 1,261.65 m² (13,580.28 ft²) and was prepared by Dovilio Nardi, Andrea Mannocchi, Marco Nardi, Matteo Nardi and Matteo Giannotte (all Italy) from NIPfood at Fiera Roma, in Rome, Italy, on 13 December 2012.
Step-by-step explanation:
A bag contains 8 red pens, 7 blue pens, and 14 black pens. Denato wants to pull a blue pen from the bag. What is the sample space for this experiment? 1. Blue, Red 2. Blue 3. Red, Blue, Black 4. Red, Black
Answer:
Red and blue is the correct answer
Step-by-step explanation:
in a school , 4/9 of the students are boys and number of girls is 90 . find the number of boys in school
4/9 of the students are boys thus 5/9 students are girls.
Let " x " be the number of all students.
So we have :
5/9 × x = 90
Multiply both sides by 9/5
5/9 × 9/5 × x = 90 × 9/5
1 × x = 9 × 9 × 10 × 1/5
x = 81 × 2
x = 162
_______________________________
number of boys = 4/9 × x
n o boys = 4/9 × 162
n o boys = 162/9 × 4
n o boys = 18 × 4
n o boys = 72
Sami made 23,400 last year in income from his job. He worked 30 hours per week and worked all 52 weeks of the year. What was his hourly pay rate?
Answer:
$15 per hour
Step-by-step explanation:
30 hours per week x 52 weeks in a year = 1560 hours per year
23,400 / 1560 = $15 per hour
the object is a circle with a pentagon inside of it each of the sides of the pentagon is a chord of the circle
Answer:
The answer to ur question should be, A Object A
Answer:
a
Step-by-step explanation:
help me pass thank you!!!
Answer:
64
Step-by-step explanation:
[tex] (\frac{m^{2} }{m + 3} )^{3} \\ = \frac{m^{6} }{(m + 3)^{3} } \\ = \frac{6 {}^{6} }{{9 {}^{3} } } [/tex]
46656/729
= 64
Only please help #2,3,5, and 6
Answer:
3.$0.9
5.9:3 =3:1
Step-by-step explanation:
3.$5.40÷6=$0.9
Write the meaning of each algebraic expression. Then, evaluate the algebraic expression for the given value.
5x - 4 If x=3
In mathematics, an algebraic expression is an expression built up from integer constants, variables, and the algebraic operations (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number). For example, 3x2 − 2xy + c is an algebraic expression.
5x−4x=3
Step 1: Simplify both sides of the equation.
5x−4x=3
5x+−4x=3
(5x+−4x)=3(Combine Like Terms)
x=3
x=3
Answer:
x=3
Karrie is 24 years old. She took her age, divided by -3, added -7, then
multiplied by -4. Her result is 2 years older than her father's age. How old is
Karrie's father? *
Answer:
58 years old
Step-by-step explanation:
24/-3 is -8
-8+-7 is -15
-15*-4 is 60
60-2 is 58
How to solve x/7 = 7
Answer:
x = 49
Step-by-step explanation:
x/7 = 7
Multiply each side by 7
7* x/7 =7* 7
x = 49
What is sin 49° to the nearest tenth
Answer:
50
Step-by-step explanation:
50???
Answer:
sin49° = 0.75471
sin 49° = 0.75471
sin 49 degrees = 0.75471
Step-by-step explanation:
i Illustrative Mathematid Kendall Hu Ant Trek The distance between Los Angeles and New York City is about 3,944 km. An ant can run about 18 mm per second. How long would it take an ant to run from Los Angeles to New York City?
One half of one tenth is what fraction?
Answer:
1/2 1/100
Step-by-step explanation:
One half of one tenth is [tex]\frac{1}{20}[/tex] fraction.
What is a fraction?A number that expresses parts of a whole object or a set of objects is known as a fraction.
Given
One half of one tenth
Rewriting in mathematical form
= [tex]\frac{1}{2} (\frac{1}{10} )[/tex]
= [tex]\frac{1}{20}[/tex]
Hence, One half of one tenth is [tex]\frac{1}{20}[/tex] fraction.
Learn more about fraction here
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Find the median of the data.
93.81.94.71.89.92.94.99
The median is
Find the mode(s) of the data,
Step-by-step explanation:
MEDIAN
71, 81, 89, 92, 93, 94, 94, 99
92 + 93 = 185 / 2 = 92.5
The median is 92.5
MODE
71, 81, 89, 92, 93, 94, 94, 99
The mode is 94
What is the answer for the diagram?
Answer:
1340-
Step-by-step explanation:
PLEASE HELP
Makayla owns a small business selling used books. She knows that in the last week 58 customers paid cash, 25 customers used a debit card, and 2 customers used a credit card.
Based on these results, express the probability that the next customer will pay with a debit card as a fraction in simplest form.
Answer:
2/5 :)
Step-by-step explanation:
58+2=60+25=85-25=60 60 = 2/5
The solution is 5/17
The probability that the next customer will pay with a debit card is given by the equation A = 5/17
What is Probability?
The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible
The value of probability lies between 0 and 1
Given data ,
Let the probability that the next customer will pay with a debit card be A
Now , the equation will be
The number of customers who paid cash last week = 58 customers
The number of customers who used debit card last week = 25 customers
The number of customers who used credit card last week = 2 customer
So ,
The total number of customers = 58 + 25 + 2
The total number of customers = 85 customers
Now , the probability that the next customer will pay with a debit card A = number of customers who used debit card last week / total number of customers
Substituting the values in the equation , we get
Probability that the next customer will pay with a debit card A = 25 / 85
On simplifying the equation , we get
Probability that the next customer will pay with a debit card A = 5 / 17
Therefore , the value of A is 5/17
Hence , the probability is 5/17
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help me please I have to pass
Answer:
Step-by-step explanation:
15% of 400
15/100*400
15*400/100
6000/100
60
therefore ur answer is 60
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]
[tex] \frac{15}{100} \times 400 \\ =15 \times 4 \\ = 60 [/tex]
[tex]\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning }}{\orange{.}}}}}[/tex]
A population of 950 bacteria grows continuously at a rate of 4.75% per day.
Write an exponential function, N (t ), that represents the bacterial population after t days.
Solve the inequity -3y + 80 > 110
Answer: y<-10
Step-by-step explanation:
i hope this help :)
Answer:
y<-10
Step-by-step explanation:
-3y+80>110
-80 -80
-3y>30
-y>10
y<-10 (when deviding by a negative, > switches to <)
Plz help me well mark brainliest if correct.....???
Answer:
D) line graph
Step-by-step explanation:
There is two lines on the graph that have points on each which makes this graph a line graph.
Hope this helped :)
Answer:
its a line graph
Step-by-step explanation:
is a graph that uses lines to connect individual data points displaying quantitative values over a specified time interval.
Given a variance of 1992.8, what is the standard deviation?
about 44.64
about 43.13
about 43.76
about 45.20
Answer:
About 44.64.
Step-by-step explanation:
Variance and standard deviation:
The standard deviation is the square root of the variance.
In this question:
Variance of 1992.8. So
[tex]s = \sqrt{1992.8} = 44.64[/tex]
So about 44.64.
A rectangular prism has a length of 5 meters, a width of 6 meters, and a height of 3 meters.
What is the volume of the prism?
Pls hurry
Give Brainlyest
volume = length x width x height
volume = 5m x 6m x 3m = 90 m³
Evaluate the expression when x=7 and y=-3. 5y2-x
the perimeter of a rectangle is 90m. The length is three less than five times the width. What is the length and the width of the rectangle?
Answer:
length : 37 m
width : 8 m
Step-by-step explanation:
perimeter = 2×l(ength) + 2×w(idth) = 90
l = 5w - 3
=> 2×(5w-3) + 2w = 90
10w - 6 + 2w = 90
12w = 96
w = 8
=> l = 5w - 3 = 5×8 -3 = 40-3 = 37
Leia needs to make at least 40 necklaces to sell at a craft show. So far, she has made 7. Which inequality shows the
number of necklaces, n, that she still needs to make?
A). n - 7 less than or equal to 40
B) n - 7 greater than or equal to 40
C). n + 7 less than or equal to 40
D). n + 7 greater than or equal to 40
Answer:
The answer is D
Hope this helps!
Brainliest??
Answer:
D
Step-by-step explanation:
the answer is D because if she already made 7 she need to add n to 7 to get 40 or greater
A machine in a candy factory can
make 62 candies in one hour. About
how long would it take to make
2,480 candies?
Answer:
40
Step-by-step explanation:
hope this helps
How can we represent three-dimensional figures in only two dimensions?
Answer: A three-dimensional figure has a length, a width, and a height. A net is a two-dimensional pattern of a three-dimensional figure, that can be folded to form the figure. Identify the net that we could fold in order to create this 3D figure. Match the 3D figure to the right with its appropriate net, below.
I need the answer fast pls
Answer:
89 b
Step-by-step explanation:
Laurel used 12 1/2 Square feet of cloth to make three dresses how many square feet of cloth required to make 12 similar dresses?
Answer:
150 square feet
Step-by-step explanation:
12 1/2 * 12 = 150