What is the anti derivative of f'(x)=19x+15?
Answer:
Part A: [tex]\displaystyle f(x) = \frac{19}{2}x^2 + 15x + C[/tex]
Part B: [tex]\displaystyle f(x) = \frac{19}{2}x^2 + 15x - 5[/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
Functions
Function NotationCalculus
Differentiation
DerivativesDerivative NotationDifferential Equations
Integration
Integrals[Indefinite Integrals] Integration Constant CIntegration 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:
Step 1: Define
Identify
[tex]\displaystyle f'(x) = 19x + 15[/tex]
Step 2: Find Antiderivative
[Derivative] Integrate both sides: [tex]\displaystyle \int {f'(x)} \, dx = \int {19x + 15} \, dx[/tex][Left Integral] Simplify: [tex]\displaystyle f(x) = \int {19x + 15} \, dx[/tex][Integral] Rewrite [Integration Property - Addition/Subtraction]: [tex]\displaystyle f(x) = \int {19x} \, dx + \int {15} \, dx[/tex][Integrals] Rewrite [Integration Property - Multiplied Constant]: [tex]\displaystyle f(x) = 19 \int {x} \, dx + 15 \int {} \, dx[/tex][Integrals] Integration Rule [Reverse Power Rule]: [tex]\displaystyle f(x) = 19 \bigg( \frac{x^2}{2} \bigg) + 15x + C[/tex]Simplify: [tex]\displaystyle f(x) = \frac{19}{2}x^2 + 15x + C[/tex]Step 3: Find Particular Solution
Substitute in function value [Function f(x)]: [tex]\displaystyle 87 = \frac{19}{2}(-4)^2 + 15(-4) + C[/tex]Evaluate: [tex]\displaystyle 87 = 92 + C[/tex]Solve: [tex]\displaystyle C = -5[/tex]Substitute in C [General Solution]: [tex]\displaystyle f(x) = \frac{19}{2}x^2 + 15x - 5[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differential Equations
Need help with this question ASAP!!!!!!
Answer:
47
Step-by-step explanation:
A right triangle is 90 degrees
90-12-31=47
In the table below, x represents miles traveled and y represents the cost to travel by train. Miles, x Cost, y 2 8.50 5 15.25 8 22.00 12 31.00 What is the y-intercept of this function? 2.25 4.00 6.50 17.13
Answer:
B. 4.00$
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
C.18 of the houses are for sale How many houses are for sale?
Step-by-step explanation:
18 ..............hope it helps
John saved $50,000. and wants to put the money into an Index Annuity that pays an average of 8.4% per year, compounded semi-annually. How long will it take him to reach his goal of $1,000,000?
Answer:
Divide 50,000 by 8.4...get that number and add it to the 50,000, divide again by 8.4 and add back, repeat until you reach 1,000,000... happy adding
2^{51} mod 22 in words, two to the power of fifty-one mod twenty-two
Since 2⁵ = 32, and
2⁵ ≡ 32 ≡ 10 (mod 22),
we have
2⁵¹ ≡ 2 • 2⁵⁰ ≡ 2 • (2⁵)¹⁰ ≡ 2 • 10¹⁰ (mod 22)
Now consider 10¹⁰ (mod 22):
10 = 2 • 5
10¹⁰ ≡ 2¹⁰ • 5¹⁰ ≡ (2⁵)² • 5¹⁰ ≡ 10² • 5¹⁰ ≡ 2² • 5¹² (mod 22)
so that
2⁵¹ ≡ 2³ • 5¹² (mod 22)
Now consider 5¹² (mod 22):
5 and 22 are coprime, and ɸ(22) = 10 (where ɸ(n) is the Euler totient function). By Euler's theorem,
5¹² ≡ 5² • 5¹⁰ ≡ 5² • 1 ≡ 25 ≡ 3 (mod 22)
and so
2⁵¹ ≡ 2³ • 3 ≡ 24 ≡ 2 (mod 22)
Another, more tedious method: Start with smaller powers of 2 and look for a pattern.
2 ≡ 2 (mod 22)
2² ≡ 4 (mod 22)
2³ ≡ 8 (mod 22)
2⁴ ≡ 16 (mod 22)
2⁵ ≡ 32 ≡ 10 (mod 22)
2⁶ ≡ 2 • 32 ≡ 2 • 10 ≡ 20 (mod 22)
2⁷ ≡ 2 • 20 ≡ 40 ≡ 18 (mod 22)
2⁸ ≡ 2 • 18 ≡ 36 ≡ 14 (mod 22)
2⁹ ≡ 2 • 14 ≡ 28 ≡ 6 (mod 22)
2¹⁰ ≡ 2 • 6 ≡ 12 (mod 22)
2¹¹ ≡ 2 • 12 ≡ 24 ≡ 2 (mod 22)
2¹² ≡ 2 • 2 ≡ 4 (mod 22)
and so on, with a cyclic pattern of length 10. That is, [tex]2^{10k+1}\equiv2\pmod{22}[/tex] for any integer k ≥ 0. So 2⁵¹ ≡ 2 (mod 22).
Tia picked 56 ounces of blueberries. She used 8 ounces to make muffins and packed the remaining blueberries into 12-ounce packages. Which expression can be used to find the greatest number of packages of blueberries that Tia packed? ;-;
Answer:
4.25
Step-by-step explanation:
Evaluate the expression when a = 4 and c = -4. -a +2c
Answer:
-12
Step-by-step explanation:
In the diagram above, 24 = 240°.
Find the measure of Z3.
23 = [ ? 1°
Answer:
∠3 = 140Step-by-step explanation:
∠4 + ∠3 = 180
40 + ∠3 = 180
∠3 = 180 - 40
∠3 = 140
what is this graph in equation form
Answer:
A linear graph
Can you helps me put them into each category you can just say the first one is blank and so on
Answer:
1st: parallel
2nd: perpendicular
3rd: neither
4th: neither
5th: neither
6th: parallel
Step-by-step explanation:
are the triangles congruent ? if they are state how they are congruent .
Answer:
Step-by-step explanation:
Not congruent
Better to say that there is not enough information to say, "Triangles are congruent"
A number N divided by -9 is -16
Answer: no
Step-by-step explanation:
algebraic expression for "a number , n, divided by 4 is 4. I
The student government snack shop sold 32 items this week. for each snack type, what percentage of all snacks sold where of that type
Answer:
0.02 Sorry If it isn't right.
Step-by-step explanation:
please help it’s due today
Answer:
-3
Step-by-step explanation:
1 - 4 = -3
2 - 1 = 1
(-3) / 1 = (-3)
The sum of the measures of the angles of a triangle is 180. The sum of the measures of the second and third angles is three times the measure of the first angle. The third angle is 15 more than the second. Let x, y, and z represent the measures of the first, second, and third angles, respectively. Find the measures of the three angles. Do not include the degree symbol in your answer.
Answer:
x = 45
y = 60
z = 75
Step-by-step explanation:
We can create three different equations with the given variables:
x + y + z = 180
y + z = 3 x
z = y + 15
then we can use this last equation to substitute for 'z" in the second equation:
y + z = 3x
y + y + 15 = 3 x
2 y + 15 = 3 x
x = 2/3 y + 5
Then we can re-write the first equation in terms of y and solve for this unknown:
2/3 y + 5 + y + y + 15 = 180
2/3 y + 2 y = 160
8/3 y = 160
y = 3 * 160 /8
y = 60
Then x = 2/3 (60) + 5 = 45
so x = 45
and finally: z = 60 + 15 = 75
so z = 75
Please help me I believe the answer is b correct me if I’m wrong
Answer:
71°
Step-by-step explanation:
h = 71° ( corresponding angles)
A plant was 46 centimetres tall. After a month it had grown 7% taller. How tall was the plant after a month?
Answer:
49.22 centimeters.
Step-by-step explanation:
7% of 46 is 3.22 which means you add 46 to 3.22and u get the answer 49.22
Step-by-step explanation:
(a) Explain how the Fundamental Theorem of Algebra is used to determine the number of roots for
2x^2 + 3x +5
(b) What are the roots of 2x^2 + 3x + 5? Show your work. Explain why you chose the method you used to find
the roots.
Answer:
Answer:
Step-by-step explanation
2x²+3x+5 roots means the zeros
So the method we will use is quadratic formula it's will tell us from the start whether this equation have a real solution no solution or one solution only calculating its discriminant
b²-4ac=3²-4(3)(5)
9-60=-51
If the discriminant is < 0 means the equation have no solution
A study found that on average there were 566,000 tweets per hour.
Using this data, how many tweets are there per minute?
A
33, 960,000
B
13,584,000
С
18,866.6
D
9,433. 3
Work Shown:
566,000 tweets = 1 hour
566,000 tweets = 60 minutes
566,000/60 tweets = 60/60 minutes .... divide both sides by 60
9,433.3 tweets = 1 minute
There were roughly 9,433.3 tweets per minute.
There are 4 stars 4 green circles and 7 red circles what's the ratio of blue stars to red circles
Answer:
4 to 7 *maybe
Step-by-step explanation:
In the function, f(x) = 6x2 – 4 , what is the value of f(-2)?
Answer:
f(-2) = 14
Step-by-step explanation:
f(-2) = 6(-2) 2 - 4
f(-2) = -12 + 2 - 4
f(-2) = -10 - 4
f(-2) = -14
Determine the slope and y-intercept of the line represented in the table below.
Answer:
i don't know . i did this in sixth grade and i failed
Step-by-step explanation:
A is plotted on a coordinate grid at (-3 1/2,1) choose the correct grid that best shows the location of the point
Hi there! Please provide the graphs in the question so that I can determine which is the right one.
Answer is c
Step-by-step explanation:
c
Help me with this someone, please!
Answer:
-45 I think
Step-by-step explanation:
6 × (-7) - 3
-42 - 3
-45
Sorry if this is wrong
A farmer plants 22,680 wheat plants in 126 rows. Each row contains the same number of plants. How many wheat plants are in each row?
Help me please
Answer:
180 plants per row
Step-by-step explanation:
This is a division problem.
When he places 22,680 plants in 126 rows, he is dividing the 22,6980 plants by 126 rows.
22,680/126 = 180
Answer: 180 plants per row
-16 + (unknown) = -6
Answer:
10
Step-by-step explanation:
Which is a different way to express 2(w + 3)?
Answer: 2w+6
Step-by-step explanation: Here you distribute. Simply multiply 2 and w which would get you 2w and 2 by 3 which would get you 6.
Find an equation of the line that satisfies the given conditions.
Through (−1, −2); perpendicular to the line 2x + 7y + 6 = 0
PLEASE HELP WILL GIVE BRAINLIEST!!! PLEASEEE NO S P A M!!!!!
The time it takes to fly from Los Angeles to New York varies inversely as the speed of the plane. If the trip takes 5 hours at 950 km/h, how long would it take at 850 km/h?
I know the answer is 5.588 but why like what are the steps to solve it?
Answer:
Step-by-step explanation:
find distance traveled: [tex]\frac{950 km}{1 hr}*{5 hrs}[/tex] = 4750 kmtotal distance / new speed: [tex]\frac{4750 km}{850 km/hr} = 5.5882 hrs[/tex]