The function f(x) = x³ - 7x + 1 for the given f''(x) = 6x, f'(-3) = 20 and f(-3) = -5. By using the antiderivative formula, the required function is evaluated.
What is the antiderivative formula?The antiderivative formula for indefinite integrals is
[tex]\int f'(x)dx = f(x) + c[/tex]
or we can also write this as
[tex]\int f^n(x)dx = f^{n-1} + c[/tex]
Calculation:It is given that,
f''(x) = 6x, f'(-3) = 20, f(-3) = -5
Then, by the antiderivative formula, we can write
[tex]\int f''(x)dx = f'(x) + c[/tex] ...(1)
On substituting, we get
[tex]\int f''(x)dx = \int 6x dx = 6\int xdx[/tex]
Since we have the formula for the indefinite integral, [tex]\int x^n dx = \frac{x^{n+1}}{n+1}+c[/tex], we get
[tex]\int f''(x)dx = 6(\frac{x^{1+1}}{1+1})+c[/tex]
⇒ [tex]\int f''(x)dx = 6(\frac{x^2}{2})+c=3x^2+c[/tex]
So, from (1), we get f'(x) = 3x² + c
But we have f'(-3) = 20. So, on substituting x = -3 in the above function f'(x), we get
f'(x) = 3x² + c
⇒ f'(-3) = 3(-3)² + c
⇒ 20 = 3(9) + c
⇒ 20 - 27 = c
∴ c = -7
So, the second derivative function is f'(x) = 3x² - 7.
From the antiderivative expression, we can write
[tex]\int f'(x)dx = f(x) + c[/tex] ...(2)
On substituting f'(x) in the above integral we get
[tex]\int f'(x) dx = \int (3x^2 +-7)dx[/tex]
⇒ [tex]\int f'(x)dx = 3\int x^2dx -7\int dx + c[/tex]
⇒ [tex]\int f'(x) dx = 3(\frac{x^3}{3})-7x+c[/tex]
⇒ [tex]\int f'(x) dx = x^3 - 7x + c[/tex]
From (2), we can write
f(x) = x³ - 7x + c
But we have f(-3) = -5;
Then,
f(-3) = (-3)^3 - 7(-3) + c
⇒ -5 = -27 + 21 + c
⇒ -5 = -6 + c
∴ c = -5 + 6 = 1
Thus, the function f(x) = x³ - 7x + 1.
Learn more about the antiderivative formula for indefinite integrals here:
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Equivalent representations of percent problems
Answer:
A. 80/100×22D. 0.8×22E. 4/5×22Explanation:
80/100×22 = 1760/100 = 17.60.8×22 = 17.64/5×22 = 88/5 = 17.617.6 is 80% of 22
1What is the area of the square?
20 square feet
5 feet
10 square feet
25 square feet
5 square feet
Need help asap
Answer:
25 square feet
Step-by-step explanation:
You would multiply 5 by 5 to get the area.
5 by 5 is 25.
Hope I helped.
brian, tim and kenny got paid a total of $240 for mowing neighborhood lawns . They split the money in the ratio of 5:9:10 . how much money did each boy make . PLEAEEEE SHOW THE work i’m really struggling rn
Answer:
$50 for Brian
$90 for Tim
$100 for Kenny
Step-by-step explanation:
Let 5x = amt for Brian
9x = amt for tim
10x = amt for ken
5x + 9x + 10x = 240
24x = 240
x = 10
5x = 5(10) = $50 for Brian
9x = 9(10) = $90 for Tim
10x = 10(10) = $100 for Kenny
Answer:
Step-by-step explanation:
5x + 9x + 10x = $240
x = $10
Brian got 5x = $50
Tim got 9x = $90
Kenny got 10x = $100
The area of a square floor on a scale drawing is 25 square centimeters, and the scale drawing is
1 centimeter:6 ft. What is the area of the actual floor? What is the ratio of the area in the drawing to the
actual area?
The area of the actual floor isſ ] square feet. The ratio of the area in the drawing to the actual
area is 1 square centimeter: square feet
View Example
f Step-by-step
Textbook
Print
Answer:
actual area = 900 square feet
ratio = 1cm2 : 36ft2
Step-by-step explanation:
square room
area = 25cm2
1 side = √ 25
= 5cm
1cm = 6ft
5cm = 5 x 6
= 30ft = 1 side
actual area = 30 x 30 = 900ft
ratio = square cm : square feet
= 25 : 900 ( simplify both ratio )
= 1cm2 : 36ft2
In 1987, a survey of 1000 young people found that 540 said they smoked cigarettes, whilst
460 said they did not. In 2017, a similar survey of another 1000 young people found that
125 said they smoked cigarettes, whilst 875 said they did not.
Calculate the ratio of smokers to non-smokers in 2017. Give your answer in simplest form:
Show your workings.
[2 marks]
Answer:
1:7
Step-by-step explanation:
125:875
Then simply
The GCF between the two is 125:
125/125 = 1
875/125 = 7
So, the answer is 1:7!
Is the Point (6,3) on the given circle.
(x - 3)2 + (y + 1)2=25
Yes or No?
Can anyone help me ?
Answer:
First Option
Step-by-step explanation:
Approximately what portion of the box is shaded blue?
Answer:
option a.
1/5 in my opinion.
a little help would be nice here pls
Answer:
11). 3x² -x 12). -5x + 5
Step-by-step explanation:
11). (4x² + x) - (x² + 2x)
4x² + x - x² - 2x
4x² - x² + x - 2x
3x² -x
12). (6x - 3) - (11x -8)
= 6x - 3 - 11x + 8
= 6x - 11x - 3 + 8
= -5x + 5
Find Q, I'm not sure if it is possible however.
9514 1404 393
Answer:
Q ≈ 0.0314148930589 radians ≈ 1.79994078613°
Step-by-step explanation:
There is no algebraic solution for the set of equations with mixed polynomial and trig functions:
x·sin(Q/2) = 5
1/2x^2(Q -sin(Q)) = π/12
__
However, we can use the first equation to substitute for x in the second equation. This gives ...
[tex]\displaystyle \frac{1}{2}\left(\frac{5}{\sin{\frac{Q}{2}}}\right)^2(Q-\sin{Q})=\frac{\pi}{12}[/tex]
This can be simplified using the half-angle identity and recast as a function of Q:
[tex]\displaystyle f(Q)=\frac{25(Q-\sin{Q})}{1-\cos{Q}}-\frac{\pi}{12}[/tex]
This function will have a zero at the desired value of Q. It can be solved iteratively. A graph shows an approximate value of Q is 0.314 (radians). The value can be refined by Newton's method iteration to give the angle to full calculator precision:
Q ≈ 0.0314148930589 radians ≈ 1.79994078613°
__
The corresponding value of x is about 318.333447755. In short, this is a very narrow sector/segment in a relatively large circle.
What is the domain of the relation? On a coordinate plane, a graph of an image has 3 connected lines. The first line goes from (negative 4, negative 4) to (negative 2, 1). The second line goes from (negative 2, 1) to (1, 1). The third line goes from (1, 1) to (6, 4). There are closed circles at (negative 4, negative 4) and (6, 4).
Given:
The graph of a relation contains three lines.
The first line goes from (-4,-4) to (-2, 1).
The second line goes from (-2, 1) to (1, 1).
The third line goes from (1, 1) to (6, 4).
There are closed circles at (-4,-4) and (6, 4).
To find:
The domain of the relation.
Solution:
Domain of relation is the set of x-values or the set of input values.
First line is defined from -4 to -2, second line is defined from -2 to 1 and third line is defined from 1 to 6.
There are closed circles at (-4, -4) and (6, 4). It means -4 and -6 are included in the domain.
Since the input values for the given relation is from -4 to 6, where -4 and 6 are included, therefore the domain of the relation is [-4,6].
Answer:
-4
Step-by-step explanation:
I need to find the value of x
Answer:
9
Step-by-step explanation:
Radius = x
The triangle in the given image is a right angled triangle.
By Pythagoras theorem,
x² + 12² = ( x + 6 )²
x² + 144 = x² + 36 + 12x
x² - x² = 36 - 144 + 12x
0 = - 108 + 12x
12x = 108
x = 108 / 12
x = 9
a blue number cube and a green number cube are rolled.Both number cubes have the number 1 through 6 on them. What is the probability of rolling a number greater than 3 on the blue cube and a number less than 4 on the green cube? ANSWER CORRECTLY FOR 200 points!
Answer:
We are assuming the numbers 1 - 6 on the cubes?
If so,
Blue (3, 4, 5, or 6) is 4/6 or 2/3 chance
Green(1,3,5) is 3/6 or 1/2 chance
To get both the P is 2/3 times 1/2
Step-by-step explanation:
if a river is 4.2 feet and it dropped 18% percenet what is the depth
HELPPP PLSSS THIS IS MY THIRD TIME POSTING THIS PLS HELP ME I WOULD MARK YOU BRAINIEST What is the slope of the line below?
(3,5)
(3, 2)
A. positive
B. undefined
C. negative
D. Zero
Answer:
B
Step-by-step explanation:
its undefined because 3/0.
Target pays $14.00 for each Halo 4 video game. The selling price is $22.00. What is the percent of markup? Round your answer to the percent.
Answer:
57%
Step-by-step explanation:
Find the markup percent by dividing the difference in price by the original price, and multiplying it by 100
(8/14) x 100
= 57
So, the percent markup is approximately 57%
??answer!?? Plsssss: )
Solve for x.
A) 6
C) 4
B) 12
D) 2
Answer:
x=4
Step-by-step explanation:
go it right on edge
PLEASE I NEED THE ANSWER QUICK
v + 25 < 5
v = ?
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{v + 25 < 5}[/tex]
[tex]\large\textsf{SUBTRACT 25 to BOTH SIDES}[/tex]
[tex]\mathsf{v + 25 - 25 < 5 - 25}[/tex]
[tex]\large\textsf{CANCEL out: 25 - 25 because that gives 0}[/tex]
[tex]\large\textsf{KEEP: 5 - 25 because it gives us v or solve for it}[/tex]
[tex]\mathsf{v < 5 - 25}[/tex]
[tex]\mathsf{5 - 25 = -20}[/tex]
[tex]\boxed{\boxed{\large\textsf{Answer: }\mathsf{\bf v < -20}}}\large\checkmark\\\boxed{\boxed{\mathsf{\bf It\ is\ an\ O P E N E D\ circle\ on\ -20\ shaded\ to\ the\ left}}}[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
. Es una característica numérica de la población, para su cálculo se emplean formulas y generalmente se indican con letras griegas. A) Estadístico o Valor Estadístico B) Parámetro C) Dato Continuo D) Dato Cuantitativo
Answer:
B) Parameter
Step-by-step explanation:
To find - It is a numerical characteristic of the population, formulas are used for its calculation and are generally indicated with Greek letters. A) Statistical or Statistical Value B) Parameter C) Continuous Data D) Quantitative Data
Answer -
The correct option is - B) Parameter
Reason -
In statistics, A parameter is a numerical characteristic of a population, as distinct from a statistic of a sample.
.............................................................................................
Answer:.............................................................................................
Step-by-step explanation:
.............................................................................................
WILL GIVE BRAINLIEST IMMEDIATELY!!!!!!!
IF YOU PUT RANDOM NONSENSE ANSWERS OR ADVERTISE SCAM WEBSITES I WILL REPORT YOU AND EMAIL BRAINLY.
4. Consider the circle to the right.
Determine m∠KNY.
SHOW ALL, I REPEAT, ALL STEPS TO BE MARKED BRAINLIEST. I will give brainliest ASAP.
Answer: Hope this helps
C. 65 this might be the answre bc of the diamiter.
I REALLY NEED BRAINLIEST!!
I think it is 65 hope this helps and i ne
Step-by-step explanation:
Answer: okay so this is a long process
Step-by-step explanation:
the measure of angle N is 65 degrees because when calculating the angle, it is always half of the arc it makes. K is 30 because the arc it makes is 60 degrees and half of 60 is 30. Y is 45 because half of 90 is 45. All of the inside angles of a triangle add up too 180 degrees. So add 30 to 45 and you would get 75, then subtract 75 from 180 to get 105. So the measure of KNY is 105 degrees.
Write a function with a slope of 4 that includes the point (−1, 3)
Answer:
I'm not sure but I think the answer is
F(x)=3
The function with a slope of 4 can be written as F(x) = 4x + 7.
What is an equation of the line?An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.
The general form of the equation of the line:-
y = mx + c
m = slope
c = y-intercept
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given that the slope is 4 and the line is passing through the point (-1,3).
The y-intercept will be calculated as,
y = mx + c
3 = 4 x -1 + c
c = 7
The equation can be written as,
y = mx + c
y= 4x + 7
To know more about an equation of the line follow
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Match each probability word to the probability. *Each will be used once*
Impossible 0
Unlikely 7/8
50/50 chance 1/3
Likely 1
Certain 1/2
attach a link if needed<3
Juice: Different
Burritos: Same
Soup: Same
Peanut Butter: Different
Now, suppose assuming the true fraction of voters is .65, the estimated standard deviation of X is given as 6.65. Suppose you find that 115 people actually voted yes in the random sample of 200. Conduct hypothesis testing using p value approach at 5% significance level to determine the validity of Candidate A’s claim that he was at least supported by 65% of the voters. (Make sure you show the steps of hypothesis testing)
Answer:
reject H0 ; conclude that there is significant evidence to conclude that candidate A is supported by less than 65% voters
Step-by-step explanation:
x = 115
n = 200
Phat = x / n = 115 / 200 = 0.575
H0 : P0 ≥ 0.65
H1 : P0 < 0.65
TEST STATISTIC :
Phat - P0 ÷ sqrt[(P0(1-P0))/n]
0.575 - 0.65 ÷ sqrt[(0.65(0.35))/200]
-0.075 ÷ 0.0337268
Test statistic -2.237
Pvalue :
P(Z < - 2.237) = 0.012643
α = 0.05
Pvalue < α
0.012643 < 0.05 ; We reject H0
We can conclude that there is significant evidence to conclude that candidate A is supported by less than 65% voters
WILL GIVE BRAINLIEST FOR RIGHT ANSWER 16 POINTS
Answer:
Absolute value means 2 equations so work below.
Step-by-step explanation:
x + 2 = 3
x = -1
x - 2 = 3
x = 5
I hope I didn't just confuse myself it's been YEARS since i've had simple questions like this (i can edit if needed)
PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!
Answer: 3/4x - 1/2x -4=12
1/4x - 4 = 12 x = 64
Mr. And Mrs. Griffin hope to send their daughter to college in fourteen years. How much money should they invest now at an interest rate of 9.5% per year, compounded continuously, in order to be able to contribute $8,500 to her education?
Answer:
$2,385.75 = P
Step-by-step explanation:
In order to calculate this we need to use the following compound interest formula and solve for the initial investment amount which is P.
A = P (1 + r/n) (nt)
A = the future value of the investment/loan, including interest
P = the principal investment amount (the initial deposit or loan amount)
r = the annual interest rate (decimal)
n = the number of times that interest is compounded per unit t
t = the time the money is invested or borrowed for
If we plug in the values provided in the question which is compounded once per year we would get the following equation which we can solve for P.
8500 = P (1 + (0.095/1))^(1*14)
8500 = P (1.095)^(14)
8500 = P (3.56285)
2,385.75 = P
Mr. and Mrs. Griffen need to invest $2,385.75 now for 14 years in order to contribute a total of $8,500
1 / 5p= 4
(what’s the correct answer)
[tex]\frac{1}{5}p = 4[/tex]
Multiply both sides by 5 to isolate p.
p = 4 * 5 = 20
p = 20