(1 point) Find the antiderivative F of f(x)=4−3(1+x2)−1 that satisfies F(1)=−3.
Answers
The value of antiderivative F will be;
⇒ F = 4x - 3 arc tan x - 7 + 3π/4
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The function is,
⇒ f (x) = 4 - 3 (1 + x²)⁻¹
Now,
Since, The function is,
⇒ f (x) = 4 - 3 (1 + x²)⁻¹
Hence, The antiderivative F of f (x) is,
⇒ F = ∫ (4 - 3 (1 + x²)⁻¹ ) dx
⇒ F = ∫ 4 dx - 3 ∫ (1 + x²)⁻¹ dx
⇒ F = 4x - 3 arc tan x + c
Where, c is constant of integration.
Here, The antiderivative of f (x) is satisfy F(1) = - 3,
So, Substitute x = 1, F = - 3
⇒ F = 4x - 3 arc tan x + c
⇒ - 3 = 4×1 - 3 arctan (1) + c
⇒ - 3 = 4 - 3π/4 + c
⇒ - 3 - 4 + 3π/4 = c
⇒ c = - 7 + 3π/4
Thus, The antiderivative F of f (x) is,
⇒ F = 4x - 3 arc tan x - 7 + 3π/4
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Related Questions
There are two numbers which add up to 20. If one number is five more than four times the other, find the numbers.
Answers
Answer:
3 and 17
Step-by-step explanation:
Let x and y represent the numbers.
x + y = 20 . . . . . . . . the numbers add up to 20
x = 5 + 4y . . . . . . . . one number is 5 more than 4 times the other
Substituting the second equation into the first:
(5 +4y) +y = 20
5y = 15 . . . . . . . . . . subtract 5
y = 3 . . . . . . . . . . . . divide by 5
x = 20 -3 = 17
The numbers are 17 and 3.
Use the Rational Zeros Theorem to write a list of all possible rational zeros of the function. f(x) = -2x4 + 4x3 + 3x2 + 18
Answers
Step-by-step explanation:
USING RATIONAL ROOT THEOREM:
a = ±2
Factors of a are ±1 ,±2
For the constant term
c= ±18
The factors of c are ±1,±2,±3,±6,±9 and ±18
THE POSSIBLE ZEROES ARE GIVEN BY
c/a=(±1,±2,±3,±6,±9,±18)/(±1 ,±2)
Therefore, the possible zeroes are
±1,±2,±3,±6,±9,±18,±1/2,±3/2,±9/2
the first term of an arithmetic sequence is equal to 200 and the common differencence is equal to -10. find the value of the 20th term
Answers
Answer:
The value for 20th term is 10.
Step-by-step explanation:
First, you have to find the formula for the sequence.
[tex]an = a + d(n - 1)[/tex]
[tex]let \: a = 200,d = - 10[/tex]
[tex]an = 200 - 10(n - 1)[/tex]
[tex]an = 200 - 10n + 10[/tex]
[tex]an = - 10n + 210[/tex]
Given that the formula of this sequence is an = -10n + 210. Next, you have to find 20th term :
[tex]let \:n = 20[/tex]
[tex]20th \: term = - 10(20) + 210[/tex]
[tex]20th \: term = - 200 + 210[/tex]
[tex]20th \: term = 10[/tex]
(Correct me if I am wrong)
Solve for the variable!
1. 2x + 21 = 40
2. 4x - 12 = 3x + 9
3. 3(x -1) + 2 = 7x
Answers
Step-by-step explanation:
1. 2x + 21 = 40
2x = 40 - 21
2x = 19
x = 19/2 = 9.5
2. 4x - 12 = 3x + 9
4x - 3x = 9 + 12
x = 21
3. 3x - 3 + 2 = 7x
3x - 1 = 7x
-1 = 7x - 3x
-1 = 4x
4x = -1
x = -1/4
= - 0.25
Which is a pair of vertical angles? ∠VRU and ∠SRT ∠TRS and ∠VRW ∠TRV and ∠WRU ∠WRV and ∠SRW
Answers
Answer:
b
Step-by-step explanation:
jus did it
I feel that I can divide the least count into 5 segments. How would I express my uncertainty of this ruler with one significant digit?
Answers
Answer:
depression
Step-by-step explanation:
Please help me figure this out
Answers
Answer:3⁴ and 81¹
Step-by-step explanation:
3⁹= 19683
3⁴= 81
-9²= -81
9⁹= 387,420,489
81¹= 81
Find the value of Y
a) 10
b)28
c)20
d)152
e)128
Answers
Answer:
I THNK MAY BE 28 by putting value of x and finding value of y.
Step-by-step explanation:
4x-12=2x+8
or,4X-2x=12+8
or,2x=20
or,x=20/2
therefore, x=10
then do, 4x-12+7y+12=180 the answer which comes is your required ans . it may be 28
Given 2x² = -8, x is
Answers
Answer:
its 2i or -2i
Step-by-step explanation:
just did it and also the next one is -4 and 10
Answer:
your answer will be "2i or -2i"
for the next it is -4 and 10
Step-by-step explanation:
Can somebody help me pleaseeeee
Multiply -5/8•(-3)
Answers
Answer:3 [ 1 5 -5 6 0 0 ]
3 x 1 = 3
3 x 5 = 15
3 x -5 = -15
3 x 6 = 18
3 x 0 = 0
3 x 0 = 0
[ 3 15 -15 18 0 0 ]
[ 3 15 ]
[ -15 18 ]
[ 0 0]
The answer is B and I hope I explained this well for you
Step-by-step explanation:
Answer:
1.875
Step-by-step explanation:
Give an answer to the picture above or below
Answers
Answer:
Graph
Step-by-step explanation:
Solve for x. −25x+175>225 AND 5x−83≥−73
Answers
Answer:
x < -2; x> or= 2
Step-by-step explanation:
-25x + 175>225
-25x>225-175
-25x>50
divide both sides by -25; we have
x <-2
the lesser than sign changes to a greater than because we are dividing by a negative number.
2. 5x - 83>_ -73
5x>_ -73 + 83
5x>_ 10
divide both sides by 5x we have
x>_ 2
Does anyone know how to answer this? The Probability that you draw a mechanical pencil from a group of 25 mechanical and wooden pencils is 3/5. How many are mechanical pencils?
Answers
Answer:
There are 15 mechanical pencils
Step-by-step explanation:
Recall that the probability of drawn a mechanical pencil from a larger group is given by the quotient of the number of mechanical pencils divided the total number of pencils in the sample.
so that means:
[tex]P=\frac{x}{25} \\[/tex]
being x the number of mechanical pencils and 25 the total of all pencils in the sample. Since they give as P as 3/5, we can solve for the number of mechanical pencils (x) using the equation:
[tex]P=\frac{x}{25} \\\\\frac{3}{5} =\frac{x}{25}\\x=\frac{3\,*\,25}{5} \\x=15[/tex]
So there are 15 mechanical pencils in the sample.
Which explains a way the U.S. government has created incentives for people to save?
A. It has enforced regulations for product advertising and labeling.
B. It has established protections for monies placed into banks.
C. It has sued companies that make fraudulent claims to gain refunds.
D. It has worked to educate consumers about their responsibilities.
Answers
Answer: B
Step-by-step explanation: B. It has established protections for monies placed in banks
whats x/7 = 4 in one step equations
Answers
Answer: x = 28
Step-by-step explanation: You multiply each place by 7 to get the x by itself and you get 28 as an answer
Answer:
28
Step-by-step explanation:
x/7=4
x=4*7
x=28
write an equation for the difference of p and 4
Answers
Answer:
p-4
Step-by-step explanation:
Difference means subtraction
p-4
Answer: p - 4
Explanation: The word difference tells us that we need to subtract.
So the difference between p and 4 can be represented as p - 4.
Enter the answer in the space provided.
Mariah walks 6 miles per hour. Bobby walks 4, 400 yards in a half-hour.
Given that 1 mile = 1,760 yards, how much faster does Mariah walk than Bobby, in miles per hour?
Enter the answer in the space provided.
Shaun rides his bike at a speed of 19 miles per hour. How far, in miles, does Shaun travel in 25 minutes when rounded to the nearest
hundredth?
Answers
Answer:
Part 1: 1 mile.
Part 2: 1.32 mph.
Step-by-step explanation:
The correct speed of Mariah walks faster than Bobby, in miles per hour - 1 mile per hour.
Shaun travel in 25 minutes in the given case, when rounded to the nearest hundredth - 7.92 miles.
Part 1.
Given:
speed of Mariah = 6 miles per hour
speed of Bobby = 4, 400 yards per half hour
= 8800 yards per hour
1 mile = 1760 yards
Solution:
To find out the speed difference of both Mariah and Bobby, we need to convert speeds in the same units that is mile:
=> speed of bobby = [tex]\frac{8800}{1760}[/tex]
=> speed of bobby = 5 miles per hour
as it is given 1 mile = 1760 yards
=> Now, the speed difference between Mariah and Bobby is
= 6 - 5
= 1 mile per hour.
Thus, Mariah walks faster than Bobby, in miles per hour - 1 mile per hour.
Part 2:
Given:
Speed of Shaun = 19 miles per hour
distance traveled in 25 minutes = ?
Solution:
To find out the traveled distance by Shaun in 25 minutes we need to find the speed per minute:
1 hour = 60 minutes
So as given, 19 miles per 60 minutes
then speed per minute = [tex]\frac{19}{60}[/tex]
= 0.316
then traveled in 25 minutes-
=> [tex]0.316*25[/tex]
=> = 7.92
Thus, Shaun travel in 25 minutes in the given case, when rounded to the nearest hundredth - 7.92 miles.
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find the inverse of the following function g(x) = -2x+3
Answers
Answer:
[tex]g(x)^-1 = \frac{-x}{2} +\frac{3}{2}[/tex]
Step-by-step explanation:
1) swap x and y
x = -2y + 3
2) solve for y
[tex]x=-2y+3[/tex]
[tex]2y=-x+3[/tex]
[tex]y=\frac{-x}{2} + \frac{3}{2}[/tex]
Answer:
[tex]\frac{y+3}{2}[/tex]
Step-by-step explanation:
60 is 150% of what in math
Answers
Answer:
40% is the answer to your question.
Select the correct answer for each statement. (k+2, k+3 , k+4) or (k+10, k+12, k+14) will yield consecutive odd integers. (k+6, k+8 , k+10) or (k+1, k+2, k+3) will yield consecutive integers.
Answers
Answer:
Step-by-step explanation:
one
The only really certain way of getting an odd integer is to do 2k + 1. Therefore the answer should be something like 2k+1, 2k+3, 2k + 5
The best I can do for the first one is to assume that k is odd and that the answer is k + 10, k+12, k+14, but I would ask your instructor if this is merely the best answer out of a poor lot or if the question really has no answer.
Two things should be noted.
1. k has to be odd.
2. The first choice has to give consecutive integers because what is added on is 2 3 and 4. Those numbers are consecutive.
Two
k+1, k+2, k+3. See point 2 above. k is a constant and any number. 1,2,3 are consecutive so the results are consecutive. Even if k < 0 the numbers will be consecutive.
k= - 10
k+1 = - 9
k+2 = -8
k+3 = - 7
These are consecutive.
Your first choice will give either consecutive odd or even numbers depending on what k is.
If k = even, then k+6, k+ 8, k+10 will all be even.
If k = odd then the givens will be odd.
2k+9, 2k+11, 2k+13 will yield consecutive odd integers.
k+6, k+8, k+10 will yield consecutive integers.
The article ``Oxygen Consumption During Fire Suppression: Error of Heart Rate Estimation" reported the following data on oxygen consumption (ml/kg/min) for a sample of ten firefighters performing a fire suppression simulation:
29.5 49.3 30.6 28.2 28.0 26.3 33.9 29.4 23.5 31.6
Compute the following:
a. The sample range.
b. The sample variance s2 from the definition (i.e. first computing deviations, then squaring them, etc.).
c. The sample standard deviation.
d. s2 using the shortcut method.
Answers
Answer:
Kindly check explanation
Step-by-step explanation:
Given the data:
29.5 49.3 30.6 28.2 28.0 26.3 33.9 29.4 23.5 31.6
Sort in ascending order of magnitude :
23.5,26.3,28.0,28.2,29.4,29.5,30.6,31.6,33.9,49.3
A) Range of the sample data:
(maximum - minimum)
49.3 - 23.5 = 25.8
B) sample variance :
S² = ∑ (x − m)²/ n − 1.
m = mean ; n = number of observations
m = (23.5 + 26.3 + 28.0 + 28.2 + 29.4 + 29.5 + 30.6 + 31.6 + 33.9 + 49.3) = 310.3 / 10 = 31.03
∑ (x − m)² = 443.801
n - 1 = 10 - 1 = 9
S² = ∑ (x − m)²/ n − 1
S² = 443.801 / 9
S² = 49.311222 = 49.31
C) The standard deviation (s):
S = √[∑ (x − m)²/ n − 1]
√variance = √49.311222
S = 7.0221949
S = 7.022
D) using statistical calculator,
S² = 49.31
Answer:
C
Step-by-step explanation:Hope this helps!:>
you get out of school and walk orth for 20 minuties yo travel 1.6km what si the average velocity
Answers
Answer: The answer would be 1.6 :)
Answer:
The average velocity is:
4.8 km/hour
Step-by-step explanation:
1 hour = 60 minutes
20 minutes = 20/60 = 0.3333 hour
Proportions
1.6km ⇔ 0.3333 hour
W km ⇔ 1 hour
W = 1.6*1/0.3333
W = 4.8 km/hour
What’s the value of x in both a & b?
Answers
Answer:
a) 7
b) 2 2/7
Step-by-step explanation:
A) 2/7=2/x
x=7
B) 2/7=x/8
cross multiply
16=7x
x=16/7, or 2 2/7, or 2.2857
Determine the 3rd term in the geometric sequence whose first term is -8 & whose common term is 6
Answers
Answer:
so the formula for finding the n th term in a geometric sequence is :
(first term) * [tex](Common Term)^{n-1}[/tex]
therefore:
the 3 rd term will be
(-8) * (6)^2
-8 * 36
-288
Solve for x
9- 2y + 8y – 7 = -22
Answers
Answer:
-4
Step-by-step explanation:
-4
Step-by-step explanation:
Find the point P where the line x = 1 + t, y = 2t, z = -3t intersects the plane x + y - z = -5.
Answers
Replace x, y, and z in the plane's equation with their appropriate parametric equations, then solve for t, then evaluate x, y, and z at this t to find the point P.
[tex]x+y-z=-5[/tex]
[tex](1+t)+2t-(-3t)=-5[/tex]
[tex]6t+1=-5[/tex]
[tex]6t=-6[/tex]
[tex]t=-1[/tex]
[tex]\implies x=0,y=-2,z=-3[/tex]
So the point P is (0, -2, -3).
Here, we are required to find the point, P where the lines:
x = 1 + t x = 1 + ty = 2t x = 1 + ty = 2tz = -3tintersects the plane x + y - z = -5.
The point, P where the lines intersects the plane is given by;
he point, P where the lines intersects the plane is given by;P (0, -2, 3)
Therefore, to find this point, we have to substitute for x, y and z in the equation of the plane.
Therefore, we have;
1 + t + 2t -(-3t) = -5.therefore 6t = - 6and ultimately t = -1To get the coordinates of the point P where the lines intersect the plane; we can then find x, y and z by substituting t into each of their equations.
Therefore;
x = 1 + (-1) = 0x = 1 + (-1) = 0y = 2(-1) = -2x = 1 + (-1) = 0y = 2(-1) = -2z = -3(-1) = 3Therefore, the point, P where the lines intersects the plane is given by;
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The sum of y and 13 divided by 2
Answers
Answer:
7.5
Step-by-step explanation:
PLZ HELP I NEED TO SUMMIT THIS
Answers
A local pizza shop has a membership program for frequent buyers the membership cost $25 per month the members get a discount price of 150 per pizza slice Aaliyah purchased a membership to this pizza shop how much would a Aaliyah I have to pay the pizza shop if she bought six slices of pizza this month what would be the monthly cost for a slice of pizza
Answers
This question was not written properly
Complete Question
A local pizza shop has a membership program for frequent buyers the membership cost $25 per month the members get a discount price of $1.50 per pizza slice. Aaliyah purchased a membership to this pizza shop , how much would Aaliyah I have to pay the pizza shop if she bought six slices of pizza this month ?
What would be the monthly cost for a slice of pizza?
Answer:
a) $34
b) $26.50
Step-by-step explanation:
From the question:
Membership for frequent buyers in a month = $25
Discount price = $1.50 per pizza slice
a) How much would Aaliyah I have to pay the pizza shop if she bought six slices of pizza this month ?
This is calculated as:
Membership cost in a month + Discount price × Number of pizzas bought
= $25 +( $1.50 × 6 slices of pizza)
= $25 + $9
= $34
b) What would be the monthly cost for a slice of pizza?
This is calculated as:
Membership cost + Discount price × Number of slices
= $25 + $1.50 × 1
= $26.50
Resuelve las siguientes situaciones problemáticas: A) en una caja de 36 naranjas, si se han descompuesto, ¿qué parte del contenido de la caja se desperdicia? B) mi hermana hizo una pizza y la dividió en 8 porciones, si mi papá, mi hermano y mi tía comieron una porción cada uno, ¿qué la parte de la pizza queda?
Answers
Answer:
gdjlicnoirfbmlyrsrloydfbm
Tenemos dos problemas de proporciones.
Las soluciones son:
A) p = 6/36 = 1/6B) p = 5/8.A) Lamentablemente el primero está incompleto, lo reescribamos como:
"en una caja de 36 naranjas, si 6 se han descompuesto, ¿qué parte del contenido de la caja se desperdicia?"
Solo para mostrar la matemática que se necesita para este tipo de problemas.
La parte que del contenido de la caja que se desperdicia será igual al cociente entre el número de naranjas que se desperdician y el número total de naranjas, o sea:
p = 6/36 = 1/6
Se desperdicia 1/6 del contenido de la caja.
B) Sabemos que la pizza originalmente tiene 8 porciones.
Luego tu papá, hermano, y tía comen una porción (3 en total)
Entonces quedan: 8 - 3 = 5 porciones.
La parte que queda será el cociente entre lo que queda y la cantidad inicial, o sea:
p = 5/8.
Quedan 5/8 de la pizza.
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