It looks like you're given
F'(x) = 3x² + 7
and
F (0) = 5
and you're asked to find F(b) for the values of b in the list {0, 0.1, 0.2, 0.5, 2.0}.
The first is done for you, F (0) = 5.
For the remaining b, you can solve for F(x) exactly by using the fundamental theorem of calculus:
[tex]F(x)=F(0)+\displaystyle\int_0^x F'(t)\,\mathrm dt[/tex]
[tex]F(x)=5+\displaystyle\int_0^x(3t^2+7)\,\mathrm dt[/tex]
[tex]F(x)=5+(t^3+7t)\bigg|_0^x[/tex]
[tex]F(x)=5+x^3+7x[/tex]
Then F (0.1) = 5.701, F (0.2) = 6.408, F (0.5) = 8.625, and F (2.0) = 27.
On the other hand, if you're expected to approximate F at the given b, you can use the linear approximation to F(x) around x = 0, which is
F(x) ≈ L(x) = F (0) + F' (0) (x - 0) = 5 + 7x
Then F (0) = 5, F (0.1) ≈ 5.7, F (0.2) ≈ 6.4, F (0.5) ≈ 8.5, and F (2.0) ≈ 19. Notice how the error gets larger the further away b gets from 0.
A better numerical method would be Euler's method. Given F'(x), we iteratively use the linear approximation at successive points to get closer approximations to the actual values of F(x).
Let y(x) = F(x). Starting with x₀ = 0 and y₀ = F(x₀) = 5, we have
x₁ = x₀ + 0.1 = 0.1
y₁ = y₀ + F'(x₀) (x₁ - x₀) = 5 + 7 (0.1 - 0) → F (0.1) ≈ 5.7
x₂ = x₁ + 0.1 = 0.2
y₂ = y₁ + F'(x₁) (x₂ - x₁) = 5.7 + 7.03 (0.2 - 0.1) → F (0.2) ≈ 6.403
x₃ = x₂ + 0.3 = 0.5
y₃ = y₂ + F'(x₂) (x₃ - x₂) = 6.403 + 7.12 (0.5 - 0.2) → F (0.5) ≈ 8.539
x₄ = x₃ + 1.5 = 2.0
y₄ = y₃ + F'(x₃) (x₄ - x₃) = 8.539 + 7.75 (2.0 - 0.5) → F (2.0) ≈ 20.164
Simplify the expression and choose the appropriate result.
3(2 + 3g)
This is from the same project that I was struggling with and was similar to the other problem but I couldn't figure it out.
9514 1404 393
Answer:
y = -1/4x^2 -3/2x +3/4
Step-by-step explanation:
You know that vertex form is ...
y = (1/(4p))(x -h)^2 +k
for a focus-vertex distance of p and a vertex of (h, k).
Here, the focus-vertex distance is 2-3 = -1 (difference of y-coordinates), and the vertex is (h, k) = (-3, 3). This means the vertex form equation is ...
y = -1/4(x +3)^2 +3
Expanding the square gives ...
y = -1/4(x^2 +6x +9) +3
y = -1/4x^2 -3/2x +3/4
_____
Additional comment
The square of a binomial is ...
(x +a)^2 = x^2 +2ax +a^2
Select the correct answer from each drop-down menu. The table represents function f, and the graph represents function g.
The line of symmetry for function F is _____
A.Y=9
B.X=-2
C.X=2
D.Y=9
and the line os symmetry for function G is____
A.x=1
B.y=7
C.x=-1
D.y=-7
The y-intercept of function F is____
A.less than
B.equal to
C.greater than
The y-intercept of function G.
Over the interval [2,4] the average rate of change of function F is _____
A.greater than
B.equal to
C.less than.
the average rate of change of function G.
Thank you and I'm sorry for take your time.
I appreciate you
Answer:
1) -9 (this is where the y values stop and 'go the other way')
2) 1 (this is where the y values also stop and 'go the other way')
3) greater than (the y intercept on a table is found by looking where x = 0 and seeing what y equals. on a graph its just where the line crosses the y axis)
4) less than (idrk know how to explain this one sorry)
Step-by-step explanation:
hope this helps <3
Answer:
The line of symmetry for function f is
x = 2 and the line of symmetry for function g is x = 1
.
The y-intercept of function f is greater than
the y-intercept of function g.
Over the interval [2, 4], the average rate of change of function f is
less than the average rate of change of function g.
Step-by-step explanation:
The students at Southern Junior high School are divided into four home rooms. Benjamin just moved into the school district and will be randomly assigned to one home room
Answer:
A 4 side dice.
Step-by-step explanation:
Benjamin has 4 possible homerooms with the same probability. This means that every homeroom has a 1/4 = 0.25 (or 25%) probability of getting chosen.
You could emulate this situation with a 4 sided dice (are like little pyramids) where each side of the dice would represent the selection of one of the homerooms.
who is willing to help me with my work for money ?
Answer:
sure, but not sure if this is allowed on brainly...
also this is just tutoring
Part C
Question
Determine the missing values in the table.
Recall that x represents the number of tickets sold and y represents the amount of money earned from ticket sales.
Type the correct answer in each box. Use numerals instead of words.
X
$20
3
6
20
$400
Answer:
40$,160$ & 60
Step-by-step explanation:
First,find the equation using y-y1/ y1-y2=x-x1=x1-x2
y-0/0-20=x-0/0-3
y=20x/3
Now put the values of x& y in the equation, for the 1st one,
y=20×6/3
=40
2nd one.y=20×24/3
=160
3rd one,
400=20x/3
X=400×3/20
=60
The values at different number of tickets and the tickets that can be bought at $400 has been determined.
What is Direct Variation?When a variable varies directly with the other variable, i.e. on increasing one variable the other variable also increases, this relation is called Direct Variation.
Let x represent the number of tickets sold
Let y represent the amount of money earned from ticket sales.
y ∝ x
y = kx
k is the proportionality constant.
The value in the table will be used to determine the value of k,
For 3 tickets, the ticket amount is $20
20 = k * 3
k = 20/3
The relation is given by
y = (20/3) x
For 6 tickets, the value will be,
y = (20/3 ) *6 = $40
For 24 tickets the value will be,
y = (20/3) * 24 = $160
For $400, how many tickets can be bought,
400 = (20/3) * x
400*3 /20 = x
60 tickets can be bought for $400
To know more about Direct Variation
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The Precision Writing Instruments Company makes two pen designs - the Cordova design and the Savannah design. These data apply, regardless of which of two pen designs is being implemented. Materials cost per pen is $6. Labor cost per pen is $5. Production overhead is
$1,000,000. Advertising and promotion is $1,000,000. Marketing research has estimated the following demand functions for the next year of sales for the two pen designs where Q represents demand in thousands and P represents price. For the Cordova design, Q = 150 - 2.5P. For the Savannah design, Q = 175 - 2.1P. A penetration strategy is proposed for the Savannah design and a price of $25 is selected. What will be the profit or loss for the first year?
9514 1404 393
Answer:
loss of $285,000
Step-by-step explanation:
The demand for the Savannah design is estimated to be ...
Q = 175 -2.1P = 175 -2.1(25) = 122.5 . . . . thousand pens
Then the contribution margin from sales will be ...
122,500($25 -$6 -$5) = $1,715,000
Against a total of $2,000,000 in production and advertising costs, the net will be a loss of ...
$2,000,000 -1,715,000 = $285,000
The first-year loss will be $285,000.
What is the solution to the equation 9(x + 2) = 27? (1 point) Group of answer choices x = 2.5 x = 0.5 x = −0.5 x = −3.5
Answer:
Well i got 1
Step-by-step explanation:
because you need to take 9*x and 9*2
9x + 18= 27
-18 -18
9x =9 divide by 9 on each side and get one
dijkstra's algorithm
Step-by-step explanation:
Answer my question....Bdjsdjrrnnrnnddddsnjjejjeje
The sum of two consecutive integers is 199. Find the integers
The two consecutive integers will be 99 and 100.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.
The sum of two consecutive integers is 199.
Let the first number be x and the next consecutive number will be (x + 1). Then the equation will be
x + x + 1 = 199
2x = 199 - 1
2x = 198
x = 198 / 2
x = 99
Then the two consecutive integers will be 99 and 100.
More about the Algebra link is given below.
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111.2 please help 20 points!!!!
Answer:
111.2
Step-by-step explanation:
It would just remain 111.2
The square root and the squared cancel out on eachother
For, square roots of number will be what times what gives you that number while squared numbers will give you a number multiplied by utsekf,
please help with this
Answer:
[tex]S_{n}[/tex] = n² + 4n ; n = 11
Step-by-step explanation:
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [2 [tex]a_{1}[/tex] + (n - 1)d]
~~~~~~~~~
[tex]a_{1}[/tex] = 5
d = 7 - 5 = 2
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2(5) + 2(n - 1)] = [tex]\frac{n}{2}[/tex] ( 8 + 2n ) = 4n + n²
[tex]S_{n}[/tex] = n² + 4n
n² + 4n = 165
n² + 4n - 165 = 0
(n + 15)(n - 11) = 0 ( n ≥ 0 ) ⇒ n = 11
0.4,0.7,1.0,1.3 what is the sequence rule
Answer:
3 plus 3, that is the sequence
Based on a survey, assume that 31% of consumers are comfortable having drones deliver their purchases. Suppose that we want to find the probability that when consumers are randomly selected, exactly of them are comfortable with delivery by drones. Identify the values of n, x, p, and q.
Answer:
P(X = 2) = 0.3157
Step-by-step explanation:
Let assume that the question wants us to determine the probability that, let say when 5 customers are randomly selected, exactly 2 of the customers are comfortable.
Then;
p = 0.31
n = 5; x = 2
q = 1 - p
= 1 - 0.31
= 0.69
∴
The probability mass function is:
[tex]P(X =x) = ^n C_r * p^x *q^{n-x}[/tex]
[tex]P(X =x) = ^5 C_2 * (0.31)^2 *0.69^{5-2}[/tex]
[tex]P(X =2) = \dfrac{5!}{2!(5-2)!} * (0.31)^2 *0.69^{3}[/tex]
[tex]P(X =2) = \dfrac{5!}{2!(3)!} * (0.31)^2 *0.69^{3}[/tex]
[tex]P(X =2) = \dfrac{5*4*3!}{2!(3)!} * (0.31)^2 *0.69^{3}[/tex]
[tex]P(X =2) = \dfrac{5*4}{2!} * (0.31)^2 *0.69^{3}[/tex]
[tex]P(X =2) =10* (0.31)^2 *0.69^{3}[/tex]
P(X = 2) = 0.3157
Please help me with this problem
solve the following equation for y
x+y=3
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Answer:
y = 3 -x
Step-by-step explanation:
Subtract x from both sides of the equation.
x -x +y = 3 -x
y = 3 - x
Answer:
y=3-x
explanation
its that
It’s 8:40 What time will it be in 3/4 hour
Answer: 9:25
Step-by-step explanation:
5.2.21-T
Question Help
Assume that when adults with smartphones are randomly selected 44%use them in meetings or classes. If 17 adult smartphone users are randomly selected, find the probability that exactly 2 of them use their smartphones in
Meetings or classes
Answer:
0.004398
Step-by-step explanation:
Given that:
p = 44% = 0.44
Number of trials (n) = 17
Probability that exactly 2 of them use smartphones in meetings or classes =?
Using the binomial probability formula :
P(x = 2)
P(x = x) = nCx * p^x * (1 - p)^(n-x)
P(x = 2) = 17C2 * 0.44^2 * 0.56^15
P(x = 2) = 136 *0.1936 * 0.0001670399
P(x = 2) = 0.00439809
P(x = 2) = 0.004398
Your payment is $375 per month for 36 months and you made a $2,500
Answer:
375 times 36
Step-by-step explanation:
Which system of equations has no solution?
A.
y = 7x +5
y = 7x + 5
B.
3x - 5y = 10
-3x + 5y = -10
C.
y = 3x - 2
y = 3x + 5
D.
3x - 5y = 10
-3x - 2y = 20
Answer:
A
Step-by-step explanation:
6/8 and 24/40 are they proportional
Answer:
no they are not
Step-by-step explanation:
It says that I need to find x for the missing angle in the equation.
Answer:
Could you possible elaborate on the question more?
A polling agency is investigating the voter support for a ballot measure in an upcoming city election. The agency will select a random sample of 500 voters from one region, Region A, of the city. Assume that the population proportion of voters who would support the ballot measure in Region A is 0.47. What is the probability that the proportion of voters in the sample of Region A who support the ballot measure is greater than 0.50
Answer:
The value is [tex]P( X > 0.50) = 0.089264[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is n = 500
The population proportion is p = 0.47
Generally given that the sample size is sufficiently large , the mean of this sampling distribution is mathematically represented as
[tex]\mu_x = p = 0.47[/tex]
Generally the standard deviation of the sampling distribution is mathematically represented as
[tex]\sigma = \sqrt{\frac{p(1- p )}{ n} }[/tex]
=> [tex]\sigma = \sqrt{\frac{ 0.47 (1-0.47 )}{ 500 } }[/tex]
=> [tex]\sigma = 0.0223[/tex]
Gnerally the probability that the proportion of voters in the sample of Region A who support the ballot measure is greater than 0.50 is mathematically represented as
[tex]P( X > 0.50) = P( \frac{ X - \mu }{ \sigma } > \frac{ 0.50 - 0.47 }{ 0.0223 } )[/tex]
[tex]\frac{X -\mu}{\sigma } = Z (The \ standardized \ value\ of \ X )[/tex]
=> [tex]P( X > 0.50) = P( Z> 1.3453 )[/tex]
From the z table the area under the normal curve to the left corresponding to 1.3453 is
[tex]P( Z> 1.3453 ) = 0.089264[/tex]
So
[tex]P( X > 0.50) = 0.089264[/tex]
Using the normal distribution and the central limit theorem, it is found that there is a 0.0901 = 9.01% probability that the proportion of voters in the sample of Region A who support the ballot measure is greater than 0.50.
In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean.
After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.
By the Central Limit Theorem, the sampling distribution of sample proportions of size n of a proportion p has [tex]\mu = p, s = \sqrt{\frac{p(1-p)}{n}}[/tex]
In this problem:
Sample of 500 voters, hence [tex]n = 500[/tex].The proportion is of 0.47, hence [tex]p = 0.47[/tex]The mean and the standard deviation are:
[tex]\mu = p = 0.47[/tex]
[tex]\sigma = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.47(0.53)}{500}} = 0.0223[/tex]
The probability that the proportion of voters in the sample of Region A who support the ballot measure is greater than 0.50 is 1 subtracted by the p-value of Z when X = 0.5, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.5 - 0.47}{0.0223}[/tex]
[tex]Z = 1.34[/tex]
[tex]Z = 1.34[/tex] has a p-value of 0.9099.
1 - 0.9099 = 0.0901
0.0901 = 9.01% probability that the proportion of voters in the sample of Region A who support the ballot measure is greater than 0.50.
A similar problem is given at https://brainly.com/question/24663213
Evaluate. 4³ +8² = ?
Answer: 128
Work: I just did 4 to the power of 3 which is 64, and I did 8 to the power of 2 which is also 64. 64 + 64 = 128, which is the answer. I hope this helps, and stay safe. :)
Logs5(3x-2) = 1 + Logs5 (x-4)
Answer:
57
Step-by-step explanation:
Two fair dice, one yellow and one blue, are rolled. The value of the blue die is subtracted from the value of the yellow die. Which of the following best describes the theoretical probability distribution?
Answer:
symmetric
Step-by-step explanation:
its correct.
Answer:
B symmetric
Step-by-step explanation:
HELPPPPPP I DONT GET THIS AT ALL
Answer:
1x1 and 20x32
Step-by-step explanation:
can someone help please
√x + 4 +
x + 4 + 2
√x + 4√2
Answer:
this is the correct answer
please help me I'm going to fail if you don't help me
Answer:
B
Step-by-step explanation:
Shigaraki told me