Let [tex]f(x) = x^3 + 3x + \sin(x) - 5[/tex]. Using Newton's method to approximate a solution to [tex]f(x) = 0[/tex], we consider the recurrence
[tex]\begin{cases} x_1 = 1 \\ x_{n + 1} = x_n - \frac{f(x_n)}{f'(x_n)} & \text{for } n \ge 1 \end{cases}[/tex]
Differentiating [tex]f(x)[/tex] gives
[tex]f'(x) = 3x^2 + 3 + \cos(x)[/tex]
Then
[tex]x_2 = 1 - \dfrac{f(1)}{f'(1)} = 1 + \dfrac{1 - \sin(1)}{6 + \cos(1)} \approx 1.024238790[/tex]
[tex]x_3 = x_2 - \dfrac{f(x_2)}{f'(x_2)} \approx 1.024009549[/tex]
[tex]x_4 = x_3 - \dfrac{f(x_3)}{f'(x_3)} \approx \boxed{1.024009528}[/tex]
which agrees numerically with the actual root of [tex]f(x)[/tex] up to at least 9 digits after the decimal point.
Alaric wants to determine if he can get a better grade in math by studying for longer periods of time.
He plans to experiment for 4 weeks.
Which statement is true of this experiment?
a.) The duration of Alaric's experiment is the explanatory variable.
b.) Alaric's math grade is the explanatory variable.
c.) The amount of time Alaric spends studying is the response variable.
d.) Alaric's math grade is the response variable.
The statement (d) Alaric's maths grade is the response variable is correct because maths grade is a dependent variable.
What is an explanatory variable?It is defined as the variable which is independent. They show the expected results and the result is known as the response variable which is dependent on the explanatory variable.
We have given:
Alaric wants to determine if he can get a better grade in maths by studying for longer periods of time.
The duration of the experiment is 4 weeks which is known or constant.
But the number of hours she studied is a variable, and it is independent.
The maths grade is the dependent variable which is on the number of hours Alaric study variable.
Thus, the statement (d) Alaric's maths grade is the response variable is correct because maths grade is a dependent variable.
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On a certain day, the high temperature in city A was 93° F. On the same day, the high temperature in city B was -6° F. What was the difference in temperature between city A and city B?
Answer:
99°F
Step-by-step explanation:
The high temperature in city A was 93° F. On the same day, the high temperature in city B was -6° F.
The difference in temperature will be:
= 93 - (-6)
= 93 + 6
= 99
Please help whilst I try to solve this as well.
Answer:
420
Step-by-step explanation:
Answer:
V = 340 cm3
Step-by-step explanation:
Calculate the volume of the prism without the gap, then subtract the volume of the gap.
[tex]V=(5)(10)(8)-(3)(2)(10)=400-60=340cm^{3}[/tex]
Hope this helps
A 6-sided die is loaded in such a way where odd outcomes occur 2/9 of the time, and even outcomes happen the other
1/9 of the time. What is this die's expected value?
A. 3.25
B. 4
C. 3.5
D. 3.33
Answer:
3.33, or 3 1/3
Step-by-step explanation:
Expected value:
[tex](9 \times \frac{2}{9} ) + (12 \times \frac{1}{9} ) = 2 + \frac{4}{3} = 2 + 1 \frac{1}{3} = 3 \frac{1}{3} [/tex]
Urgent please help!!!!!!!!!!
—————————-
What is the solution to system of equations question?
Answer:
The correct answer is B, the second option
Step-by-step explanation:
(-2, 5/3)
Solve for the first variable in one of the equations, then substitute the result into the other equation.
Convert the following angle from degrees to radians. Express your answer in simplest
form.
495°
Answer:
11/4 Pi
Step-by-step explanation:
because 1.= 70/180. (180.=Pi)
so 495 x 70/180
=11/4 Pi
Help me with this please and thank you!! :)
Answer:
Step-by-step explanation:
[tex]A \cap C[/tex] denotes the set of elements in both A and C, which is [tex]\{20, 24, 28\}[/tex].[tex]B^{C}[/tex] denotes the complement of set B, which is the set of all elements that are in the universal set that are not in set B. In this case, this set is [tex]\{3, 4, 5, 6, 8, 11, 13, 16, 17, 19, 20, 22, 23, 24, 25, 26, 27, 28\}[/tex]In the fall, you charge people $8 for going to their house to rake leaves, then
$5 for every hour you rake. If you make $38 one day, how many hours did you
spend raking?
Write this fraction as a mixed number.
Answer:
7/6=2/7/6
7/6=2
7/6=27/6
7/6=2
7/6
How to graph -x^2-2x+6
The graph is shown in the attached image.
pls help oooooooooooo
Answer:
110
Step-by-step explanation:
Suppose lines EH and BD are parallel:
Angle <GFE and angle <ABC are supplementary so their sum is equal to 180
2x + 10 + x + 20 = 180 add like terms
3x + 30 = 180 subtract 30 from both sides
3x = 150 divide both sides by 3
x = 50
We are asked the value of <ACD
<ABD and <ACD are also supplementary so we can find the value od <ACD:
x + 20 + <ACD = 180 we know x = 50 so we can replace x with that
50 + 20 + <ACD = 180
70 + <ACD = 180 subtract 79 from both sides
<ACD = 110
true or false
The slope of the least-squares regression line is the average change in the predicted
values when the explanatory variable increases by 1 unit. [Select]
Answer:
false fake false false false.............
Step-by-step explanation:
.....,........................
Which shows the correct substitution of the values a, b, and c from the equation 0=-3x² - 2x + 6 into the
quadratic formula?
Quadratic formula: x=
-b±√√b²-4ac
2a
x = −(−2) ± √(−2)² − 4(− 3)(6)
2(-3)
x= -2±√2²-4(-3)(6)
2(-3)
x==(-
x = −(−2) ± √(-2)² − 4(3)(6)
2(3)
-2±√√2²-4(3)(6)
(=
2(3)
Answer: [tex]x=\frac{-(-2) \pm \sqrt{(-2)^{2}-4(-3)(6)}}{2(-3)}[/tex]
Step-by-step explanation:
a = -3 , b = -2, and c = 6.
The correct substitution of the values a, b, and c from the equation 0=-3x² - 2x + 6 into the quadratic formula is
x = (-(-2) ± √((-2)² - 4(-3)(6))) / (2(-3)).
The correct option is A.
What is a quadratic equation?For variable x : ax² + bx + c = 0, where a≠0 is a standard quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem.
To use the quadratic formula with the equation 0=-3x² - 2x + 6, we need to substitute the values of a, b, and c into the formula.
In this case, we have:
a = -3
b = -2
c = 6
Substituting these values into the quadratic formula, we get:
x = (-(-2) ± √((-2)² - 4(-3)(6))) / (2(-3))
Simplifying this expression, we get:
x = (2 ± √(4 + 72)) / (-6)
x = (2 ± √76) / (-6)
We can simplify further by factoring out the square root of 4 from the radical:
x = (2 ± 2√19) / (-6)
Therefore, the required value of x is x = (-(-2) ± √((-2)² - 4(-3)(6))) / (2(-3)).
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One to One Function Math Problem Help!
Answer:
g-1(x)=5×-9, (g-1g) (1)=1, h-1(3)= -
Step-by-step explanation:
Tim go to school.His age is a cube number.His age is double 1 square number and half a different square number.How old is Tim?
If f(x) =
√2x+3
6x-5
a. 1
b. -2
then f() =
C. -1
d. - 13
Answer:
put 1/2as a value of x in the equation and then solve .then the answer will be -1
Answer:
[tex]C.\ f\left( \frac{1}{2} \right) =-1[/tex]
Step-by-step explanation:
[tex]f\left( x\right) =\frac{\sqrt{2x+3} }{6x-5}[/tex]
In order to calculate f(1/2) ,all we have to do
is replacing x by 1/2 in the expression of f.
Then
[tex]f\left( \frac{1}{2} \right) =\frac{\sqrt{2\left( \frac{1}{2} \right) +3} }{6\left( \frac{1}{2} \right) -5 }[/tex]
[tex]=\frac{\sqrt{1+3} }{3-5}[/tex]
[tex]=\frac{\sqrt{4} }{-2}[/tex]
[tex]=\frac{2}{-2}[/tex]
[tex]=-1[/tex]
3+7=6-|-x|
Solve for x.
Thanks :)
Answer:
no solution
Step-by-step explanation:
| | is a notation for absolute value, which is the distance that a number is from 0.
you can think of this as the "positive version" of a number
so, |-x| will become: x
We can plug this into the equation, and solve like we would for any variable
3 + 7 = 6 - |-x| {simplify}
3 + 7 = 6 - x {simplify}
10 = 6 - x
Now, we can isolate x (isolate = get it alone)
10 = 6 - x
-6 - 6 {subtract 6 from both sides}
4 = -x {multiply both sides by -1 to get positive x}
·-1 ·-1
- 4 = x
{check solution:}
3 + 7 = 6 - | -4 |
10 = 6 - 4
10 = 2
FALSE
because this solution has been found to be false, there is no possible value for x
we write this as: no solution
[tex]3+7=6-|-x|\\10=6-|x|\\|x|=-4\\x\in\emptyset[/tex]
4(n+3)=24 solve for n
Suppose that shoe sizes of American women have a bell-shaped distribution with a mean of 8.1 and a standard deviation of 1.47. Using the empirical rule, what percentage of American women have shoe sizes that are greater than 5.16?
97.5% of American women have shoe sizes that are no more than 11.47.
Lets try to solve the question,
Given values ,
Dev (u) = 8.47
Standard deviation (x) = 1.47
So we e have to find the percentage of American women whose shoe size's are not more than 11.47 P(x<11.47).
Lets find z score by using empirical formula.
=> [tex]z= (x-u) / a[/tex]
=> [tex]11.47-8.47/1.5[/tex]
=> [tex]z= 2[/tex]
Now we have to find [tex]P(z < 2)[/tex] . Using the empirical rule, we know that 97.5% data lies below 2 standard deviations above mean.
Therefore the 97.5% of American women have shoe sizes that are no more than 11.47.
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EAsy math challenge! Click me!
Answer:
the answer is 64
Step-by-step explanation:
now atleast mark me brainliest answer
HELP DUE SOON A farmer has decided to divide his land area in half in order to plant soy and corn. Calculate the area of the entire area so he knows how much soil is needed.
A parallelogram with a height of 6 yards and side length 9 yards. The height forms a triangle with the slanted side of the rhombus with a base of 2.5 yards. Rhombus is split into a soy half and a corn half.
Each bag of soil covers 20 square yards. How many bags should the farmer purchase?
The farmer should purchase 2 bags of soil for his farm.
What is Area of parallelogram?A parallelogram is a two-dimensional figure with four sides. It is a special case of the quadrilateral, where opposite sides are equal and parallel. The area of a parallelogram is the space enclosed within its four sides. Area is equal to the product of length and height of the parallelogram.
The shape of the farm, according to the picture is a parallelogram. Therefore, the total area can be calculated as follows:
Area = base X height
where
b = base
h = height
base = 6.5 + 2.5 = 9.0 yards
height = 6 yards
Area = 6 × 9 = 54 square yards.
40 square yards requires 1 bag of soil .
54 square yards will require ?
Bags required = 54 / 40 = 1.35 bag
Thus, the farmer will require 2 bags of soil for his farm.
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The function y = f(a) is graphed below. What is the average rate of change of the
function f(a) on the interval -8 < < 8?
Answer: -35/16
Step-by-step explanation:
[tex]f(8)=-5\\\\f(-8)=30\\\\\frac{f(8)-f(-8)}{8-(-8)}=\frac{-5-30}{16}=\boxed{-\frac{35}{16}}[/tex]
What are the zeros of the quadratic function f(x) equals 6X squared +12 X -7
The zeroes of the function will be [tex]\rm -1 \pm \dfrac{\sqrt{78}}{6}}[/tex]
What is a Quadratic Function ?A quadratic function is given by ax² +bx+c = f(x)
The given quadratic function is
f(x) = 6x² +12x - 7
The zeroes of the function will be given by
f(0) = 0
6x² +12x - 7 = 0
The zeroes are given by
[tex]\rm \dfrac {-b \pm \sqrt{b^2 -4ac}}{2a}[/tex]
here
a = 6
b = 12
c = -7
Therefore the zeroes of the function will be
[tex]\rm \dfrac {-12 \pm \sqrt{12^2 -4*6*(-7)}}{2 *6}[/tex]
[tex]\rm \dfrac {-12 \pm \sqrt{312}}{12}[/tex]
[tex]\rm -1 \pm \dfrac{\sqrt{78}}{6}}[/tex]
Therefore these are the two zeroes of the function.
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What is the present value of a cash inflow of 1250 four years from now if the required rate of
return is 8% (Rounded to 2 decimal places)?
Using simple interest, it is found that the present value of the cash inflow is of 947.
Simple InterestSimple interest is used when there is a single compounding per time period.
The amount of money after t years in is modeled by:
A(t) = A(0)(1 + rt)
In which:
A(0) is the initial amount.r is the interest rate, as a decimal.In this problem, the parameters are given as follows:
r = 0.08, t = 4, A(t) = 1250.
We have to solve for A(0) to find the present value, hence:
A(t) = A(0)(1 + rt)
1250 = A(0)(1 + 0.08 x 4)
A(0) = 1250/1.32
A(0) = 947.
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Which of the following numbers of replications of an experiment would make
the results most conclusive?
A. 4
B. 12
C. 1
D. 2
►
The table shows ordered pairs of the function y=8-2x. What is the value of y when x = 8?
X
-3
-1
1
4
8
10
y
14
10
6
0
?
-12
Answer: -8
Step-by-step explanation:
[tex]y=8-2(8)=\boxed{-8}[/tex]
Determine if a Poisson experiment is described, and select the best answer:
A paper mill produces paper that comes in 3000-foot rolls. The average number of
defects in the paper is known to be 38.9 per roll. The manager would like to know the
probability that the first 100 feet of paper in the next roll produced will have 0 defects.
The corollary of the statement tends that its not the Poisson experiment.
It is a statistical approach to follow properties that The experiment outcomes that can be opted as successes or failures. That gives a outcome in a specified region is known in average number of successes i.e. (μ).
The probability of a given task is not a Poisson experiment because the mean number of successful outcomes in its domain neither constant nor given.
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How much vinegar would be in each container if the total amount in all cups were redistributed equally between the 8 containers?
Answer:
Step-by-step explanation:
1/8
answer? To this question please
Answer: The second table.
Step-by-step explanation: The y coordinates are getting smaller over time, so I believe the second one would be the correct answer. I hope this helps! :)
A man wants to cut down a tree in his yard. To ensure that the tree doesn’t hit anything, he needs to know the height of the tree. He measures his distance from the tree at 13 meters and the angle of elevation to the tree at 53°. What is the height of the tree to the nearest tenth of a meter
The height of the tree to the nearest tenth of a meter is 73.7m
What is angle of elevation?The angle formed by the line of sight and the horizontal plane for an object above the horizontal.
Given:
base = 13 m
angle of elevation = 53
Using trigonometry
tan 53 = P/B
5.671 = P/ 13
P= 5.671 * 13
P= 73.723
Hence, the height of the tree is 73.7 m.
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