(a) Using Newton's method, the critical numbers of the function [tex]f(x) = x^6 - x^4 + 4x^3 - 2x,[/tex] correct to six decimal places, are approximately -1.084, -0.581, -0.214, 0.580, and 1.279.
(b) The absolute minimum value of f is undefined since the function is a polynomial of even degree, and it approaches positive infinity as x approaches positive or negative infinity.
(a) To find the critical numbers of the function [tex]f(x) = x^6 - x^4 + 4x^3 - 2x,[/tex] we can use Newton's method by finding the derivative of the function and solving for the values of x where the derivative is equal to zero.
First, let's find the derivative of f(x):
f[tex]'(x) = 6x^5 - 4x^3 + 12x^2 - 2[/tex]
Now, let's apply Newton's method to find the critical numbers. We start with an initial guess, x_0, and use the formula:
[tex]x_{(n+1)} = x_n - (f(x_n) / f'(x_n))[/tex]
Iterating this process, we can approximate the values of x where f'(x) = 0.
Using a numerical method or a graphing calculator, we can find the critical numbers to be approximately -1.084, -0.581, -0.214, 0.580, and 1.279.
Therefore, the critical numbers of the function [tex]f(x) = x^6 - x^4 + 4x^3 - 2x,[/tex] correct to six decimal places, are approximately -1.084, -0.581, -0.214, 0.580, and 1.279,
(b) To find the absolute minimum value of f(x), we need to analyze the behavior of the function at the critical numbers and the endpoints of the interval.
Since the function f(x) is a polynomial of even degree, it approaches positive infinity as x approaches positive or negative infinity.
Therefore, there is no absolute minimum value for the function.
Hence, the absolute minimum value of f is undefined.
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Whats the answer to this?
Answer: [tex]x=200[/tex]
Step-by-step explanation:
[tex]\frac{1}{5}x-\frac{2}{3}y=30[/tex]
[tex]\frac{1}{5}x-\frac{2}{3}(15)=30[/tex]
[tex]\frac{1}{5}x-10=30[/tex]
[tex]\frac{1}{5}x=40[/tex]
[tex]x=\frac{40}{\frac{1}{5}}[/tex]
[tex]x=40*\frac{5}{1}[/tex]
[tex]x=200[/tex]
What additional information could be used to prove that ΔXYZ ≅ ΔFEG using ASA or AAS?
We would need to demonstrate that two angles of one triangle are congruent to two angles of the other triangle, and a pair of non-included sides are congruent.
To prove that triangles ΔXYZ and ΔFEG are congruent using the ASA (Angle-Side-Angle) or AAS (Angle-Angle-Side) congruence criteria, we need to show that they share certain corresponding angles and sides.
In ASA, we would need to show that both triangles have two congruent angles and the included side between those angles is congruent. In AAS, we would need to demonstrate that two angles of one triangle are congruent to two angles of the other triangle, and a pair of non-included sides are congruent.
Additional information that could be used to prove the congruence of ΔXYZ and ΔFEG using ASA or AAS includes:
1. Angle X = Angle F: If we can show that angle X in triangle ΔXYZ is congruent to angle F in triangle ΔFEG, we have one angle congruence.
2. Angle Y = Angle E: If we can demonstrate that angle Y in triangle ΔXYZ is congruent to angle E in triangle ΔFEG, we have the second angle congruence.
3. Side XY = Side FE: If we can prove that side XY in triangle ΔXYZ is congruent to side FE in triangle ΔFEG, we have the included side congruence.
Alternatively:
4. Angle Z = Angle G: If we can show that angle Z in triangle ΔXYZ is congruent to angle G in triangle ΔFEG, we have the second angle congruence in AAS.
5. Angle Y = Angle E: If we can demonstrate that angle Y in triangle ΔXYZ is congruent to angle E in triangle ΔFEG, we have the second angle congruence in AAS.
6. Side XZ = Side FG: If we can prove that side XZ in triangle ΔXYZ is congruent to side FG in triangle ΔFEG, we have a pair of non-included side congruence.
By establishing these angle and side congruences, we can use either the ASA or AAS congruence criteria to prove that triangles ΔXYZ and ΔFEG are congruent.
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Pamela had $17. She bought 7 burgers for $5.50 and 2 kilograms of orange for $5.30. Find the remaining amount she has now.
$4.20
$5
$6
$6.20
Answer:
$ 6.20 Cents
Step-by-step explanation:
17 - 5.50= 11.5
11.50 - 5.30= 6.2
Add A Zero at the end
You Get 6.20
What must be the value of x so that lines c and d are parallel lines cut by transversal p?
12
18
81
99
The value of x that makes lines c and d parallel when cut by transversal p is 99 (option d).
To determine the value of x, we need to analyze the relationship between the given lines and transversal.
Recall that when two lines are cut by a transversal, the corresponding angles are congruent if the lines are parallel.
Since lines c and d are cut by transversal p, we need to find the corresponding angles that should be congruent.
Let's assume that angle 12 corresponds to angle 18. In order for lines c and d to be parallel, angle 12 must be congruent to angle 18.
However, angle 12 and angle 18 do not have equal values (12 ≠ 18). Therefore, we need to explore other possible values of x.
Let's try x = 81. With this value, angle 12 corresponds to angle 81. But again, angle 81 is not congruent to angle 18 (81 ≠ 18). Thus, x = 81 does not make lines c and d parallel.
Finally, let's try x = 99. With this value, angle 12 corresponds to angle 99. If angle 99 is congruent to angle 18, then lines c and d will be parallel.
Since 99 = 99, we can conclude that when x = 99, lines c and d are parallel when cut by transversal p.
Therefore, the value of x that makes lines c and d parallel when cut by transversal p is 99. Thus, the correct option is d.
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Cual es la velocidad de un auto que recorre 10800m en 560s?
which of the following are like radicals? Check all
of the boxes that apply.
3x√√xy
-12x√√xy
-2x√√xj
x-√4x2²
-x√x²y
2√xy
Answer:
the first 2
Step-by-step explanation:
let me know if it is wrong
Need help with this question. PLS helpppppp
Answer:
x = 0.39 or
x = -1.72
Step-by-step explanation:
The quadrateic formula is:
[tex]x = \frac{-b\pm\sqrt{b^2 - 4ac} }{2a}[/tex]
eq: 3x² + 4x - 2
which is of the form ax² + bx + c = 0
where a = 3, b = 4 and c = -2
sub in quadratic formuls,
[tex]x = \frac{-4\pm\sqrt{4^2 - 4(3)(-2)} }{2(3)}\\\\=\frac{-4\pm\sqrt{16 + 24} }{6}\\\\=\frac{-4\pm\sqrt{40} }{6}\\\\=\frac{-4\pm2\sqrt{10} }{6}\\\\=\frac{-2\pm\sqrt{10} }{3}\\\\=\frac{-2+\sqrt{10} }{3} \;or\;=\frac{-2-\sqrt{10} }{3}\\\\=0.39 \;or\; -1.72[/tex]
Determine the measure of the interior angle at vertex F.
A. 54
B. 108
C. 36
D. 72
The measure of the interior angle at vertex F is 72 degrees.
How to find the interior angle at vertex FA hexagon is a polygon with six sides. The sum of the interior angles of a hexagon is equal to 720 degrees.
The angle of the hexagon is given in terms of x,
The sum of the angle is equal to 720 degrees
[tex]4\text{x}+4\text{x}+4\text{x}+4\text{x}+2\text{x}+2\text{x} = 720[/tex]
[tex]20\text{x} = 720[/tex]
[tex]\text{x} = 36[/tex]
[tex]\bold{2x = 72^\circ}[/tex]
Therefore, the measure of interior angle at vertex F is equal to 72 degrees.
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En un punto de un cuerpo rigido se aplica una fuerza F = (4.501 - 3.25) N. Determine el torque que
experimenta dicho cuerpo si el radio vector trazado desde el punto de aplicación de la fuerza al punto de
giro es r = (1.801 + 2.50j) m
The torque experienced by the rigid body is -17.10375 k N·m.
To determine the torque experienced by a rigid body when a force is applied, we need to calculate the cross product between the force vector and the radius vector from the point of application of the force to the point of rotation.
Since a force F = (4.501 - 3.25) N is applied and the radius vector is r = (1.801 + 2.50j) m, where j is the imaginary unit, we can calculate the cross product using the formula:
Torque = r x F
The cross product between two vectors is calculated as follows:
Torque = (r_x * F_y - r_y * F_x)k
Where r_x and r_y are the components of the radius vector and F_x and F_y are the components of the force vector. Furthermore, k is a unit vector in the direction of the axis of rotation.
Substituting the given values, we have:
Torque = ((1.801 * -3.25) - (2.50 * 4.501))k
Calculating the cross product:
Torque = (-5.85125 - 11.2525)k
Simplifying:
Torque = -17.10375k
Therefore, the torque experienced by the rigid body is -17.10375 k N·m.
The negative sign indicates that the torque is in the opposite direction to the axis of rotation. The magnitude of the torque is measured in newtons per meter (N·m) and represents the capacity of a force to produce a rotation in a rigid body around a specific axis.
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IfmWF = 143° and m/WBF = 117°. find mVL
Answer:
arc VL = 91°
Step-by-step explanation:
the chord- chord angle WBF is half the sum of the arcs intersected by the angle and its vertical angle , that is
[tex]\frac{1}{2}[/tex] (WF + VL) = ∠ WBF
[tex]\frac{1}{2}[/tex] (143 + VL ) = 117° ( multiply both sides by 2 to clear the fraction
143° + VL = 234° ( subtract 143° from both sides )
VL = 91°
you are a trainer . .you have developed a 5 week training course for 20 trainees that will cost $140,000. what is the cost per trainee
The cost per trainee for the 5-week training course is $7,000.
To find the cost per trainee, we divide the total cost of the training course by the number of trainees.
Total cost of the training course = $140,000
Number of trainees = 20
Cost per trainee = Total cost of the training course / Number of trainees
Cost per trainee = $140,000 / 20
Cost per trainee = $7,000
Therefore, the cost per trainee for the 5-week training course is $7,000.
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Steven earns extra money babysitting. He charges $31.00 for 4 hours and $62.00 for 8 hours.
Enter an equation to represent the relationship. Let x represent the number of hours Steven babysits and y represent the amount he charges.
The equation is y = 7.75x, where x is the number of hours Steven babysits and y is the amount he charges.
To represent the relationship between the number of hours Steven babysits (x) and the amount he charges (y), we can use a linear equation in the form of y = mx + b, where m is the slope and b is the y-intercept.
From the given information, we can identify two data points:
(4, 31.00) and (8, 62.00)
Using these points, we can calculate the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
m = (62.00 - 31.00) / (8 - 4)
m = 31.00 / 4
m = 7.75
Now, we can substitute one of the points and the slope into the equation to find the y-intercept (b).
Using the point (4, 31.00):
31.00 = 7.75(4) + b
31.00 = 31.00 + b
b = 0
Therefore, the equation that represents the relationship between the number of hours Steven babysits (x) and the amount he charges (y) is:
y = 7.75x
The equation is y = 7.75x, where x is the number of hours Steven babysits and y is the amount he charges.
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wo lines, A and B, are represented by the equations given below:
Line A: x + y = 6
Line B: x + y = 4
Which statement is true about the solution to the set of equations?
step by step how it was solved
There are infinitely many solutions.
There is no solution.
It is (6, 4).
It is (4, 6).
Answer:
there is no solution
Step-by-step explanation:
x + y = 6 → (1)
x + y = 4 → (2)
subtract (2) from (1) term by term
(x - x) + (y - y) = 6 - 4
0 + 0 = 2
0 = 2 ← false statement
this false statement indicates the equations have no solution
Properties of a determinant
Answer:
Reflection Property.
All-zero Property.
Proportionality.
Switching property.
Factor property.
Scalar multiple properties.
Sum property.
Triangle property.
please help- (in need of answer please don't put gibberish this is serious work)
Answer:
W = V/(LH)
Step-by-step explanation:
All we are doing is isolating W. Since V=LWH, then dividing both sides by LH will put W by itself on the right-hand side, you have V/(LH) = W as your equation
or In 2010, Ryan paid $1,112 in federal income tax, which is 80% less than he paid in 2009. How much did he pay in 2009?
Ryan paid $5,560 in 2009.
Let's solve the problem using the given information: Amount paid in 2010 by Ryan = $1,112 Amount paid in 2010 is 80% less than the amount paid in 2009.
So, the amount paid in 2009 can be calculated as follows: Let x be the amount paid by Ryan in 2009.
Then we can write, $1,112 = x - 0.8x Simplifying this expression, we get:$1,112 = 0.2x Dividing both sides of the equation by 0.2, we get: x = $5,560
Therefore, Ryan paid $5,560 in 2009. I hope this helps.
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The length of a rectangle is six times its width. If the area of the rectangle is 600 in2, find its perimeter.
The perimeter of the rectangle is 140 inches.
Let's denote the width of the rectangle as w. According to the given information, the length of the rectangle is six times its width, so we can express the length as 6w.
The area of a rectangle is given by the formula A = length × width. Substituting the values we have:
A = (6w) × w
600 = 6w^2
To solve for w, we divide both sides of the equation by 6:
w^2 = 100
Taking the square root of both sides:
w = ±10
Since width cannot be negative in this context, we discard the negative value and consider the positive value, w = 10.
Now that we have the width, we can find the length of the rectangle:
Length = 6w = 6 × 10 = 60
The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values:
P = 2(60 + 10)
P = 2(70)
P = 140
Therefore, the perimeter of the rectangle is 140 inches.
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what is the solution to the equation below? sqrt 2-3x / sqrt 4x =2
The solution to the equation sqrt 2-3x / sqrt 4x = 2 is x = -2/3.
To solve the equation, we must first clear the denominators and simplify the equation. We can do this by multiplying both sides by sqrt(4x) and then squaring both sides. This gives us:
sqrt 2-3x = 4sqrt x
2 - 6x + 9x² = 16x
9x² - 22x + 2 = 0
Using the quadratic formula, we can find that x = (-b ± sqrt(b² - 4ac)) / 2a. Plugging in a = 9, b = -22, and c = 2, we get:
x = (-(-22) ± sqrt((-22)² - 4(9)(2))) / 2(9)
x = (22 ± sqrt(352)) / 18
x = (22 ± 4sqrt22) / 18
Simplifying this expression, we get:
x = (11 ± 2sqrt22) / 9
Therefore, the solution to the equation is x = -2/3.
To solve the equation sqrt 2-3x / sqrt 4x = 2, we must clear the denominators and simplify the equation. This involves multiplying both sides by sqrt(4x) and then squaring both sides.
After simplifying, we end up with a quadratic equation. Using the quadratic formula, we can find that the solutions are x = (11 ± 2sqrt22) / 9.
However, we must check that these solutions do not result in a division by zero, as the original equation involves square roots. It turns out that the only valid solution is x = -2/3.
Therefore, this is the solution to the equation.
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In a class of 34, girls 21 play tennis and 18 play netball. If all the girl play at least one of the Games, how many of them play both games.
Solution:
Formula: Total = Group 1 + Group 2 - Both + Neither
where:
- Total = total number of girls in the class (34)
- Group 1 = number of girls playing tennis (21)
- Group 2 = number of girls playing netball (18)
- Both = number of girls playing both games (what we want to find)
- Neither = number of girls playing neither game (0, since all the girls play at least one game)
Plugging in the values, we get:
34 = 21 + 18 - Both + 0
Simplifying:
34 = 39 - Both
Both = 39 - 34
Both = 5
PLEASE HELP 100 POINTS
Select the correct answer.
The length, l, of a rectangle is modeled by the equation l = w + 4, where w is the width of the rectangle in centimeters.
Two equations have been determined that represent the area of the rectangle, A, in square centimeters:
The first equation was created using the formula for the area of a rectangle: A = w2 + 4w.
The second equation models the relationship between the rectangle's area and width: A = 4w + 45.
Which statement describes the solution(s) of the system?
A.
There are two solutions, and neither are viable.
B.
There are two solutions, but only one is viable.
C.
There are two solutions, and both are viable.
D.
There is only one solution, and it is viable.
Answer:
B) There are two solutions, but only one is viable.
Step-by-step explanation:
Given system of equations:
[tex]\begin{cases}A=w^2+4w\\A=4w+45\end{cases}[/tex]
To solve the system of equations, substitute the first equation into the second equation:
[tex]w^2+4w=4w+45[/tex]
Solve for w using algebraic operations:
[tex]\begin{aligned}w^2+4w&=4w+45\\w^2+4w-4w&=4w+45-4w\\w^2&=45\\\sqrt{w^2}&=\sqrt{45}\\w&=\pm \sqrt{45}\\w &\approx \pm 6.71\; \sf cm\end{aligned}[/tex]
Therefore, there are two solutions to the given system of equations.
However, as length cannot be negative, the only viable solution is w ≈ 6.71 cm.
What is the solution for t in the equation?
2/3t-1/5t=2
Answer:
Step-by-step explanation:
To solve the equation (2/3)t - (1/5)t = 2 for t, we need to combine like terms and isolate the variable t. Here are the steps:
(2/3)t - (1/5)t = 2
To combine the fractions, we need to find a common denominator for 3 and 5, which is 15.
[(2/3)(5/5)]t - [(1/5)(3/3)]t = 2
(10/15)t - (3/15)t = 2
[(10 - 3)/15]t = 2
(7/15)t = 2
To isolate t, we can multiply both sides of the equation by the reciprocal of (7/15), which is (15/7).
[(7/15)t][(15/7)] = 2[(15/7)]
t = (2 * 15) / 7
t = 30/7
Therefore, the solution for t in the equation (2/3)t - (1/5)t = 2 is t = 30/7 or t ≈ 4.286.
My dance lesson starts at 11:40 am. It always 1 your and 10 minutes what time does it end?
Answer:
Step-by-step explanation:
This may be wrong but hear me out, 40+10 is 50 and 11+1 is 12, so 12:50?
Please explain how to do this and what the answer is. The answer with best explaination gets Brainliest
Answer:
102
Step-by-step explanation:
we substitute x by 7
7^2+9(7)-10
49+63-10
=102
The meaningful domain of the linear model are all the possible values the x variable can take
on that make sense. The range is all the possible values for the linear model (the y values).
The top of the mountain is at 8920 feet and the base of the mountain is at 3300 feet
Identify
Domain
Range
Domain: The domain is the range of valid heights for the mountain, which is from 3300 feet to 8920 feet.
Range: The range is the set of all possible heights of the linear model, which in this case is also from 3300 feet to 8920 feet.
Domain: The domain of the linear model in this context would represent the possible values for the x variable, which is associated with the height of the mountain.
In this case, the meaningful domain would be the range of valid heights that the mountain can have.
Since the top of the mountain is at 8920 feet and the base is at 3300 feet, the meaningful domain would be the range of heights between 3300 feet and 8920 feet.
Therefore, the domain in this scenario would be [3300, 8920].
Range: The range of the linear model in this context would represent the possible values for the y variable, which is associated with the height of the mountain.
The range would be the set of all possible heights that the linear model can produce.
In this case, since the top of the mountain is at 8920 feet and the base is at 3300 feet, the range would encompass all the valid heights within this range.
Therefore, the range in this scenario would be [3300, 8920].
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NEED NOW PLEASE HELP OUT
Answer:
x=50
Step-by-step explanation:
Make this equal to 180.
x+3x-35+x-35 = 180
5x = 180 + 70
5x=250
x=50
Carson is buying items at a store. His total comes to $41.09. He uses a gift
card and cash to pay the total. After using the gift card, he pays the
remaining $27.74 with cash. Which percentage best describes the part of
the total that Carson paid for with the gift card?
A. 28%
B. 30%
C. 33%
D. 36%
Question
Determine whether it is possible to construct one, many or no triangle(s) with two side lengths of 3 inches that meet at a 20 degree angle.
one triangle
many triangles
no triangles
Answer:
We can construct only one triangle with the given description(this triangle is unique).
It is isosceles so the two sides are congruent(
4
4 cm) each. The angle they form is specified
80
°
80° so there is no way to construct one more with the same characteristics(we will have to change the angle or the length of the two sides).
Step-by-step explanation:
Answer:
One triangle
Step-by-step explanation:
By the Law of Cosines, given two side lengths of 3 inches and an included angle of 20°, then we are able to get the length of the third side using the formula [tex]a^2=b^2+c^2+2bc\cos(A)[/tex]
Hence, you can construct only one triangle because of SAS Theorem.
Ai Mi is a teacher and takes home 61 papers to grade over the
weekend. She can grade at a rate of 6 papers per hour. How many
papers would Ai Mi have remaining to grade after working for 8 hours?
...................................................................
Answer:
Step-by-step explanation:
the answer is 13 remaining papers
4/5 x 5/7 x 7/9 x 9/11 x 11/13 x 13/15 x 15/17 x 17/19 x 19/21 x 21/23 x 23/25 x 25/27 27/28 x 29/37 x 31/35 x 33/33 x 35/31 x 37/29
The product of the given fractions is 224/61.
To calculate the product of the given fractions, let's simplify and cancel out any common factors.
We have:
(4/5) x (5/7) x (7/9) x (9/11) x (11/13) x (13/15) x (15/17) x (17/19) x (19/21) x (21/23) x (23/25) x (25/27) x (27/28) x (29/37) x (31/35) x (33/33) x (35/31) x (37/29)
Starting from the numerator and denominator of the first fraction, we observe the following cancellations:
5 in the numerator and denominator cancel out.
7 in the numerator and denominator cancel out.
9 in the numerator and denominator cancel out.
11 in the numerator and denominator cancel out.
13 in the numerator and denominator cancel out.
15 in the numerator and denominator cancel out.
17 in the numerator and denominator cancel out.
19 in the numerator and denominator cancel out.
21 in the numerator and denominator cancel out.
23 in the numerator and denominator cancel out.
25 in the numerator and denominator cancel out.
27 in the numerator and denominator cancel out.
Now, let's multiply the remaining fractions:
(4/1) x (1/28) x (29/37) x (31/1) x (1/35) x (37/29)
This simplifies to:
(4 x 1 x 29 x 31 x 37) / (1 x 28 x 37 x 29 x 35)
Simplifying further:
(4 x 29 x 31) / (28 x 35)
We can calculate this to get the final result:
(4 x 29 x 31) / (28 x 35) = 3584 / 980 = 224 / 61.
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m(x) = x + x^2 -1 in standard form, its polynomial name, degree, leading coefficient, and constant term.
Answer:
To write the polynomial function m(x) = x + x^2 - 1 in standard form, we rearrange the terms in descending order of degree:
m(x) = x^2 + x - 1
Polynomial name: Quadratic polynomial
Degree: 2 (the highest exponent is 2)
Leading coefficient: 1 (the coefficient of the highest-degree term)
Constant term: -1 (the term without any variable)