Where the voice rises and falls. But inflection also describes a departure from a normal or straight course.
What is inflection point and how to find an inflection point?
Inflection points for the given equation x^2e^{-2x} are
f'(x) =[tex]2x2xe^{(-2x)}-2{(x2)} e^{(-2x)}[/tex]
f'(x) =[tex]-2(x-1)xe {(^-2x)}[/tex]
The point of inflection, also known as the inflection point, is when the function's concavity changes. Changing the function from concave down to concave up, or vice versa, signifies that. In other words, an inflection point is the location at which the rate of slope shift from a growing to a decreasing way, or vice versa, occurs. There is no doubt that those positions are neither local maxima nor minima. They are fixed points.On a curve, an inflection point is when the concavity changes, according to definition. (i.e., a shift in the sign of curvature). We are aware that the function is concave up if f " > 0, and that it is concave down if f " 0. The point of inflection on a graph is where the function switches from positive to negative, or from negative to positive, at a particular value of x = c.x= -b±√(b^2 - 4ac)/2a
x=4±√(16+16)4
x=4±4√2/4
x=[tex]\sqrt{2+2/2}[/tex]
x=[tex]\sqrt{2-2/2}[/tex]
We get,
x=[tex]\sqrt{(2+2)/2^{2}*\sqrt{2+2}[/tex]
so, inflection points are,
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Find the values of x and y.
Answer:
x = 30y = 5Step-by-step explanation:
You want to know the values of x and y in the given figure.
Equilateral triangleThe left-side triangle has angles marked as congruent. Hence it is an equilateral triangle, which also has congruent sides.
8y = 40
y = 40/8 = 5
Isosceles triangleThe angle at the middle of the longest line is supplementary to the adjacent angle in the equilateral triangle, hence is 120°.
The marked side length of 40 and the equilateral triangle side length of 40 mean the triangle on the right is an isosceles triangle with an a.pex angle of 120°. Its congruent base angles (x°) must be (180° -120°)/2 = 30°.
x° = 30°
The values of x and y are 30 and 5, respectively.
A bag contains 12 red, 3 blue, and 5 yellow marbles, what is the probability of drawing a blue or yellow marble?
Answer:
the chance to pull a blue marble is 3/20
the chance to pull a yellow marble is 5/20
Given g(x) = 3x + 6, identify the domain, range, and x-intercept of the function. Domain: 3 < x < 6; Range: −6 < y < ∞; x-intercept (2, 0) Domain: 3 < x < 6; Range: −∞ < y < 6; x-intercept (−2, 0) Domain: −∞ < x < ∞; Range: −∞ < y < ∞; x-intercept (2, 0) Domain: −∞ < x < ∞; Range: −∞ < y < ∞; x-intercept (−2, 0)
The linear function g(x) = 3 · x + 6 has the following features:
Domain: - ∞ < x < + ∞
Range: - ∞ < y < + ∞
x-Intercept: (- 2, 0)
How to find the domain, range and x-intercept of a linear function
In this problem we must determine the domain, the range and the x-intercept of a linear function, that is, a polynomial of the form y = m · x + b, where m is the slope and b is the x-intercept. We must find the information by understanding the following features:
The domain of a linear function is all real numbers.The range of a linear function is all real numbers. The y-intercept of the function is the point of the linear function where x = 0.If we know that the function is g(x) = 3 · x + 6, then its domain and range are - ∞ < x < ∞ and - ∞ < y < ∞ and its x-intercept is:
0 = 3 · x + 6
- 3 · x = 6
x = - 2
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Step-by-step explanation:
The given function is g(x) = 3x + 6.
Domain: The domain of a function is the set of all possible input values (x) for which the function is defined. Since the function is a linear equation, it is defined for all real values of x. Therefore, the domain of the function is: Domain: -∞ < x < ∞ Range: The range of a function is the set of all possible output values (y) that the function can produce. The slope of the given function is positive (3), so the function increases without bound as x increases.
Therefore, the range of the function is: Range: -∞ < y < ∞ x-intercept: The x-intercept of a function is the point at which the graph of the function intersects the x-axis. To find the x-intercept, we set y = 0 and solve for x. 0 = 3x + 6 -6 = 3x -2 = x Therefore, the x-intercept is (-2, 0).
So, the correct option is: Domain: -∞ < x < ∞; Range: -∞ < y < ∞; x-intercept (-2, 0).
help meeeeeeeeeee pleaseee
There would be 52 atoms after 25 years and it would take 13 years for half the number of atoms to remain.
What is radioactive decay?We know that the term radioactive decay has to do with the break down of a substance to form the daughter nuclei of the particular element. In this case, we have the decay function of the element to be; A(t) =200e^-0.054t.
t is the time taken for decay.
Now in 25 years we would have;
A(t) =200e^-0.054(25)
A(t) = 52 atoms
The time that it would take for half of the original number to remain is obtained from;
100 = 200e^-0.054t
100/200 = e^-0.054t
0.5 = e^-0.054t
ln(0.5) = -0.054t
t = ln(0.5)/-0.054
t = 13 years
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Which system of linear inequalities is graphed?
y ≤3x-2
x+ 2y≥4
y≥3x-2
x+2y ≤4
y< 3x-2
x+2y>4
y>3x-2
x+2y <4
The system of linear inequalities is graphed is y≥3x-2; x+2y ≤4. Hence option b is the correct.
What is inequality?
In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.
The graph consists of two inequalities.
Since the graph lines are solid, thus the inequality sign either "less than or equal" or "greater than or equal".
First find the equation of line.
One line passes through the points (0,2) and (4,0).
The equation of line that passes through the point (a,0) and (0,b) is
x/a + y/b = 1
The equation of the line is x/4 + y/2 =1
(x + 2y)/4 = 1
x + 2y = 4
The equation of the inequality will be either x + 2y ≤ 4 or x + 2y ≥ 4.
Putting x =0 and y = 0 in x + 2y ≤ 4
0 + 0 ≤ 4
0≤ 4 (true)
In the graph (0,0) includes in the shaded region. Therefore the inequality is x + 2y ≤ 4.
The second line passes through the points (0,-2) and (3,7).
If a line passes through the points (x₁, y₁) and (x₂, y₂), then the equation of line is y - y₁ = [(y₂ - y₁)/(x₂ - x₁)](x - x₁).
The equation of the line is
y - 7 = (7 + 2)/(3 - 0)(x - 3)
y - 7 = 3x -9
y = 3x - 2
The equation of the inequality will be either y ≥ 3x-2 and y ≤ 3x-2:
Putting x =0 and y = 0 in y ≥ 3x-2
0 ≥ 0-2
0 ≥ -2 true
In the graph (0,0) includes in the shaded region. Therefore the inequality is y ≥ 3x-2.
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PLEASE HURRY I NEED TO FINISH MY TEST!!
Determine which integer in the solution set will make the equation true.
8x − 4 = 2(2x + 4)
S: {−4, 0, 3, 12}
A.−4
B.12
C.0
D.3
Answer: x=3
Step-by-step explanation:
When you plug in each number only 3 is the right answer.
A. 8(-4)-4=2(2(-4)+4)
-36=8 False
B. 8(12)-4=2(2(12)+4)
92=56 False
C. 8(0)-4=2(2(0)+4)
-4=8 False
D. 8(3)-4=2(2(3)+4)
20=20 True
how manys pounds of mixed nuts that contain 20% peanuts must eugene add to 16 pounds of mixed nuts that contain 70% peanuts to make a mixture with 60% peanuts?
We might add 10 pounds of mixed nuts which include 20% peanuts by solving the governing equations.
What are equations?An equation is a claim that shows the equality of two mathematical expressions.
For instance, the equal sign separates the two equations that make up the equation 3x + 5 = 14: 3x + 5 and 14.
So, we need a total of x pounds of mixed nuts.
Peanuts weigh 0.70 pounds in this combo.
Three pounds of peanuts are used to create the 20% mixture, or 0.20*15.
The equation we got: 0.70 x + 3 = 0.40(x + 15)
Now, solve as follows:
0.70 x + 3 = 0.40(x + 15)
0.70 x + 3 = 0.40(x + 15)
0.70x + 3 = 0.40x + 6
0.70x - 0.40x = 6 - 3
0.30x = 3
x = 10 pounds
Therefore, we might add 10 pounds of mixed nuts which include 20% peanuts by solving the governing equations.
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Describe how the given function can be obtained by transforming the graph of the reciprocal function f(x)=x/1
(Just do letter A ty)
Translate the graph [tex]5[/tex] units right, reflect over the [tex]x[/tex]-axis, and then perform a vertical stretch with a factor of [tex]3[/tex].
solve 6(z-1) + 14 = -40
Answer:
z = -8
Step-by-step explanation:
6(z-1) + 14 = -40
6z - 6 + 14 = -40 Distribute the 6
6z + 8 = -40 Combine Like Terms
6z = -48 Subtract 8 on Both Sides
z = -8 Divide by 6 on Both Sides
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The maximun value (63) is located at point (1, 2).
Step-by-step explanation:Used method: Graph method from operations research.1. Graph the restrictions.Check attached image 1.
The purple coloured area represents the resulting area of possible answers that meet all the requirements established by the restrictions within the cartesian plane.
2. Find all extreme values.In this step, we need to look for extreme values, these are normally found on the edges and corner of the area drawn by all the restrictions.
Check attached image 2 to see the extreme values.
Point A is located at: (-3, -2)
Point B is located at: (-3, -4)
Point C is located at: (3, -4)
Point D is located at: (1, 2)
3. Evaluate all extreme points using the given function.Given function: [tex]P=10x+6y+41[/tex]
Since we are tryong to obtain the point where there is a maximun value for function "P", we need to evaluate all the extreme points and choose the one that makes the function return the maximum value out of all 4 points.
Evaluating the points:
[tex]P(-3, -2)=10(-3)+6(-2)+41=-1\\ \\P(-3, -4)=10(-3)+6(-4)+41=-13\\ \\P(3, -4)=10(3)+6(-4)+41=47\\ \\P(1, 2)=10(1)+6(2)+41=63[/tex]
4. Conclude.The maximun value (63) is located at point (1, 2).
Note:There's a different method called "Simplex" that can also be used to solve these type of optimization problems. It's more complicated but can be useful when working with more than 2 variables.
A rectangle’s width w, height h, and area A are all functions of time t. At the instant when the rectangle’s area is 20 square inches and the width is 4 inches, the height is decreasing at a rate of 3 inches per second while the area is increasing at a rate of 7 square inches per second. Determine the rate of change of the width of the rectangle at that instant.
The rate of change of the width of the rectangle at that instant is 3.8 inches/sec.
What is meant by a rectangle?Rectangulus, a combination of the Latin words rectus (as an adjective, right, appropriate), and angulus, is where we get the word rectangle (angle).
A crossed rectangle is a crossed quadrilateral made up of two opposing sides and the two diagonals of a rectangle. It is a specific case of an antiparallelogram with angles that are not all equal and right angles, even though opposite angles are. Other geometries, including spherical, elliptic, and hyperbolic, with opposite sides of equal length and equal angles that are not right angles.
We have,
W=width of the rectangle
H=height of the rectangle
A=Area of the rectangle
We know that,
A=W×H
A=20, W=4
20=4×H
H=5 inches
dA/dt=7 (inches)²/sec
dH/dt= -3 inches/sec
dA/dt=W.(dH/dt)+H×dW/dt
dA/dt=4(-3)+5(dW/dt)
7=-12+5(dW/dt)
dW/dt=19/5
dW/dt=3.8 inches/sec
Therefore, the rate of change of the width of the rectangle at that instant is 3.8 inches/sec.
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The two figures are congruent. Find the measure of the requested side or angle
angle A = 63.7°, B= 26.3°, D= 49° , then angle C = 221
What are congruent shapes?Two shapes that are the same size and the same shape are congruent.Congruent shapes are shapes that are exactly the same.
The corresponding sides are the same and the corresponding angles are the same.
This means the corresponding angles of the two shapes are equal.
With this, angle A = 63.7°, angle B= 26.3° , angle D =49°
The sum of angles in a quadrilateral is 360°
therefore angle C = 360-(63.7+49+26.3)
C = 360-139
C = 221°
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A figure was rotated 270° clockwise about the origin.
Which is most likely the new figure?
Answer:
Step-by-step explanation:
It will lie in quadrant 3
Step-by-step explanation:
Here, we want to know where the resulting image will lie after the rotation
After the rotation, it is expected that the resulting image will lie in quadrant 3
First 90 to quadrant 1
second 90 to quadrant 2
Third 90 to quadrant 3
Answer:
B is the correct answer
Step-by-step explanation:
i think:)
Here is a system of equations: (3x - y = 17 x+4y =10 .Solve the system by graphing the equations (by hand or using technology).
how do you solve it step by step ?
The graph of the system of equations is shown below, and the solution is: (6, 1).
What is the Solution of a System by Graphing?When a system of equations are plotted on a graph, the lines of the two equations in the system will intersect at a point. The coordinates of that point represents the solution of the system of equations.
In the graph shown below in the attachment, the red line represents the line 3x - y = 17, which has a slope of 3 and intercepts the y-axis at -17.
The green line represents the equation, x + 4y = 10, which has a slope of -1/4 and a y-intercept of 2.5.
Both lines intersect at point (6, 1).
Therefore, the solution is (6, 1)
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Consider all three-digit numbers that can be created from the digits 0-9 where the first and last digits must be even and no digit can repeat. Assume that numbers can start with 0. What is the probability of choosing a random number that starts with 6 from this group? Enter a fraction or round your answer to 4 decimal places, if necessary.
The probability of choosing a random number that starts with 6 from this group is 1/5 Or 0.2.
What are permutation and combination?A permutation is an arrangement of things where order matters, AB and BA are two different permutations.
The combination is a selection of things where order does not matter, AB and BA are the same combinations.
Given, All three-digit numbers that can be created from the digits 0-9.
So, The digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 total of 10 digits.
No. of even digits is 4 and the number of odd digits is 5.
The total number of 3 digits that can be formed where the first and last digits must be even and no digit can repeat and can start with 0 is,
= 5×10×4.
= 200.
The number of digits starts with 6 in this group is,
= 1×10×4.
= 40.
∴ The probability of choosing a random number that starts with 6 from this group is (40/200) = 1/5 Or 0.2
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What is the sum of the series sum from n equals 1 to infinity of negative 3 times three eighths to the n power question mark
Answer:
[tex]\textsf{A)} \quad -\dfrac{9}{5}[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{5.5 cm}\underline{Sum of an infinite geometric series}\\\\$S_{\infty}=\dfrac{a}{1-r}$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\ \phantom{ww}$\bullet$ $r$ is the common ratio.\\\end{minipage}}[/tex]
Given sum:
[tex]\displaystyle \sum^{\infty}_{n=1} -3\left(\dfrac{3}{8}\right)^n[/tex]
Therefore, the first term in the series is:
[tex]a_1=-3\left(\dfrac{3}{8}\right)^1=-\dfrac{9}{8}[/tex]
The common ratio, r, is:
[tex]r=\dfrac{3}{8}[/tex]
Substitute the first term, a, and common ratio, r, into the formula:
[tex]\implies S_{\infty}=\dfrac{-\frac{9}{8}}{1-\frac{3}{8}}[/tex]
[tex]\implies S_{\infty}=\dfrac{-\frac{9}{8}}{\frac{5}{8}}[/tex]
[tex]\implies S_{\infty}=-\dfrac{9}{5}[/tex]
Therefore, the sum of the given series is:
[tex]-\dfrac{9}{5}[/tex]The radius of a cylindrical construction pipe is 2.5. If the pipe is 28ft long, what is its volume?
Use the value 3.14 for π, and round your answer to the nearest whole number.
Be sure to include the correct unit in your answer.
Answer:V = 550 ft^3
Step-by-step explanation:
The volume of a cylinder is
V = pi r^2 h
We know the radius is 2.5 and the height is 28
V = 3.14 * (2.5)^2 * 28
V =549.5 ft^3
Rounding to the nearest whole number
V = 550 ft^3
Which equation best represents a line perpendicular to a line passing through points (–1, 2) and (1, –8)?
Let the equation of the line be ax + by + c = 0. Then the equation of the perpendicular line that is perpendicular to the line ax + by + c = 0 is given as bx - ay + d = 0
The equation of the line passing through (-1, 2) and (1, -8). Then the equation of the line will be
y + 8 = [(-8 - 2) / (1 + 1)] (x - 1)
y + 8 = -5x + 5
y = - 5x - 3
The equation that best represents a line perpendicular will be y = - 5x - 3.
Hello can someone please help me out? Thank you i will give brainly
Answer:
Area = 28.27 in²
Step-by-step explanation:
Now we have to,
→ find the area of the circle.
Formula we use,
→ π × r²
Now the required area will be,
→ π × r²
→ 3.14 × 3²
→ 3.14 × 9
→ 28.27 in²
Hence, the area is 28.27 in².
You have one type of candy that sells for $2.00/lb and another type of candy that sells for $8.90/lb. You would like to have 55.2 lbs of a candy mixture that sells for $2.50/lb. How much of each candy will you need to obtain the desired mixture?
You will need ___ lbs of the cheaper candy
and ____ lbs of the expensive candy.
You will need 51.2 lbs of the cheaper candy and 4 lbs of the expensive candy.
What is equation of two variables?A equation is supposed to be straight condition in two factors in the event that it is written as hatchet + by + c=0, where a, b and c are genuine numbers and the coefficients of x and y, i.e an and b separately, are not equivalent to nothing. For instance, 10x+4y = 3 and - x+5y = 2 are straight conditions in two factors
According to given information:Let x be number of pounds of cheaper candy and y represent that of expensive candy.
Then, x + y = 55.2----(1)
And
2x + 8.9y = 55.2(2.5) = 138
2x + 8.9y = 138---------(2)
On solving above two equation, we get
x = 51.2
y = 4
Thus, cheaper candy are of 51.2 ib and expensive are of 4 ib
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9. RWS congruent to TUV. Find the values of x and y.
The value of x would be 11° and the value of y would be 6.
What are congruent triangles?
Two triangles are congruent if all of their sides are the same - so side, side, side. We also know they are congruent if we have a side and then an angle between the sides and then another side that is congruent-- so side, angle, side.
ΔRWS ≅ ΔTUV
As both triangles are congruent then we can say that
∠S ≅ ∠V
so ∠S = 29°
Now in ΔRWS,
By using the sum of all angles of the triangle property, we can write
∠R +∠W + ∠S = 180°
(8x - 27)° + 90° + 29° = 180°
8x = 180° - 92°
8x = 88°
x = 88/8
x = 11°
Now Side RS ≅ Side TV
3y + 7 = 25
3y = 25 - 7
3y = 18
y = 18/3
y = 6
Hence, the value of x would be 11° and the value of y would be 6.
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simplify 3/7 + 1/7 please answer
Answer:
2/7 ≈0.285714286
Step-by-step explanation: 3/7−1/7
Since 3/7 and 1/7 have the same denominator, subtract them by subtracting their numerators.
3−1 over 7
Subtract 1 from 3 to get 2.
2/7
the Factor
so 2/7 ≈0.285714286
The number line shows the elevation of the bottom of a harbor and the elevation of a fish swimming closer to the surface A what change in elevation is necessary for the fish to reach bottom B once the fish reaches the bottom what change in elevation will bring it back up to the surface
The elevation needs to be smaller than the decrease of the elevation like this.
What is the elevation on the number line?
The elevation of a location describes its height above or below the sea level, which has an elevation of 0. Elevations below the sea level are represented by negative numbers, and elevations above the sea level are represented by positive numbers.
Whatever number is larger than the number of the elevation of the bottom of the harbor
the elevation needs to be smaller than the decrease of the elevation like this.
e.g.
The temperature elevated by 28 degrees and then decreased by 30 degrees.
Hence, the elevation needs to be smaller than the decrease of the elevation like this.
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download short story a vacation trip roger paré pdf free
To find a book it is necessary to write the name "a vacation trip" in the search engine and add the word PDF to obtain better results.
¿How to download a book from the internet?To download a book from the Internet it is necessary to review various pages since some do not contain the complete book and others may have some type of virus that can damage the device.
In the same way, there are some platforms or applications that require a subscription payment to be able to access the content in an unlimited way.
¡Hope this helped!
The lengths of footlong sub sandwiches at a local sub shop follow an approximately normal distribution with unknown mean
and standard deviation 0.2 inch. If 20% of these sandwiches are shorter than 11.7 inches, find the mean length u.
Mean
inches
(Round to 2 decimal
Answer:
Step-by-step explanation:
What is the mean of this data 678,592,652,800,502,396,502,301
Hello,
I hope you and your family are doing well!
To find the mean of a set of numbers, you need to add up all of the numbers and divide the sum by the total number of numbers in the set.
In this case, the mean would be calculated as follows:
(678 + 592 + 652 + 800 + 502 + 396 + 502 + 301) / 8 = 515.25
So the mean of this data set is 515.25.
The mean is a measure of the central tendency of a data set and can be used to represent the entire set of numbers by giving a single value that is representative of the set as a whole. It is also known as the average.
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help. plsss i dont understand so gimme a answer or something
A manufacturing company finds that they can sell 250 items at $3.50 per item and 350 items at $2.50 per item.
If the relationship between the number of items sold a and the price per item p is a linear one:
Find a formula that gives a in terms of p: x =
Now use the formula to find the number of items they will sell if the price per item is $1.50.
They will sell…
items if the price is $1.50.
Answer:
a = 600 -100pa = 450 for p = 1.50Step-by-step explanation:
You want the formula that represents (p, a) = (3.50, 250) and (2.50, 350) as a linear function. Then you want the value of 'a' for p = 1.50.
SlopeWe can see from the ordered pairs that 'a' goes up by 100 when p goes down by 1.00. The slope is ...
m = ∆a/∆p = 100/(-1) = -100
InterceptThe y-intercept (b) can be found by solving the slope-intercept equation for b:
y = mx +b
b = y - mx
For (x, y) = (3.50, 250), the value of 'b' is ...
b = 250 -(-100)(3.50) = 600
EquationThe slope-intercept equation for 'a' in terms of p is ...
a = -100p +600
Evaluation
The value of 'a' for p = 1.50 is ...
a = -100(1.50) +600
a = 450
They will sell 450 items if the price per item is $1.50.
If cos (0) = -3.29, what is cos (+0)?
A. -3.29
B. 3.29
C. 73.1°
D. -73.1°
Answer:
A
Step-by-step explanation:
There is no difference between -0 and +0.
So the ans is -3.29 itself.
Determine the probability: There is a 40% chance of rain this weekend.
a. 0.60
b. 0.40
c. 40
d. 4
Answer:
Step-by-step explanation: