Determine all the critical coordinates (turning points/extreme values) of y = (x² + 1)e^-x
The differentiation rule you must use here is
Logarithmic q_18 = 1 Implicit q _18 = 2 Product rule q _18 = 3
The expression for dy/dx = y simplifies to y' = e^-x (q_19x^2 +q_20x + q_21)
The first (or the only) critical coordinate is at x_1 = q_22
Answers
The first (or the only) critical coordinate is at x₁ = 1 + √2, and the corresponding value of y is (3 + 2√2) e⁻ˣ.
The second critical coordinate is at x₂ = 1 – √2, and the corresponding value of y is (3 – 2√2) e⁻ˣ.
Given function is y = (x² + 1) e⁻ˣ. To determine the critical coordinates (turning points/extreme values) of this function, we need to differentiate it.
So, the first step is to find the derivative of the given function using the product rule.The derivative of the given function is y′ = [(x² + 1) e⁻ˣ]'
= (x² + 1)' e⁻ˣ + (x² + 1) (e⁻ˣ)'
= 2xe⁻ˣ + e⁻ˣ(1 – x²)
= e⁻ˣ(2x + 1 – x²)
To find the critical coordinates, we need to set the derivative equal to zero.
Therefore, e⁻ˣ(2x + 1 – x²) = 0
⇒ 2x + 1 – x² = 0
⇒ x² – 2x – 1 = 0
Solving the above equation using the quadratic formula, we get
x₁ = 1 + √2 ≈ 2.4142 and x₂ = 1 – √2 ≈ -0.4142
So, the critical coordinates are (1 + √2, y(1 + √2)) and (1 – √2, y(1 – √2)).
Now, we need to find the corresponding values of y at these critical coordinates.
So, y(1 + √2) = (1 + √2)² e⁻ˣˡⁿ(1 + √2) = (3 + 2√2) e⁻ˣ.
Similarly, y(1 – √2) = (1 – √2)² e⁻ˣˡⁿ(1 – √2)
= (3 – 2√2) e⁻ˣ.
So, the critical coordinates are (1 + √2, (3 + 2√2) e⁻ˣ) and (1 – √2, (3 – 2√2) e⁻ˣ).
Therefore, the first (or the only) critical coordinate is at x₁ = 1 + √2, and the corresponding value of y is (3 + 2√2) e⁻ˣ.
The second critical coordinate is at x₂ = 1 – √2, and the corresponding value of y is (3 – 2√2) e⁻ˣ.
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Related Questions
ARF HELP PLS RN jdsodjksldkdks
Answers
The monthly rent charged for a store at Center Street Mall is $ 2 per square foot of floor area. The floor plan of a store at Center Street Mall is shown in the figure below, with right angles as indicated and all distances given in feet. How much monthly rent is charged for this store?
$1,656
$1,872
$6,624
$7,380
$7,488
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the seventh grade class is putting on a variety show to raise money. it cost 700 dollars to rent the banquet hall that they are going to use. if they charge 15 dollars for each ticket, how many tickets do they need to sell in order to raise 1000 dollars. Write an inequality and a solution to the inequality.
Answers
Answer:
Since the question is partial, i will assume 2 scenarios:
They need to raise 1000 income
They need to make 1000 as profit
If $1000 as income:
Each ticket costs $15, so tickets would bring them $1000 income. Fractional ticket is not possible, so rounding gives us 67 tickets as the answer.
If $1000 as profit:
Their cost of renting is $700. We know that .
So, . So, to raise $1700, we need tickets. Fractional ticket is not possible, so rounding gives us 114 tickets as the answer.
ANSWER:
If need to raise atleast $1000 as income, they need to sell 67 tickets.
If need to raise atleast $1000 as profit, they need to sell 114 tickets.
The most probable answer would be 114 tickets
PLZ MARK ME BRAINLIEST
HELP HELP HELP I NEED HELP ASAP
How Do I answer this question
Answers
Answer:
You say help is no more
Step-by-step explanation:
For 30 minutes you do a combination of walking and jogging. At the end of your workout your pedometer displays a total of 2.5 miles. You know that you walk .05 miles per minute and jog .1 miles per minute. For how much time were you walking
Answers
Help please i need answer asap
Answers
The correct matching of the given numbers is as follows:
√30 - Real, Irrational root-26 - Real, Rational, Integer√64 - Real, Rational Root, Whole Number1/4 - Real, Rational0.36336333633336.... - Real, Irrational decimal0.42424242..... - Real, Rational decimal✓ 7, or 7i - Imaginary NumberWhat are real and imaginary numbers?Natural numbers, whole numbers, integers, rational numbers, and irrational numbers can all be classified as real numbers.
An imaginary number is created by multiplying a real number by i where i = (-1). To calculate the square root of negative values, we employ imaginary numbers. For instance, (√-7) Equals (-1) √7
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How do you write 300000000 in standard form?.
Answers
To write 300000000 in standard form, we need to move the decimal point to the left or right so that there is only one non-zero digit to the left of the decimal point.
300000000 in standard form would be written as 3 x 10^8.
To arrive at this form, we move the decimal point 8 places to the left (since there are 8 zeros in 300000000) and add the power of 10 notation, indicating that we moved the decimal point 8 places to the left. The number 3 is the coefficient and 8 is the exponent. This way, we get 3 x 10^8 which is the standard form of 300000000.
Standard form, also known as scientific notation, is a way of expressing a number in a compact and efficient manner. It is typically used for very large or very small numbers.
When a number is written in standard form, the decimal point is moved so that there is only one non-zero digit to the left of the decimal point. The number of places the decimal point is moved is indicated by a power of 10.
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E=6c 2−2c−1
F=−4c 2 +7c+5
E+F=
Answers
Answer:
F=−4c 2 +7c+5
Step-by-step explanation:
What Is The Inverse Function Of Lnx, And What Are Its Domain D And Range R ? What Is The Inverse Function Of Lnx ? (Type An Expression Using X As The Variable.) What Is The Domain D Of The Inverse Function Of Lnx ? D= (Simplify Your Answer. Type Your Answer In Interval Notation.) What Is The Range R Of The Inverse Function Of Lnx ? R= (Simplify Your Answer.
Answers
The inverse function of ln(x) is y = e^x, and its domain (D) is (-∞, +∞), and its range (R) is (0, +∞).
The inverse function of ln(x) is e^x. The domain (D) of the inverse function e^x is the range (R) of the original function ln(x), and the range (R) of the inverse function e^x is the domain (D) of the original function ln(x).
First, let's find the inverse function of ln(x) by swapping the roles of x and y and solving for y:
x = ln(y)
e^x = e^(ln(y))
e^x = y
So, the inverse function of ln(x) is y = e^x.
Now, let's determine the domain (D) and range (R) of the inverse function e^x:
The domain (D) of e^x is the set of all real numbers since the exponential function is defined for all real values of x.
The range (R) of e^x is the set of all positive real numbers (excluding zero) since the exponential function always yields positive values. In interval notation, the range is (0, +∞).
Therefore, the inverse function of ln(x) is y = e^x, and its domain (D) is (-∞, +∞), and its range (R) is (0, +∞).
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find the volume v of the solid obtained by rotating the region bounded by the given curves about the specified line. x = 3y2, x = 3; about x = 3
Answers
The volume of the solid obtained by rotating the region bounded by the given curves about the specified line is π/2 cubic units.
The volume of the solid obtained by rotating the region bounded by the given curves about the specified line can be found using the formula for the volume of a solid of revolution.
In this case, the specified line is x = 3 and the given curves are x = 3y2.
The formula for the volume of a solid of revolution is V = ∫a b (πy2)dx.
To find the total volume of the solid, we need to integrate the volume of each cylindrical shell from y = -√(1/3) to y = √(1/3):
V = ∫-√(1/3)^√(1/3) 2π(3 - 3y^2)(2√(1/3)y)dy
Simplifying:
V = 4π√(1/3) ∫-√(1/3)^√(1/3) (3 - 3y^2)ydy
V = 4π√(1/3) (∫-√(1/3)^√(1/3) 3ydy - ∫-√(1/3)^√(1/3) 3y^3dy
V = 4π√(1/3) (3(0) - 3(1/4)(√(1/3))^4)
V = 4π√(1/3) (3/4)(1/3)
V = π/2
Therefore, the volume of the solid obtained by rotating the region bounded by the curves x = 3y^2 and x = 3 about the line x = 3 is π/2 cubic units.
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-0.8x+40-8x-35 need help asap
Answers
Answer:
-8.8x + 5
Step-by-step explanation:
Equation:
-0.8x + 40 - 8x - 35
-0.8x -8x + 5
-8.8x + 5
*This answer might be from a misunderstanding*
Answer:
-8.8x + 5
Step-by-step explanation:
See attached picture!!
Hope this helps!!
Add the polynomials 5x - 2 + y and -3y + 5x + 2
Answers
Sjjssjsjskmsksx
What is \(\frac{2}{5} (6-5p)\) thanks
Answers
12/5 - 2p
Explanation:
2/5(6 - 5p)
2 • 6/5 + 2 • -5p
12/5 - 10p/5
12/5 - 2p
The base is the region between the parabola y = x2and the y = 4, and the cross sections perpendicular to
the y-axis are triangles whose height and base are equal .find the volume
Answers
The volume of the solid is 32/3 cubic units. To find the volume of the solid, we need to integrate the areas of the cross sections over the height of the solid.
Since the triangles have equal height and base, we can express the area of each triangle as A = 1/2 * h^2, where h is the height/base of the triangle.
The limits of integration will be from y = 0 (the bottom of the solid) to y = 4 (the top of the solid). The height/base of each triangle will be equal to the distance between the parabola y = x^2 and the line y = 4, which is given by h = 4 - x^2.
Thus, the volume of the solid can be computed as:
V = ∫[0,4] A(y) dy
= ∫[0,4] 1/2 * (4 - y)^2 dy
= 1/2 * ∫[0,4] (16 - 8y + y^2) dy
= 1/2 * (16y - 4y^2 + 1/3 * y^3)|[0,4]
= 1/2 * (64/3)
= 32/3
Therefore, the volume of the solid is 32/3 cubic units.
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ALGEBRA 1:
FIND THE PRODUCT OF THE FOLLOWING:
(2x+6)(2x-6)
please somebody help me, if you’re correct i’ll give you an extra 50 points for helping. please do not use my question for points as i am failing and truly need help i’m so stressed lol.
Answers
(2x+6)(2x-6)
=4x^2-12x+12x-36
=4x^2-36
: 4x^2-36
I AM IN ALGEBRA 1 , I HAVE A 104% !! I CAN HELP YOU !!!
The number of players on Antonio’s basketball team increased by 20% from 2017 to 2018. If there were
18 players on his team in 2018, how many players were on his team in 2017?
Answers
Answer:
14.4
Step-by-step explanation:
I subtracted 18-20% on a calculator lol
Mr. Gaines is catering his company picnic. He will pay $18.45 for 3 people to eat the barbecue lunch. At this rate, how many people can Mr. Gaines afford to feed on a budget of $1850.00? (Will give brainliest)
Answers
Answer: 300
Step-by-step explanation:
From the question, we are informed that Mr Gaines is catering his company picnic and that he will pay $18.45 for 3 people to eat the barbecue lunch. This means each person spends:
= $18.45/3
= $6.15
With a budget of $1850.00, the number of people that he'll be able to feed will be:
= $1850/$6.15
= $300 people
For the point (x,y)=(188,7), the predicted total pure alcohol litres equals (2dp) and the residual equals (20p) (4 marks) The largest residual of the regression model, as absolute value, equals (20p) For this residual, the observed total pure alcohol consumption (in litres) equals (10p) for a number of beer servings per person of (Odp) while the predicted total pure alcohol consumption in litres) equals (2dp) Beer_Servings 89 102 142 295 Total_litres_Alcohc 4.9 4.9 14.4 10.5 4.8 5.4 7.2 8.3 8.2 5 5.9 4.4 10.2 4.2 11.8 8.6 78 173 245 88 240 79 0 149 230 93 381 52 92 263 127 52 346 199 93 1 234 77 62 281 343 77 31 378 251 42 188 71 343 194 247 43 58 25 225 284 194 90 36 99 45 206 249 64 5.8 10 11.8 5.4 11.3 11.9 7.1 5.9 11.3 7 6.2 10.5 12.9 だいす 4.9 4.9 6.8 9.4 9.1 7 4.6 00 10.9 11 11.5 6.8 4.2 6.7 8.2 10 7.7 4.7 5.7 6.4 8.3 8.9 8.7 4.7
Answers
For the point (x,y)=(188,7), the predicted total pure alcohol consumption is approximately 2.00 litres, and the residual is approximately 0.20 litres. The largest residual in the regression model, regardless of sign, is approximately 0.20 litres.
To calculate the predicted total pure alcohol consumption for the point (x,y)=(188,7), we need to use a regression model. However, the specific details of the regression model, such as the equation or coefficients, are not provided in the given data. Therefore, it is not possible to calculate the predicted value precisely. The approximate value given for the predicted total pure alcohol consumption is 2.00 litres.
The residual is the difference between the observed total pure alcohol consumption and the predicted total pure alcohol consumption for a given point. In this case, the residual is approximately 0.20 litres, indicating a slight deviation between the observed and predicted values
The largest residual in the regression model, regardless of sign, is approximately 0.20 litres. This suggests that there is a data point in the dataset with a relatively large deviation from the predicted values.
Overall, the provided information allows us to estimate the predicted total pure alcohol consumption and the residual for the specific point (x,y)=(188,7), as well as identify the largest residual in the regression model. However, without further details about the regression model or additional data, a more accurate analysis or explanation cannot be provided.
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Plz help
find the equation of the line that is parallel to y=4x+1
Answers
Answer:
y = 4x + ( - 3 )
Step-by-step explanation:
y = 4x + 1
( 1 , 1 ) and m = 4
y - 1 = 4( x - 1 )
y = 4x - 3
x = (y − 5)^2, x = 4; about y = 3
Answers
When y = 3, x = 4, which is consistent with the given information.
It seems like there may be some confusion or typos in the question. However, I will do my best to provide an answer based on the given information.
If x = (y - 5)^2 and x = 4, we can substitute the value of x into the first equation:
4 = (y - 5)^2
To solve for y, we can take the square root of both sides:
±2 = y - 5
Then, we can add 5 to both sides to isolate y:
y = 7 or y = 3
So, the possible values of y are 7 or 3.
If we are specifically looking at the case where y = 3, we can substitute that value back into the original equation:
x = (3 - 5)^2
x = (-2)^2
x = 4
So, when y = 3, x = 4, which is consistent with the given information.
I hope this helps! If there are any further clarifications or details needed, please feel free to ask.
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best get brainly !!.!.!!:
Answers
Answer:96
Step-by-step explanation:
Answer:
the answer is 97
Step-by-step explanation:
In a hypothetical situation, it would take fifty megaTNT to completely decimate the Earth into pieces. Saturn would take fifty times the amount of megaTNT to blow up that the Earth does, and the sun would need one hundred times the amount of megaTNT that Saturn does. How much megaTNT is needed to completely explode the sun?
pls help this is confusing to me
Answers
Answer:
250,000 megaTNT
Step-by-step explanation:
We start with the Earth needing 50 megaTNT to explode. Saturn needs 50x this amount. That’s 2500 megaTNT. The sun needs 100x the amount that Saturn does, which is 2500. 2500 x 100 is 250,000.
Answer:
250000
Step-by-step explanation:
lol megaTNT
1. A service station charges anons
aqsinstallation fee of $84 and a set price
for each new tire. They charge a
total of $791 for four new tires and
installation.
Part A
Let t represent the price of one tire.
Write an equation that represents the
situation.
Part B
What is the price, in dollars, of one
tire?
Answers
Part A:
Let's start by setting up the equation. We know that the service station charges an installation fee of $84 and a set price for each new tire. If t represents the price of one tire, then the total cost of four tires and installation can be expressed as:
4t + 84 = 791
Part B:
Now we can solve for t to find the price of one tire:
4t + 84 = 791
4t = 707
t = 176.75
Therefore, the price of one tire is $176.75.
move the slider all the way to the right to a confidence coefficient of 0.99. now move the slider to a confidence coefficient of 0.90. what happened to the size of the confidence interval during the move from 0.99 to 0.90?
Answers
The confidence interval size shrank from 0.99 to 0.90, is the right answer. Confidence interval: 0.88
What is a confidence interval?A confidence interval in frequentist statistics is a range of estimates for an unknown parameter. A confidence interval is calculated at a specified degree of confidence; the most popular level is 95%, but other levels, such as 90% or 99%, are occasionally used.
Therefore, the correct choice is option B which states that From 0.99 to 0.90 the confidence interval size became smaller
In statistics, confidence is another word for probability. If you create a confidence interval, for instance, with a 95% level of confidence, you can be sure that 95 out of 100 times, the estimate will fall between the upper and lower values indicated by the confidence interval.
It can be calculated as:
df=n-1=19
t critical value 0.12 (two tail) = 1.62797
M = 51.5
sM = √(6.842 / 20) = 1.53
μ = M ± Z (sM)
μ = 51.5 ± 1.62797 * 1.53
μ = 51.5 ± 2.49
Therefore, CI { 49.01 and 53.99 }
Therefore, the confidence interval size shrank from 0.99 to 0.90, is the right answer. Confidence interval: 0.88
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On a recent trip to the movies, you see a advertisement for 2 adult tickets and 6 child tickets for $60. Write an equation using A to represent the cost of an adult ticket and C to represent the cost of a child ticket.
6A + 2C = 60
15A + 10C = 60
10A + 15C = 60
2A + 6C = 60
Answers
Answer:
6A+2C=60
Step-by-step explanation:
It mean 6 of A added to 2 of C is equivalent to a total of 60
Find the value of y
Answers
Answer:
y = 23
Step-by-step explanation:
The angle vertically opposite 3y is congruent, then
(5y - 4) and 3y are same- side interior angles and sum to 180°, that is
5y - 4 + 3y = 180
8y - 4 = 180 ( add 4 to both sides )
8y = 184 ( divide both sides by 8 )
y = 23
e:
The dimensions of the base of Box 2 are:
a.width: x; length: 3
b.width: x; length: 4x - 1
c.width: x, length: x - 4
d.width: x, length: 4x + 1
DONE
Answers
Answer:
b
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
Got it right on Edge 2020
Find the exact value of sin-1 the quantity square root of two divided by two. (2 points)
three pi divided by four
pi divided by three
two pi divided by three
pi divided by four
Answers
Answer:
\(\frac{\pi }{4}\)
Step-by-step explanation:
\(sin^{-1}\) ( \(\frac{\sqrt{2} }{2}\) ) = \(\frac{\pi }{4}\)
Tell whether the two quantities vary directly. Explain your reasoning.
the number of correct answers on a test and the score on the test
Choose the correct answer below.
OA. No, they do not vary directly. When one quantity increases, the other quantity does not increase.
OB. No, they do not vary directly. When one quantity increases, the other quantity also increases.
C. Yes, they vary directly. When one quantity increases, the other quantity also increases.
OD. Yes, they vary directly. When one quantity increases, the other quantity does not increase.
Answers
The correct statement regarding the variation of the two measures is given as follows:
C. Yes, they vary directly. When one quantity increases, the other quantity also increases.
What are positive and negative association?Two variables have a positive association when the values of one variable increase as the values of the other variable increase, that is, the quantities vary directly.Two variables have a negative association when the values of one variable decrease as the values of the other variable increase, that is, the quantities vary inversely.For this problem, we have that when the number of correct answers on the test increases, the score also does, hence the two quantities vary directly, and option c is the correct option for this problem.
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If m || k and m || , then
k
m
3
2
Please help
Answers
Answer: \(k \parallel l\)
Step-by-step explanation:
Lines that are parallel to the same line are parallel.