find an equation of the tangent line to the graph of f(x) = xe^−x at its inflection point.
Answers
Answer:
y = (4 -x)e^-2
Step-by-step explanation:
You want an equation of the tangent line to the graph of f(x) = xe^−x at its inflection point.
Inflection pointThe inflection point on a curve is the point where the second derivative is zero, where the curve changes from being concave downward to concave upward, or vice versa.
We can use the product rule to differentiate f(x):
(uv)' = u'v +uv'
f'(x) = 1·e^-x +x·(-1)(e^-x) = (e^-x)(1 -x)
Then the second derivative is ...
f''(x) = (-e^-x)(1 -x) +(e^-x)(-1) = (e^-x)(x -2)
The second derivative is zero where one of its factors is zero. e^-x is never zero, so we have ...
(x -2) = 0 ⇒ x = 2
The point of inflection occurs at x = 2.
Point-slope equationThe point-slope equation of the line with slope m through point (h, k) is ...
y -k = m(x -h)
For this problem, we have ...
m = f'(2) = (e^-2)(1 -(2)) = -e^-2
(h, k) = (2, f(2)) = (2, 2e^-2)
So, the equation of the tangent line is ...
y -2e^-2 = -e^-2(x -2)
In slope-intercept form, this is ...
y = (-e^-2)x +4e^-2
__
Additional comment
We can rearrange the equation to ...
y = (4 -x)e^-2
Usually a tangent line touches the graph, but does not cross it. The tangent at the point of inflection necessarily crosses the graph.
Related Questions
What is the value of the logarithm?
log (750)
Round the answer to the nearest thousandth.
Enter your answer in the box.
Answers
The value of the given logarithm log(750)=2.875.
What is meant by logarithm?Commonly employed in science and engineering, the base-10 logarithm is also known as the decimal or common logarithm. Since its derivative is so straight forward, the natural logarithm, whose base is the number e 2.718, is widely used in both mathematics and physics. Computer science typically use the binary logarithm, which has a base of 2.
John Napier developed logarithms as a way to make calculations simpler in 1614. To make high-accuracy calculations simpler, they were quickly embraced by surveyors, scientists, engineers, navigators, and other professionals. Inefficient multi-digit multiplication steps can be swapped out for quicker addition and table lookups when using logarithm tables.
Given,
We have to find the logarithm value of log(750)
By using the logarithm calculator we get
log(750)=2.875
Therefore, the value of the given logarithm log(750)=2.875
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At Sparky' Candy World, Mile pent a total of $13. 75 on gummy bear and jelly bean. He bought 2. 5 pound of gummy bear at $3. 40 per pound. If jelly bean cot $1. 50 per pound, how many pound of jelly bean did he buy?
Answers
By solving this question of algebra we can calculate that Mile bought 3.5 pounds of jelly bean.
What is algebra?Algebra is the study of using variables to denote some quantity, and then solving equations to calculate the value of the quantity based on some conditions given.
How to solve questions of algebra?Let x be the amount of gummy bear bought and y be the amount of jelly bean bought. Then, 3.40x + 1.5y = 13.75 (total amount of money)
x = 2.5 (given in question)
then,
3.40 (2.5) + 1.5y = 13.75
y = 3.5 pounds
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The distance between (-7, a) and
(5, 1) is 13 units.
Find two possible values for a.
Answers
Answer:
1
Step-by-step explanation:
you will be required to find a magnitude of the two points that is (5,1) -(-7,a) =(12,1-a)
then find square root using the formula √x^2+y^2
thus (√12^2+a^2)=13 thus 12+a= 13 hence a=13-12
a=1
(v³ + 2v² - 21v +21) ÷ (v + 6)
Answers
Answer:
v3+2v2−21v+21/v+6
Step-by-step explanation:
There are no solutions to this equation
Find two pairs of conjugates with a product of 3.
Answers
Answer:
Step-by-step explanation:
21:
3,7
Let's solve. 3x a) 3X 8 10. d) { + 14/= 1/1/2 ¼ 4 / = 7 3 8) ²³² + ³ = 5 X
Answers
Answer: hmmmm who knows?
Step-by-step explanation: but you got it good luck!
The diameter of ball bearing are ditributed normally. The mean diameter i 81 millimeter and the variance i 16. Find the probability that the diameter of a elected bearing i greater than 85 millimeter. Round your anwer to four decimal place
Answers
the probability that the diameter of a elected bearing is greater than 85 millimeter P(diameter > 85) = P(z > (85-81)/4) = P(z > 1) = 0.1587
The diameter of ball bearings is normally distributed, with a mean of 81 millimeters and a variance of 16.
To calculate the probability that a selected bearing has a diameter greater than 85 millimeters, we first calculate the z-score for 85 millimeters.
We subtract 81 from 85 to get 4, and divide by 4 to get 1 for the z-score.
We the look up the probability for a value of 1 in the z-table, which is 0.1587.
This is the probability that a selected bearing has a diameter greater than 85 millimeters, rounded to four decimal places.
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how should the decimal point in 52.48be m
Answers
Answer:
5 spaces right
hope this helps
The scale factor of two triangles is 2:5. If the smaller triangle has side length of 30, what would be the length of the corresponding side on the bigger triangle?
Answers
Answer:
75
Step-by-step explanation:
From the way you've typed the question, it would appear that the ratio of the size of the smaller side to the ratio of the size of the larger side is 2:5.
Therefore, if the smaller side is 30, you can use the ratio the find the larger side:
[tex]S:L\\2:5\\\\[/tex]
(×15 to make the smaller side 30)
[tex]30:75[/tex]
Therefore, the bigger triangle would have side length 75.
Which equation has infinitely many solutions? 5(2x 4) = 10x – 12 5(2x 4) = 10(x 2) 5(2x 4) = 12x 5(2x 10) = 20(x 1)
Answers
The equation that has infinitely many solutions is 5(2x + 4) = 10(x + 2).
An equation can have infinitely many solutions when both sides of the equation satisfy the same conditions. The system of an equation has infinitely many solutions when the lines are coincident, and they have the same y-intercept. If the two lines have the same y-intercept and the slope, they are actually in the same exact line. For the given equations it can determine if the equation has infinitely many solutions by simplifying the equation and see if both sides are equal. Hence,
5(2x + 4) = 10x – 12
10x + 20 ≠ 10x - 12
5(2x + 4) = 10(x + 2)
10x + 20 = 10x + 20
5(2x + 4) = 12x
10x + 20 ≠ 12x
5(2x + 10) = 20(x + 1)
10x + 50 ≠ 20x + 20
Hence, 5(2x + 4) = 10(x + 2) has infinitely many solutions.
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what is the answer to -4(r+2)=4(2−2r)
Answers
Please answer the question in the photo.
Answers
Answer:
m it's equal to 6 because division its equal subtract the power
Step-by-step explanation:
A* to the power 9 divided by A* to the power 3 its equal to 9-3 = A* to the power its a
A^6
find the curvature at the point (2, 8, −1). x = 2t, y = 8t3/2, z = −t2
Answers
The curvature at the point (2, 8, −1). x = 2t, y = 8t^3/2, z = −t^2 is 0.039
In this question we need to find the curvature of r(t) = <2t, 8t^3/2, -t^2> at the point (2, 8, -1).
The derivative of r(t) with respect to t is:
r'(t) = <2, 12t^1/2, -2t>
The point (2, 8, -1) corresponds to t = 1,
and r′(1) = <2, 12(1)^1/2, -2(1)>
r'(1) = <2, 12, -2>
|r'(1)| = √(2^2 + 12^2 + (-2)^2)
|r'(1)| = √(4 + 144 + 4)
|r'(1)| = √(152)
|r'(1)| = 12.32
Now, r''(t) = <2, 6t^-1/2, -2>
and r′'(1) = <0, 6, -2>
r′(1) × r′′(1) = <0, 72, 4>
|r′(1) × r′′(1) |
= √(0^2 + 72^2 + 4^2)
=72.11
So, the curvature of r(t) would be,
κ(1) = |r′(1) × r′′(1)| ÷ |r′(1)|^3
k(1) = 72.11 / 12.32³
k(1) =0.039
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Lydia is playing Galaxy 8RX. After three misses, the game is over. Last week, Lydia kept track of how long her games lasted. She made a line plot of her data. Lydia said, “My best time is 2 3/4 minutes longer than my worst time because 4 1/4 - 1 1/2 = 2 3/4
Answers
if two sides of a triangle are 22 in and 13 in, what is the smallest whole number value for the 3rd side?
Answers
If two sides of a triangle are 22 in and 13 in, then is the smallest whole number value for the 3rd side will be 10
According to the rule of triangle the sum of first angle and second angle should be greater than the third angle.
first angle+ second angle > third angle
Here
22-13 = 9
so to became a triangle the minimum value of the third side will be 10(9+1).
Therefore, If two sides of a triangle are 22 in and 13 in, then is the smallest whole number value for the 3rd side will be 10
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Write an equation of the line that passes through (4, 8) and is perpendicular to the line y = x-5.
An equation of the perpendicular line is
Answers
The slope of a line that is perpendicular to the line y = x - 5 is the negative reciprocal of the slope of y = x - 5. The slope of y = x - 5 is 1, so the slope of the line that passes through (4, 8) and is perpendicular to y = x - 5 is -1.
We can use the point-slope form of a line to write the equation of the line that passes through (4, 8) and has a slope of -1. The point-slope form of a line is given by the equation y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line. In this case, (x1, y1) is (4, 8) and m is -1, so the equation of the line is y - 8 = -1(x - 4). Simplifying this equation, we get y - 8 = -x + 4. Adding 8 to both sides of the equation, we get y = -x + 12. This is the equation of the line that passes through (4, 8) and is perpendicular to y = x - 5.
Find −1/2(−4/5) . Write your answer as a fraction in simplest form.
Answers
Answer:0.4 as a decimal,2/5 as a fraction
Step-by-step explanation:
cual es la respuesta
Answers
The verdict on each of the given scenarios are as follows;
1. Yes, enough information is given to conclude that the triangles are congruent by the side-side-side SSS congruence theorem.2. No, the information conveyed through the triangles is not enough to conclude that the triangles are congruent.3. Yes, the two triangles given are congruent by virtue of the HL Congruence theorem.Which congruence theorems render the triangles congruent?By observation:
1. Since the two Triangles represented in 1. share a side and also, the two corresponding sides are congruent; it can be concluded that the two triangles are congruent.
2. By observation, although two sides are said to be congruent in the triangles; it cannot be concluded that the triangles are congruent neither by HL nor SSS congruence theorem.
3. The two Triangles share the diagonal which serves as the hypothenuse of both triangles; in addition, one of the other side lengths of the triangles are congruent; Therefore, the triangles are congruent by the HL congruence theorem.
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Can someone help me with Question 2b of this assignment? I'd deeply appreciate it! :)
Answers
Answer:
x=-6
Step-by-step explanation:
[tex]\frac{1}{2} x[/tex]-6=2x+3
∴2×( [tex]\frac{1}{2} x[/tex]-6)=2×(2x+3)
∴x-12=4x+6
∴3x=-18
∴x=-6
the plane traveling from boston traveled at an average speed of 360 miles per hour. the plane traveling from kansas city arrived at 10:34 a.m. how many minutes before the plane from boston arrived did the plane from kansas city arrive?
Answers
From Boston to Kansas City, it takes 20 minutes to get there. When calculating the plane's arrival time, multiply the 360 mph speed from Boston by the 864 mi distance to Chicago.
what is distance ?Regardless of an object's beginning or ending position, we can define distance as the amount of ground it has traveled.
given
When calculating the plane's arrival time, multiply the 360 mph speed from Boston by the 864 mi distance to Chicago.
Distance = rate*time
864 = 360t,
t = 2.4
In other words, the flight arrived after 2.4 hours. Given that this is longer than two hours, divide the number by sixty to determine the time in minutes:
60 * 2.4 = 144 minutes. Assess the flight's travel time from Kansas City now.
It took 2 hours, 4 minutes, or 124 minutes from the time it departed at 8:30 AM to the time it arrived at 10:34 AM.
According to this, the jet from Kansas City arrived 144 – 124 = 20 minutes earlier than the plane from.
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Jamie has a fish tank with clownfish and goldfish. There are 8 fish in total, and 2/8 of them are clownfish. Jamie decides to double the amount of clownfish in the tank. How many clownfish are in the tank now? What fraction of the fish are clownfish?
Answers
Answer:
1/ There are 4 clownfish in the tank now
2/ 4/10
Step-by-step explanation:
1/ We know the original number of clownfish is 2/8, which means there are 2 clownfish in a tank with a total number of 8 fish.
So now she wants to double the clownfish. So there will be 4 clownfish in the tank now.
2/ We know that there was eight fish in the tank, and now there are 2 more, so the total will be 10! And we know that now there are 4 clownfish, so our fraction is 4/10
An engineer makes different-size samples of a new material. The table shows volumes and the related masses. What would be the mass of 100 cubic centimeters of the material? Of 500 cubic centimeters of the material? Use pencil and paper. Explain how you can use mental math to find the answer.
The mass of 100 cubic centimeters of the material would be [answer] enter your response here grams.
Answers
Answer:
The mass of 100 cubic cm = 1,000 grams.
The mass of 500 cubic cm = 5,000 grams.
Step-by-step explanation:
90/10=9
140/10=14
250/10=25
100x10=1000
500x10=5000
Points A, B, and C are collinear. What is the slope of AB in simplest form?
Answers
The slope of the line AB in simplest form is 3/2.
What is slope?The slope is the rate of change of the y-axis with respect to the x-axis.
The equation of a line in slope-intercept form is y = mx + b, where
slope = m and y-intercept = b.
We know the greater the absolute value of a slope is the more steeper is it's graph or rate of change is large.
We also know that the slope is rise over run, rise represents the y-axis and run represents the x-axis.
From B to C rise is 3 and from B to C run is 2.
Therefore, the slope of the line AB is 3/2.
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Stephan borrowed $125 to buy an electric scooter. The function f(x) = 125 - 12.5x
can be used to represent the amount of money Stephan owes on the loan, where X is the number of weeks that Stephan pays towards the loan.
Answers
The amount that Stephen owed after 2 weeks is $100.
How to illustrate the expression?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.
In this case, Stephan borrowed $125 to buy an electric scooter and the function f(x) = 125 - 12.5x
can be used to represent the amount of money Stephan owes on the loan, where X is the number of weeks that Stephan pays towards the loan.
The amount after 2 weeks will be:
f(x) = 125 - 12.5x
= 125 - 12.5(2)
= 125 - 25
= $100
The amount is $100.
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Complete question
Stephan borrowed $125 to buy an electric scooter. The function f(x) = 125 - 12.5x
can be used to represent the amount of money Stephan owes on the loan, where X is the number of weeks that Stephan pays towards the loan. What is the amount owed after 2 weeks?
Pranv and Paul improve the yard by planting grass sod and shrubs they bought their supplies from the same store craft spent $90 on 10 feet of grass and grass sod and five shrubs paul spent $50 on 5 feet of grass sod and three shrubs find the cost of one foot of grass sod and a cost of one shrub
Answers
Answer:
The cost of one foot of grass sod is $9 and the cost of one shrub is $18.
Step-by-step explanation:
Since Pranv and Paul both bought their supplies from the same store, we can assume that they paid the same price per foot of grass sod and per shrub. From the information given, we know that Pranv spent $90 on 10 feet of grass sod and 5 shrubs, which means that he paid 90/10 = $9 per foot of grass sod and 90/5 = $18 per shrub. We also know that Paul spent $50 on 5 feet of grass sod and 3 shrubs, which means that he paid 50/5 = $10 per foot of grass sod and 50/3 = $16.67 per shrub. Since both Pranv and Paul paid the same price per foot of grass sod and per shrub, the cost of one foot of grass sod is $9 and the cost of one shrub is $18.
Find the Perimeter of the figure below, composed of a rectangle and a semicircle. Round to the nearest tenths place.
Answers
(Equivalent Algebraic Expressions MC)
Which expression is equivalent to (m−2n−3)−4?
A m^-6 n^-7
B m^8 n^12
C m^-8 n^-12
D 1/m^6 n^7
Twice w is at most 30
Answers
Answer:
2w [tex]\leq[/tex] 30
Step-by-step explanation:
Two times the value of w must be less than or equal to 30
Answer: w < = 15
Step-by-step explanation:
Our equation is
2w < = 30
Divided by 2 both sides
w < = 15
A certain arcade game gives players tickets. The table below shows the number of tickets a player gets for the number of points.
Answers
Answer: Each point appears to give the same number of tickets
9 points give 54 tickets
Step-by-step explanation:
Each point appears to give the same number of tickets
To find the number of tickets, a point gives
divide the number of tickets by the number of points.
18/3 = 6
you get six tickets per point
find the number of points that give 54 tickets by dividing 54 by 6
54/6=9
9 points give 54 tickets
Harry needs wood pieces to complete a project in woodshop class. He needs four pieces of wood that have a length of two and five eighths feet and two pieces of wood that are one and one fifth feet. What is the total amount of wood that Harry will need for the project?
twelve and nine tenths feet
three and 33 over 40 feet
three and 6 over 13 feet
two and one fifth feet
Answers
Answer: twelve and nine-tenths feet
Step-by-step explanation:
I turned the fractions into decimals cus I find that easier.
5/8 = .625 + 2 = 2.625
2.625(4) = 10.5 (multiply by 4 because it is 4 pieces)
1/5 = 0.2 + 1 = 1.2
1.2(2) = 2.4 (multiply by 2 because it is 2 pieces)
2.4 + 10.5 = 12.9
.9 can also be 9/10ths
Answer:
12 9/10
Step-by-step explanation:
The four pieces of wood: 4 x 2 5/8 = 10.5 or 10 1/2
The two peices of wood: 2 x 1 1/5 = 2.4 or 2 2/5
The total of both: 10 1/2 + 2 2/5= 12.9 or 12 9/10
for a normal distribution, assume the 'population' standard deviation is 7.7. what is the maximal margin of error associated with a 90% confidence interval for the true population mean if n
Answers
for a normal distribution, assume the 'population' standard deviation is 7.7. .645 * 7.7 / √(n) is the maximal margin of error associated with a 90% confidence interval for the true population mean if n
The margin of error is calculated as
Margin of Error = Critical Value * Standard Deviation / √(Sample Size)
= 1.645 * 7.7 / √(n)
= 1.645 * 7.7 / √(n)
The margin of error is a measure of the accuracy of an estimate based on a sample from a population. It is calculated by taking the critical value (1.645, for a 90% confidence interval) multiplied by the population standard deviation (7.7), divided by the square root of the sample size (n). The higher the sample size, the smaller the margin of error. This means that a larger sample size gives a more accurate estimate of the true population mean.
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