The slope of the curve y=x^2-e^-x at its point of inflection is ?
Answers
the slope of the curve\(y = x^2 - e^(-x)\)at its point of inflection is 2 - 2ln(2).
To find the slope of the curve\(y = x^2 - e^(-x)\) at its point of inflection, we need to take the second derivative of the function with respect to x and evaluate it at the x-coordinate of the inflection point.
The first derivative of the function is:
\(y' = 2x + e^(-x)\)
The second derivative is:
\(y'' = 2 - e^(-x)\)
The inflection point occurs where the concavity of the curve changes, which means where the second derivative is equal to zero or undefined. In this case, the second deriative is defined for all real numbers, so the inflection point occurs where:
\(2 - e^(-x) = 0\)
Solving for x, we get:
\(e^(-x) = 2\)
Taking the natural logarithm of both sides, we get:
ln\((e^(-x)) = ln(2)\)
-x = ln(2)
x = -ln(2)
Therefore, the inflection point occurs at (-ln(2), f(-ln(2))), where f(x) = x^2 - e^(-x).
Now, we can find the slope of the curve at this point by plugging in x = -ln(2) into the first derivative:
\(y' = 2x + e^(-x)y'(-ln(2)) = 2(-ln(2)) + e^(ln(2))y'(-ln(2)) = -2ln(2) + 2y'(-ln(2)) = 2 - 2ln(2)\)
Therefore, the slope of the curve \(y = x^2 - e^(-x)\)at its point of inflection is 2 - 2ln(2).
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Related Questions
What is the line’s slope?
Answers
0
Because the line isn't increasing or decreasing, it's just flat, so it's 0.
Answer:
Step-by-step explanation:
It doesn't matter what value x has. y is always 2. That means that the slope has disappeared.
The slope must be zero.
Find the output, y, when the input, x, is -9.
y =
Answers
Answer:
when x=-9, y=1
Step-by-step explanation:
the graph shows when the x is at -9, the y is at 1
tickets to a movie cost $10.50 for adults and $7.25 for students. you and a few friends purchased 8 tickets for $61.25. how many adult tickets and student tickets were purchased?
Answers
Answer:
1 adult ticket and 7 student tickets were purchased
Step-by-step explanation:
let a represent number of adult tickets purchased and s the number of student tickets purchased, then
a + s = 8 ( subtract s from both sides )
a = 8 - s → (1) ← based on total tickets purchased
10.5a + 7.25s = 61.25 → (2) ← based on cost of tickets
substitute a = 8 - s into (2)
10.5(8 - s) + 7.25s = 61.25
84 - 10.5s + 7.25s = 61.25
84 - 3.25s = 61.25 ( subtract 84 from both sides )
- 3.25s = - 22.75 ( divide both sides by - 3.25 )
s = 7
substitute s = 7 into (1)
a = 8 - 7 = 1
that is 1 adult ticket and 7 student tickets were purchased
40. Noor is packing chocolates into boxes. The boxes come in small, medium and large sizes. A large box holds twice as many chocolates as a medium box and three times as many chocolates as a small box. Noor fills three times as many small boxes as medium boxes and twice as many medium boxes as large boxes. Altogether she packs 1296 chocolates. In total, how many chocolates does she pack into the small boxes.
Answers
The number of chocolate which goes into the small boxes is 100 chocolate
EquationChocolate in small boxes = xChocolate in medium boxes = 3xChocolate in large boxes = 3x + 2(3x)= 3x + 6x
= 9x
Total chocolate = 1296x + 3x + 9x = 1296
13x = 1296
x = 1296/13
x = 99.6923076923076
Approximately,
x = 100 boxes
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what's the estimate of 6.48 + 9.34 and what's the estimate 15.71 + 12.2
Answers
Answer:
Your Estimated Equations and Answers: 6+9= 15 ; 16+12 = 28
Step-by-step explanation:
Estimating can be equivalent to rounding. This is because you're trying to find an approximate number or sum.
6.48 + 9.34 is your first question.
You should round it to the nearest whole number.
6.48 ~ 6 and 9.34 ~ 9
*Rounding rules applied here*
(~ this sign is the approximate or rounded to symbol)
Now, do 6+9 =
6+9= 15
______________________________________________
15.71 + 12.2 is your next question.
Same as last, round to the nearest whole number.
15.71 ~ 16 and 12.2 ~ 12
Now, do 16+12
16+12 = 28
Estimate a 15% tip on a dinner bill of $49.35 by first rounding the bill amount to the nearest ten dollars.
Answers
9514 1404 393
Answer:
$7.50
Step-by-step explanation:
Rounded to the nearest $10, the $49.35 bill becomes $50.
We can find 10% of that amount by moving the decimal point to the left. 10% of $50 is $5.00.
Then 5% of $50 is half of 10%, so is $5/2 = $2.50.
The estimated tip of 15% is the sum of 10% and 5% of the bill, so is ...
15%($50) = 10%($50) +5%($50) = $5.00 +2.50 = $7.50
The estimated 15% tip is $7.50.
21. Write the equation of the line (in point-slope form) passing through the points (2,7) and (-1,8).
Answers
The equation of the line (in point-slope form) passing through the points (2,7) and (-1,8) is y - 7 = -1/3(x - 2).
What is the point-slope form?Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
Where:
m represents the slope.x and y are the points.At point (2, 7), an equation of this line can be calculated by using the point-slope form:
y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
y - 7 = (8 - 7)/(-1 - 2)(x - 2)
y - 7 = -1/3(x - 2).
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An examination paper has 150 multiple-choice questions of one mark each, with each question having four choices. Each incorrect answer fetches -0.25 mark. Suppose 1000 students choose all their answers randomly with uniform probability. The sum total of the expected marks obtained by all these students is?
Answers
The sum of expected marks is given as follows:
9375.
How to obtain the expected marks?Each question has four choices, hence the probability of choosing the correct choice is given as follows:
p = 1/4 = 0.25.
Then the expected number of correct answers is given as follows:
E(X) = 0.25 x 150
E(X) = 37.5.
Then the expected grade for a single student is given as follows:
37.5 - 0.25(150 - 37.5) = 9.375.
The expected sum for the 1000 students is then given as follows:
1000 x 9.375 = 9375.
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What are the coordinates of A'?
Answers
Answer:
(6,-2)
Step-by-step explanation:
The picture as shown, A would be flipped across the line which leaves it landing on (6,-2)
Hope this helped you :)
A piece of furniture cost $450.12. If the sales tax is 7% what is the amount of sales tax for the piece of furniture? Round your answer to the nearest hundredth
Answers
Answer:
Sales tax: $31.51
■ Cost/Price before ST: $450.12
■ Total Cost/Price including ST: $481.63
Step-by-step explanation:
it is what it is.
Round 478.54 to nearest tenth
Answers
Answer:
478.5
Step-by-step explanation:
The 4 is less than 5 so it rounds down.
Answer:
478.5
Step-by-step explanation:
the weight of an apple is 150g, rounded to the nearest 5g. What is the lower bound of the weight of the apple?
What is the upper bound of the weight of the apple?
Answers
Answer:
1 answer
Answer:lower bound = 147.5gupper bound = 152.5gStep-by-step explanation:if you were rounding a single digit number to the nearest 5, ...
Step-by-step explanation:
State whether the decay is linear or exponential, and answer the associated question. The value of a car is decreasing by 9% per year. If the car is worth $11 comma 000 today, what will it be worth in two years? g
Answers
Answer:
ExponentialA(2)=$9109.10Step-by-step explanation:
Since the value of the car decreases by a common factor each year, the decay is exponential.
An exponential decay function is of the form
\(A(t)=A_0(1-r)^t$ where:\\Initial Value, A_0=\$11,000\\$Decay Factor, r=9%=0.09\)
Therefore, the function modeling the car's decay is:
\(A(t)=11000(1-0.09)^t\)
We want to determine the car's value in two years.
When t=2
\(A(2)=11000(1-0.09)^2\\A(2)=\$9109.10\)
The value of the car in 2 years will be A(t)=$9109.10
Final value of the car after 2 years will be $9109.10
Value of the car decay by 9%.
Since, 9% is a common factor by which the value of car is decreasing,
Therefore, decay will be exponential.
Expression for the exponential decay is given by,
\(P=P_0(1-\frac{r}{100} )^t\)
Here, \(P=\) Final price
\(P_0=\) Initial price
\(r=\) Rate of decay
\(t=\) time
If initial price of the car \(P_0=11000\), rate of decay \(r=0.09\) and \(t=\) Number of years
By substituting the values in the expression,
P = \(11000(1-0.09)^2\)
= 11000(0.91)²
= $9109.10
Therefore, final value of the car after 2 years will be $9109.10
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Expand and simplify (2x - 1)(x + 3)(x - 5)
Answers
Answer:
2x^3-5x^2-28x+15 -------------------------expanded
2x^3-5x^2-28x+15--------------------simplified
Step-by-step explanation:
\left(2x-1\right)\left(x+3\right)\left(x-5\right)
=2x^2x+2x^2\left(-5\right)+5xx+5x\left(-5\right)-3x-3\left(-5\right)
simplyfied
\left(2x^2+5x-3\right)\left(x-5\right)
=2x^2x+2x^2\left(-5\right)+5xx+5x\left(-5\right)-3x-3\left(-5\right)
=2x^3-5x^2-28x+15
In the figure below, find the exact value of x. (Do not approximate your answer.)
Answers
Triangle ADC also has a right angle at D, making it a right-angled triangle.
The exact value of x be 2.25.
What is meant by "Pythagoras Theorem"?The hypotenuse's square is equal to the sum of its two other side squares of a right-angled triangle, according to the Pythagoras theorem.
Triangle ADB exists even a right-angled triangle with right-angle at D.
Therefore, Base of Triangle ADB = BD = 4,
Height of Triangle ADB = AD = 3,
Hypotenuse of Triangle ADB = AB
Using the Pythagoras Theorem, we get,
\($\left[(A D)^2+(B D)^2\right]=(A B)^2$\)
substitute the values in the above equation, we get
or,\($(A B)^2=\left[(3)^2+(4)^2\right]$\)
simplifying the equation, we get
or, \($(A B)^2=[9+16]$\)
or, \($(A B)^2=25$\)
or, \($\sqrt{(A B)^2}=\sqrt{25}$\)
or, AB = 25
Triangle ADC is also a right-angled triangle with right-angle at D.
Therefore, Base of Triangle ADC = DC = x
Height of Triangle ADC = AD = 3,
And, Hypotenuse of Triangle ADC = AC
Using the Pythagoras Theorem, we get,
\(& {\left[(D C)^2+(A D)^2\right]=(A C)^2} \\\)
simplifying the equation, we get
\(& \text { or },(A C)^2=\left[(3)^2+(x)^2\right] \\\)
\(& \text { or },(A C)^2=\left[9+x^2\right]\)
Triangle ABC is also a right-angled triangle with right-angle at A. Therefore, Base of Triangle ABC = AC,
Height of Triangle ABC = AB = 5,
And, Hypotenuse of Triangle ABC = BC = (4 + x)
Using the Pythagoras Theorem, we get,
\(& {\left[(A C)^2+(A B)^2\right]=(B C)^2} \\\)
\(& \text { or, }(B C)^2=\left[(A C)^2+(A B)^2\right] \\\)
substitute the values in the above equation, we get
\(& \text { or, }(4+x)^2=\left[\left(9+x^2\right)+(5)^2\right] \\\)
simplifying the equation, we get
\(& \text { or, }\left[4^2+(2 \times 4 \times x)+x^2\right]=\left[9+x^2+25\right] \\\)
\(& \text { or, }\left[16+8 x+x^2\right]=\left[(9+25)+x^2\right] \\\)
\(& \text { or, }\left[16+8 x+x^2\right]=\left[34+x^2\right] \\\)
\(& \text { or, }\left[16+8 x+x^2\right]-\left[34+x^2\right]=0 \\\)
\(& \text { or, },(16-34)+8 x+\left(x^2-x^2\right)=0 \\\)
8x - 18 = 0
8x = 18
\(& \text { or, } x=\frac{18}{8} \\\)
\(& \text { or, } x=\frac{9 \times 2}{4 \times 2} \\\)
\(& \text { or, } x=\frac{9}{4} \\\)
Therefore, the value of x be 2.25.
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What is this? I can't figure it out and forgot how to do it
Answers
answer
x =21.24
Step-by-step explanation:
180 (n-2)
7 sides
180 * 5 = 900
add up all the sides and = them to 900
25x + 369 = 900
25x = 531
x = 21.24 = answer
In a class in which the final course grade depends entirely on the average of four equally weighted 100-point tests, Brad has scored 82, 94, and 92 on the first three. What range of scores on the fourth test will give Brad a B for the semester (an average between 80 and 89, inclusive)? Assume that all test scores have a non-negative value.
Express your answer in interval notation.
Answers
Answer:
70 ≤ (94 + 89 + 78 + s)/4 ≤ 79
280 ≤ 261 + s ≤ 316
19 ≤ s ≤ 55
Step-by-step explanation:
shareholders. Calculate the amount of dividend r of dividend received by Bishwant. Curriculum Development Centre. Sanothimi. Bhaktanur 65 Vedanta Excel in Mathematics - Booeceived by Mrs. Rai. b) A Business Company sold 2,500 shares at Rs 1,200 per share. Bishwant bought 450 shares. If the company earned a net profit of Rs 39,00.000 in a year and it announced to distribute 18% dividend from the net profit to its shareholders, find the amount
Answers
3900000×18% = 702000
702000÷2500 = 280.8 per share dividend
450×280.8 = 126360
the difference between a two-digit number and that number reversed is 18. What could that number be. List all possibility's.
Answers
9514 1404 393
Answer:
20, 31, 42, 53, 64, 75, 86, 97
Step-by-step explanation:
The difference of 18 means the difference of digits is 18/9 = 2. Since the number you seek is the larger number, the 10s digit will be 2 more than the 1s digit. Possible numbers are ...
20, 31, 42, 53, 64, 75, 86, 97
_____
If t and o are the tens and ones digits respectively, the relation you seek is ...
(10t +o) -(10o +t) = 18
9(t -o) = 18
t - o = 2 . . . . as above
Since both t and o must be single digits, the minimum will be t=2, o=0, and the maximum will be t=9, o=7.
Answer:
10a+b=10b+a-18
9a+9b = -18
9(a+b) = -18
a+b = 18/9
a + b =2
Step-by-step explanation:
\(y=\frac{3}{2} x^{3}\)
Answers
Answer:
Its should be 2/3
Step-by-step explanation:
( PLEASE I NEED HELP AASP!!)
Answers
Answer:
2/3 * 660
Step-by-step explanation:
If we convert 65% to a decimal, we get 0.65.
First, it will helpful to find exactly what is 65% of 668:
0.65 * 668 = 434.2 and thus 65% of 668 is exactly 434.2.
Similarly, if you convert 2/3 to a decimal, you get 0.66 repeating.
2/3 * 660 = 440 which is only 10.2 units larger than 434.2. Thus, 2/3 * 660 is the most accurate estimate of 65% of 668.
MATH PLEASE HELP
Paul wants to put a fence around his vegetable garden in the backyard. The price of fencing is $1.65 per linear foot. Given a diagram of his vegetable garden below, how much will it cost him for the fencing?
Answers
Answer:
total perimeter =14+23+9+11+23-11=69cm×1/30=2.3ft
total cost =perimeter ×rate=2.3×1.65=$3.795
Answer:
The perimeter of a rectangle is 2L + 2W, where L and W are the length and width, respectively. The dimensions of the garden are given, 6 x 12 ft.
Step-by-step explanation:
hope it help :):):):):):)
3. What is the value of |—9|?
A. 18
B. 9
C. 0
D. -9
Answers
Answer:
B) 9
Step-by-step explanation:
The answer s 9 because the absolute value symbols in the question mean the distance away from 0. In this case, -9 is 9 away from 0 so the answer is 9.
hope this helped!
Which triangle is congruent to KLM?
Answers
On of the triangles will be surely congruent to KLM. Hope you got it lol
A six sided die is rolled 60 times and the die landed on the number five a total of 12 times. What is the EMPIRICAL probability that the die should land on 5
Answers
Answer:
1/5
Step-by-step explanation: 60/12+48-53+5
The empirical probability that the die should land on five is 1/5.
What is probability?Probability is the chance of occurrence of a certain event out of the total no. of events that can occur in a given context.
We know that empirical probability is a type when the outcome of the next event depends upon the occurrence of the previous events.
Given A six-sided die is rolled 60 times and the die landed on the number five a total of 12 times.
Here no. of sample space N(S) = 60 and N(5) = 12.
∴ The probability of occurrence of number five(5) is = N(5)/N(S) = 12/60.
= 1/5.
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Jerome hiked three-fourths of a mile in two-thirds of an hour. What was his hiking speed in miles per hour? Show all work.
Answers
Answer:
1.125 or 11/8
Step-by-step explanation:
3/4÷2/3=1.125
= 11/8
For the figure shown on the right find M 1
Answers
Using the sum of the internal angles of a triangle and supplementary angles, it is found that the measure of angle 1 is of 121º.
What is the sum of the internal angles of a triangle?The sum of the three internal angles of a triangle is of 180º.
Hence, the measure of the remaining interior angle is given by:
60º + 61º + x = 180º
x = 59º.
What are supplementary angles?
Two angles are supplementary if the sum of their measures is of 180º.
An interior angle is supplementary with it's respective exterior angle, hence:
m<1 + 59º = 180º
m<1 = 121º.
The measure of angle 1 is of 121º.
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(3.76x 10-8 )-(2.94 x 10-8)
Write your answer in scientific notation
Answers
At a workshop , each of the 100 participants hugs each other participants once. Find the total number of hugs?
Answers
Answer:
10000
Step-by-step explanation:
100 hugs x 100 hugs
= 10,000 hugs.
CAN SOMEONE PLS HELP ME I WILL MAKE BRAINLIEST PLSSS
Answers
Answer:
a) 300 miles
b) 2pm}
That is all I can help you :(
Step-by-step explanation:
8am + 6hrs =14hrs =2pm