Find the derivative of the function with solutions.y = In( e^(3 - x^2 ) + 9 ))
Answers
Answer:
[tex]\frac{dy}{dx}=-\frac{2xe^{3-x^2}}{e^{3-x^2}+9}[/tex]Explanation:
We were given the function:
[tex]y=\ln\left(e^{3-x^2}+9\right)[/tex]We are to find the derivative of this function, we have it shown below:
[tex]\begin{gathered} y=\operatorname{\ln}(e^{3-x^{2}}+9) \\ If:y=ln(u) \\ Then:y^{\prime}=\frac{u^{\prime}}{u} \\ y^{\prime}=\frac{dy}{dy} \\ u=e^{3-x^2}+9 \\ u^{\prime}=-2xe^{3-x^2} \\ y^{\prime}=\frac{u^{\prime}}{u} \\ \Rightarrow y^{\prime}=\frac{-2xe^{3-x^2}}{e^{3-x^2}+9} \\ But:y^{\prime}=\frac{dy}{dx} \\ \frac{dy}{dx}=-\frac{2xe^{3-x^2}}{e^{3-x^2}+9} \\ \\ \therefore\frac{dy}{dx}=-\frac{2xe^{3-x^2}}{e^{3-x^2}+9} \end{gathered}[/tex]Related Questions
x 8 x 7 x 5 x 6 a planned building was going to be 100 feet long, 75 feet deep, and 30 feet high. the owner decides to increase the volume of the building by 10% without changing the dimensions of the depth and the height. what will be the new length of this building?
Answers
The new length of the building will be 110 feet.
Volume of Cuboid:
Volume of cuboid is
V = length x breadth x height cubic unit
Given,
The building was going to be 100 feet long, 75 feet deep, and 30 feet high.
Therefore, the volume will be:
= 75 × 100 × 30 ft³
= 225000 ft³
Now owner decided increase the volume of the building by 10% without changing the dimensions of the depth and the height.
There was an increase by 10%,
New volume will be,
V' = 225000 + (10% × 225000)
= 247500 ft³
Therefore, the new length will be:
as,
Volume = length x breadth x height
length = Volume/ (breadth x height)
New length will be
= 247500/(30 × 75)
= 110 feet
Thus the new length of the building will be 110 feet.
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The speeders soccer team charge $12 to watch each car at a fundraiser car wash. The team collected a total of $672 by the end of the day. How many cars did the team was?
Answers
Answer:
they washed 55 cars
Step-by-step explanation:
I did the math good luck
Write the equation of a line in slope-intercept form that goes through points (1,5) and (9, -6).
Answers
Answer:
y-21 = 4(x+9)
WILL GIVE BRAINLIEST
find all values of x for which (f∘g)(x)=(g∘f)(x).
f(x)=x/(x+2), g(x)=x^2
Answers
Step-by-step explanation:
(f○g)(x) means f(g(x))
(g○f)(x) means g(f(x))
f(g(x)) means to use the expression of g(x) as input to f(x). so, we replace all simple x in f(x) by g(x) = x².
f(g(x)) = x²/(x² + 2)
using the same principle we get for
g(f(x)) = (x/(x + 2))² = x²/(x + 2)²
now we need to solve
x²/(x² + 2) = x²/(x + 2)²
let's multiply both sides with both denominators :
x²(x + 2)² = x²(x² + 2)
x²(x² + 4x + 4) = x²(x² + 2)
so, one solution is clear : x = 0.
because then we have 0 = 0.
for x <> 0 we can divide both sides by x² and get
x² + 4x + 4 = x² + 2
4x + 4 = 2
4x = -2
x = -2/4 = -1/2
both expressions are equal for x = 0 and x = -1/2
y=-x+7
Graph it also if you can
Answers
Answer:
Hope this helps!!
The measures of the exterior angles of an octagon are x°x°, 2x°2x°, 3x°3x°, 4x°4x°, 5x°5x°, 6x°6x°, 9x°9x°, and 10x°10x°. Solve for xx.
Answers
Answer:
x=10
Step-by-step explanation:
Given: =The exterior angles of an octagon are x°,2x°,3x°,4x°,5x°,6x°,7x°,8x°.
Then, x°+2x°+3x°+4x°+5x°+6x°+7x°+8x° =360°
⇒ 36x = 360
⇒ x= 10
The point-slope form of a line that has a slope of 2/3 and passes through point (6,0) is shown?
y-0=2/3(x-6)
What is the equation in slope-intercept form?
y-2/3x-12
y-2/3x-6
y-2/3x-4
y-2/3x-8
Answers
Answer:
See below
Step-by-step explanation:
y-0=2/3(x-6) (expand L side)
What is the equation in slope-intercept form?
y = 2/3 x - 4
Write a polynomial P(x) of degree 4 and with zeros 1, 3/2, (which of multiplicity one) and 0 (of multiplicity 2).
Answers
Answer
The polynomial is
P(x) = 2x⁴ - 5x³ + 3x²
Explanation
We are told to write a polynomial of degree 4 with zeros (roots)
x = 1
x = (3/2) = 1.5
x = 0
x = 0 (multiplicity of 2 means it appears twice)
So, we can piece together the polynomial
P(x) = (x - 1) (x - 1.5) (x) (x)
We can write this as
P(x) = x² (x - 1) (x - 1.5)
= (x³ - x²) (x - 1.5)
We can multiply through by 2 to turn the 1.5 into a whole number
P(x) = (x³ - x²) (2x - 3)
= x³ (2x - 3) - x² (2x - 3)
= 2x⁴ - 3³ - 2³ + 3x²
= 2x⁴ - 5x³ + 3x²
Hope this Helps!!!
when was the temperature decreasing
Answers
Answer:
I need you to be more specific and answer options. That is the only way anyone can answer this question.
Step-by-step explanation:
Find x of the triangle
Answers
Answer:
x=65
Step-by-step explanation:
47+68+x=180
x=65
:]
Answer: 65 = x
Step-by-step explanation:
1) First find the mini triangles, left and right angles
We will be calling the left one A and the right one B.
2) Next use triangle sum to find B.
62 + 50 + b = 180
b=68
3) Use triangle sum again to find A.
53 + 80 + a = 180
a = 47
4) Use triangle sum to find the top mini angle.
47 + 68 + c = 180
c = 65
5) Since x is in the vertical angle of c, they are equal
c = x
65 = x
If the area of a square is 139cm squared, what would the length of the side be?
Answers
The length of the side is 11.79cm
How to find the area of the square?The area is the entire amount of space occupied by a flat (2-D) surface or shape of an object.
On a sheet of paper, draw a square with a pencil.
It is a two-dimensional figure.
The area of a shape on paper is the area it occupies.
Area of a square i= 139cm^2
a^2 = 139
The length of the side (a) = [tex]\sqrt{139}[/tex] = 11.79cm
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assume 11% of the population is left-handed. assume this percentage is also true for all college students. a random sample of 209 college students from a campus with 5225 students is taken and whether or not they are left-handed is recorded.
Answers
After finding the probability we find that 0.04 students are left-handed from the 209 students randomly selected from the campus.
11 % of the population is left-handed so here we have to find the probability of left-handed students if 209 random students are selected from 5225 students on campus here Favorable outcome is 209 and the total outcome is 5225, so the favorable outcome upon the total number of the outcome.
According to the probability formula :
Probability = [tex]\frac{favorable outcome}{Total number of outcome}[/tex]
Probability = 209 / 5225
After diving the above equation we find that 0.04 students are left-handed from the 209 students randomly selected from the campus.
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Can someone answer this please?
Answers
1. The cheapest meat is Ms barker free Ronge whole chicken in $6 per kilo.
2. The cost of 200 grams of honey leg ham is $3.4.
What is Division method?
Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.
For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
The cost of all meat is shown in figure.
Now,
By the figure, we get;
The cheapest meat is Ms barker free Ronge whole chicken which is in
$6 per kilo.
And, The cost of honey leg ham = $17 per kilo
Since, 1 kilograms = 1,000 grams
The cost of 1 gram of honey leg ham = $17/1000
So, The cost of 200 grams of honey leg ham = 200 × 17 / 1000
= $3.4
Thus,
1. The cheapest meat is Ms barker free Ronge whole chicken in $6 per kilo.
2. The cost of 200 grams of honey leg ham is $3.4.
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For Kimberly's P.E final she must either walk or run at least 5 miles this week. She knows it would take her 15 minutes to run a mile and 40 minutes to walk a mile, Kimberly only has 6 hours in which she must accomplish this final. Write an equation that represents Kimberly's P.E final for both walking and running. Define all variables
Answers
The equation for Kilberly's running or walking will be R+4w ≤ 6.
What is inequality?When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relationship between variables and the numbers.
Given that For Kimberly's P.E final she must either walk or run at least 5 miles this week. She knows it would take her 15 minutes to run a mile and 40 minutes to walk a mile, Kimberly only has 6 hours in which she must accomplish this final.
Let the running is represented by 'R' and walking by 'w". The equation will be written as below:-
R + 4W ≤ 6
Put the running and walking times in the equation above.
15 + ( 4 x 40 ) ≤ 6
175 minute ≤ 6 x 60
175 minutes ≤ 360 minutes.
Therefore, Kimberly covers the distance in less than 6 hours.
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among all rectangles that have a perimeter of 48, find the dimensions of the one whose area is largest. write your answers as fractions reduced to lowest terms.
Answers
among all rectangles that have a perimeter of 48 Then the dimensions of the one whose area is largest is 12 by 12
The formula for calculating the perimeter of a rectangle is expressed as:
P = 2(L + W)
L is the length of the rectangle
W is the width
Given that the perimeter is 156, hence;
2(L + W) = 48
2L + 2W = 48
L + W = 24
W = 24 - L
The area of the rectangle is expressed as:
A = LW
A = L(24-L)
A = 24L - L^2
To get the dimensions of the one whose area is largest, dA/dL = 0
dA/dL = 24 - 2L
0 = 24 - 2L
2L = 24
L = 24/2
L = 12
Recall that 2(L+W) = 48
2(12 + W) = 48
12 + W = 24
W = 24 - 12
W = 12
Hence the dimensions of the one whose area is largest is 12 by 12
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. let ???? be a discrete random variable that is uniformly distributed over the set of integers in the range [????, ????], where ???? and ???? are integers with ???? < 0 < ????. find the pmf of the random variables max(0,????) and min(0,????).
Answers
Filling in the blanks, I assume you're talking about a random variable [tex]X[/tex] distributed uniformly over the integers [tex]a\le x\le b[/tex]. Let both [tex]a,b>0[/tex] so we can write the support of [tex]X[/tex] as the set
[tex]S = \{-a, -a+1, -a+2, \ldots, -1, 0, 1, \ldots, b-2, b-1, b\}[/tex]
Note that [tex]|S| = a+b+1[/tex], so the PMF of [tex]X[/tex] is
[tex]\mathrm{Pr}(X=x) = \begin{cases}\frac1{a+b+1} & \text{if } x\in S \\ 0 & \text{otherwise}\end{cases}[/tex]
Let [tex]Y=\max\{0,X\}[/tex]. Then
[tex]Y = \max\{0,X\} = \begin{cases}0 & \text{if } X\le0 \\ X & \text{if } X>0 \end{cases}[/tex]
which tells us
[tex]\displaystyle \mathrm{Pr}(Y=0) = \mathrm{Pr}(X\le0) = \sum_{x=-a}^0 \mathrm{Pr}(X=x) = \frac{a+1}{a+b+1}[/tex]
and
[tex]\displaystyle \mathrm{Pr}(Y\neq0) = \mathrm{Pr}(X>0) = \sum_{x=1}^b \mathrm{Pr}(X=x) = \frac b{a+b+1}[/tex]
Hence the PMF of [tex]Y[/tex] is
[tex]\mathrm{Pr}(Y=y) = \begin{cases}\frac{a+1}{a+b+1} & \text{if } y=0 \\\\ \frac b{a+b+1} & \text{otherwise}\end{cases}[/tex]
Let [tex]Z=\min\{0,X\}[/tex]. The same reasoning applies, but this time
[tex]Z = \min\{0,X\} = \begin{cases} 0 & \text{if } X \ge 0 \\ X & \text{if } X < 0 \end{cases}[/tex]
Now
[tex]\displaystyle \mathrm{Pr}(Z=0) = \mathrm{Pr}(X\ge0) = \sum_{x=0}^b \mathrm{Pr}(X=x) = \frac{b+1}{a+b+1}[/tex]
and
[tex]\displaystyle \mathrm{Pr}(Z\neq0) = \mathrm{Pr}(X<0) = \sum_{x=-a}^{-1} \mathrm{Pr}(X=x) = \frac a{a+b+1}[/tex]
so that
[tex]\mathrm{Pr}(Z=z) = \begin{cases}\frac{b+1}{a+b+1} &\text{if }z=0 \\\\ \frac a{a+b+1} & \text{otherwise}\end{cases}[/tex]
the population of rabbits on an island is growing exponential in the year 2008, the population of rabbits was 7100 and by the year 2013 the population had grown to 8900 . Predict the population of rabbits by the year 2023 to the nearest whole number
Answers
The population of rabbits by the year 2023 is 13985.
What will the population be?We have to use the following exponential function. This will be:
y = a b^t
In 2008 means, t=0
So we have 7100 = a b^0
a = 7100
y = 7100b^t
In 2013 means t = 2013-2008 =5
8900 = 7100 b⁵
b⁵ = 89/71
b = 1.046
So the equation will be
y = 7100 (1.046)^t
For 2023, t=2023-2008= 15
y = 7100(1.046)¹⁵
= 13985
The population is 13985.
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Mike and Raymond each read the same book.Mike reads 182 pages in 7 hours.Raymond reads 168 pages in 6 hours. Based on the rates which statement is true? select TWO correct choices
A.Mike reads faster than Raymond.
B.Raymond reads faster than mike.
C.Mike reads 2 more pages than raymond in one hour.
D.Raymons reads 52 pages in 3 hours.
E.Mike can read 13 pages in half an hour.
Answers
Answer:
B and c
Step-by-step explanation:
182/7=26
168/6=28
10-2y=46 solve for y
Answers
Answer:
-18
Step-by-step explanation:
first subtract ten from both sides now you're left with -2y=36 ,lastly divide both sides by -2 and you're left with y= -18
The price of an item yesterday was %130.Today, the price rose to $169 . Find the percentage increase.
Answers
The percentage increase when the price of an item increased is 30%.
How to calculate the percentage?From the information, the price of an item yesterday was $130 and today, the price rose to $169.
The increase in the price will be:
= $169 - $130
= $39
Therefore, the percentage increase will be:
= Increase in price / Original price × 100
= 39 / 130 × 100
= 30%
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Which inequality in vertex form represents the region less than the quadratic function with vertex (-2, 2) and
includes the point (-4, 14) on the boundary?
Answers
Answer:
(a) y < 3(x +2)² +2
Step-by-step explanation:
You want to know the inequality representing the region less than the quadratic with vertex (-2, 2) and containing the point (-4, 14).
Vertex formThe vertex form equation for a quadratic with vertex (h, k) and some scale factor 'a' is ...
y = a(x -h)² +k
For the given vertex (-2, 2), the boundary line equation is ...
y = a(x -(-2))² +2 = a(x +2)² +2
Scale factorThe value of 'a' is positive when the curve opens upward.
Here, the point (-4, 14) has a y-value greater than that of the vertex, so we know the curve opens upward (a > 0).
The only reasonable answer choice is ...
y < 3(x +2)² +2
The distance between Q(-1, a) and P(3, -2) is 4√5. Find all possible values of a
Answers
The numerical values of a in the points Q(-1, a) and P(3, -2) with a distance of 4√5 are 6 and -10.
What is the numerical value of a?The distance formula used in finding the distance between two points is expressed as;
D = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² )
Given the data in the question;
Point Q( -1, a )
x₁ = -1y₁ = aPoint P( 3, -2 )
x₂ = 3y₂ = -2Distance D = 4√5To find the numerical value of a, plug the given coordinates into the distance formula and simplify.
D = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² )
4√5 = √( ( 3 - (-1) )² + ( -2 - a )² )
4√5 = √( ( 3 - (-1) )² + ( -2 - a )² )
Square both sides
( 4√5 )² = ( 3 - (-1) )² + ( -2 - a )²
( 4√5 )² = ( 3 + 1 )² + ( -2 - a )²
( 4√5 )² = ( 4 )² + ( -2 - a )²
80 = 16 + ( -2 - a )²
80 - 16 = ( -2 - a )²
64 = ( -2 - a )²
( -2 - a )² = 64
Expand the parenthesis
( -2 - a )( -2 - a ) = 64
a² + 4a + 4 = 64
a² + 4a + 4 - 64 = 0
a² + 4a - 60 = 0
solve for a
( a - 6 )( a + 10 ) = 0
a - 6 = 0, a + 10 = 0
a = 6, a = -10
Therefore, the values of a are 6 and -10.
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(2x^2+4x-7)(3x-1) use a table
Answers
The solution for the given binomial multiplication is 6x³ + 10x² - 17x - 7
Given,
The binomials; (2x² + 4x - 7) (3x - 1)
We can use FOIL method to solve this;
FOIL method;
Binomials are multiplied using the FOIL Method. An acronym is FOIL FOIL. First, Outside, Inside, and Last are the letters that stand for the order of multiplying terms. To get your answer, multiply the first term, then the outside term, then the inside term, then the last term, and then combine terms that are similar.
Here,
(2x² + 4x - 7) (3x - 1)
= (3x × 2x²) + (3x × 4x) - (3x × 7) - 2x² + 4x - 7
= 6x³ + 12x² - 21x - 2x² + 4x - 7
= 6x³ + 10x² - 17x - 7
That is,
The solution for the given binomial multiplication is 6x³ + 10x² - 17x - 7
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"Complete the table" can someone help on thi thank you!
Answers
Answer:
2000 pounds is 1 ton
6 tons is 12,000
7 tons is 14,000
16,000 pounds is 8 tons
f(x) = −3|x −1| + 4
Answers
Answer:
Find the Inverse f(x)=3x-1/4. f(x)=3x−14 f ( x ) = 3 x - 1 4. Step 1. Write f(x)=3x−14 f ( x ) = 3 x - 1 4 as an equation. y=3x−14 y = 3 x - 1 4.
Step-by-step explanation:
Calculate the number of students per teacher at West Elementary school
Answers
Ok, so
We know that, at West Elementary school, there are 438 students and 22 full-time teachers. We want to know the number of students per teacher. This is:
[tex]\frac{438\text{students}}{22\text{teachers}}=19.91\frac{students}{teacher}[/tex]On a standardized exam, the scores are normally distributed with a mean of27 and a standard deviation of 4. Find the Z-score of a person who scored 17on the exam.
Answers
mean = 27
standard deviation = 4
n = 17
z = ?
[tex]\begin{gathered} \text{ z = }\frac{X\text{ - }\mu}{\sigma} \\ \text{ z = }\frac{27\text{ - 17}}{4} \\ \text{ z = }\frac{10}{4} \\ \text{ z = 2.5} \end{gathered}[/tex]Result :
z = 2.5
-24 = -12v solve for v and simplify as much as posible
Answers
Answer:
divide both sides by the coefficient of v which is 12
-24/-12=-12v/-12
-2=v
17x-5
16x + 3 what is x
Answers
Answer:
x = 8
Step-by-step explanation:
17x-5 = 16x + 3
Step 1: Subtract 16x from both sides.
17x−5−16x=16x+3−16x
x−5=3
Step 2: Add 5 to both sides.
x−5+5=3+5
x=8
The solution to the equation is x = 8.
To solve the equation 17x - 5 = 16x + 3 and find the value of x, we can follow these steps:
Start by simplifying both sides of the equation by combining like terms. Add 5 to both sides to move the constant term to the right side of the equation:
17x - 5 + 5 = 16x + 3 + 5
17x = 16x + 8
Next, we want to isolate the x term on one side of the equation.
Subtract 16x from both sides:
17x - 16x = 16x - 16x + 8
x = 8
Therefore, the solution to the equation is x = 8.
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How can you determine which of the numbers below is greatest 13/20, 5/8, 3/5, 3/10
Answers
Answer:
13/20 is the greatest because it is equal to 65% of 100%.
Step-by-step explanation:
5/8 = to 12.5x5=62.5%. 3/5= 20x3=60%. 3/10 = 10x3=30%. So 13/20 is the greatest.