Differentiate. y = (x2 - 2x+8)e^x A. (x^2 + 4x + 6)e ^x B. (x^3/3 + 6x +8)e^x C. (2x - 2)e^x D. (x^2 + 6)e^x
Answers
To differentiate the function `y = (x^2 - 2x + 8)e^x`, we use the product rule. The product rule states that the derivative of a product of two functions u(x) and v(x) is given by `d/dx(uv) = u(dv/dx) + v(du/dx)`.
Let's apply this to `y = (x^2 - 2x + 8)e^x`.
First, we let `u(x) = x^2 - 2x + 8` and `v(x) = e^x`.
Then, we find `du/dx` and `dv/dx` using the power rule and the derivative of `e^x`, respectively. `u(x) = x^2 - 2x + 8` `⇒` `du/dx = 2x - 2``v(x) = e^x` `⇒` `dv/dx = e^x`.
Using the product rule, we have: `y = u(x)v(x)` `⇒` `dy/dx = u(x)(dv/dx) + v(x)(du/dx)`.
Substituting `u(x)`, `v(x)`, `du/dx`, and `dv/dx`, we get:`dy/dx = (x^2 - 2x + 8)(e^x) + (e^x)(2x - 2)`.
Simplifying, we get:`dy/dx = (x^2 + 4x + 6)e^x`.
Therefore, the correct answer is A. `(x^2 + 4x + 6)e^x`.
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Related Questions
What is the slope of a line perpendicular to the line y = -1/4x − 1?
Answers
Answer:
4
Step-by-step explanation:
The slope of a line that is perpendicular is the negative inverse of the original. The slope of the given line is -1/4. This means that the slope of the perpendicular line will be 4.
The slope of a line perpendicular to the line; y = -1/4x -1 is:. 4
The line y = -1/4x − 1 takes the slope-intercept form of a straight line; y = mx + c.
In essence, the slope of the line y = -1/4x − 1 is;
m1 = -1/4Also, the slope of two perpendicular lines are related as follows;
m1m2 = -1The slope of the line perpendicular to line y = -1/4x − 1 is therefore;
m2 = -1/(-1/4)m2 = 4.In essence, the slope of a line perpendicular to the line; y = -1/4x -1 is:. 4.
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Shandra drove 220 miles in 5 hours. if she continued at the same rate, how long would it take to travel 352 miles?
Answers
Answer:
8 Hours
Step-by-step explanation:
We know she travels 220 miles in 5 hours, so lets create an equation with a ratio which finds the miles she drives in a single hour, multiply that by x, and then set it equal to 352.
\(\frac{220}{5}x=352\)
Multiply both sides by 5
\(220x=1760\)
Divide both sides by 220
\(x=8\)
Therefore it would take 8 hours.
8 Hours long would it take to travel 352 miles,
What is speed?The distance that an object travels in relation to the amount of time it takes to do so can be used to define speed. In other words, it is a measurement of an object's motion's speed without direction Velocities are what we get when speed and direction are combined. The SI unit system is most frequently used to express speed units. In that system, since distance is measured in metres and time is measured in seconds, speed is expressed in metres per second, or m/s. Three components make up the speed formula: distance, time, and speed.
We know she travels 220 miles in 5 hours, so lets create an equation with a ratio which finds the miles she drives in a single hour, multiply that by x, and then set it equal to 352.
Multiply both sides by 5
Divide both sides by 220
Hence, it would take 8 hours.
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How do transformations relate to shapes?
Answers
Answer: A non-rigid transformation can change the size or shape, or both size and shape, of the pre image. Two transformations, dilation and shear, are non-rigid. The image resulting from the transformation will change its size, its shape, or both.
Step-by-step explanation:
Can someone please help me with this math problem please:):)
Answers
Answer:
y = 126° + 29° = 155°
Step-by-step explanation:
I think this may be a solution:
126°+29°=155°
So, y=155°
tuition at FSU used to cost $85/credit hour. Four years later it is $147/credit hour. What is the percent change?
Answers
The percent change in tuition at FSU from $85/credit hour to $147/credit hour is approximately 72.94%.
To calculate the percent change, you can use the formula:
Percent Change = [(New Value - Old Value) / Old Value] × 100
In this case, the old value is $85/credit hour and the new value is $147/credit hour.
Percent Change = [($147 - $85) / $85] × 100 = ($62 / $85) × 100 ≈ 72.94%
The tuition at FSU has increased by approximately 72.94% over the four-year period.
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pls help with this question
Answers
Answer:
x<56
Step-by-step explanation:
Since the dot over 56 isn't filled in, the inequality doesn't include 56 (so we'll use < or > not \(\leq\) or \(\geq\))
Now, let's look at the direction of the shading: is it going to the left of 56 or to the right?
This shading is to the left of 56, which indicates that it's all of the numbers less than 56.
As said above, the inequality doesn't include 56
therefore, it will be x<56 (x is less than 56, and 56 is not included)
hope this helps!
Answer:
x<56
Step-by-step explanation:
First off look at the number the dot is on.
Its at 56.
So next we see if the dot is filled in or not.
If the dot is filled in, then its either less than equal to or greater than equal to
If the dot is empty, then its less than or greater than
The dot is not filled in
So next see which way the line is going
The line is going left, which means that the number is getting smaller
Make the equation
start with x
x
The sign will be < because x has to be less than 56.
x < 56
An easy trick to remember which way the sign goes in these types of questions [not in all cases though] is look which way the line is going.
Think of the signs as arrows
If you have < then the line goes <-- left
If you have > then the line goes --> right
If you need further assistance, don't be afraid to reach out. I hope this helps!
Lydia is deciding between two different movie streaming sites to subscribe to. Plan A costs $5 per month plus $2.50 per movie watched. Plan B costs $24 per month plus $1.50 per movie watched. Let A represent the monthly cost of Plan A if Lydia watches : per month, and let B represent the monthly cost of Plan B if Lydia watches z movies per month. Write an equation for each situation, in terms of x, and determine which plan would be cheaper if Lydia plans on watching 21 movies each BE - iss cheaper than when watching 21 movies.
Answers
I set the equations up like this :
5+2.50x=
24+1.50x=
Only because thats how many movies she plans on watching.
5+2.50(21)=57.50
24+1.50(21)=55.50
Simplify:1/6x+42+2/5x-8/3x-19
Answers
Answer:
C; -21/10X + 23
Step-by-step explanation:
Combine like terms and simplify
O is the center of a circle. The radius of the circle is 26cm. The distance from O to the mid-point of chord AB is 24cm. Work out the length of chord AB :)
(MARKED BRAINLIESTS)
Answers
Answer: 20 cm
Step-by-step explanation:
Lucy has $7 less than Kristine and $5 more than Nina together,the three have $35 how much does Lucy have?
Answers
Lucy has $7 less than Kristine and $5 more than Nina together, the three have $35. Lucy has $11.
Let's denote the amount of money that Kristine has as K, the amount of money that Lucy has as L, and the amount of money that Nina has as N.
According to the given information, we can form two equations:
Lucy has $7 less than Kristine: L = K - 7
Lucy has $5 more than Nina: L = N + 5
We also know that the three of them have a total of $35: K + L + N = 35
We can solve this system of equations to find the values of K, L, and N.
Substituting equation 1 into equation 3, we get:
K + (K - 7) + N = 35
2K - 7 + N = 35
Substituting equation 2 into the above equation, we get:
2K - 7 + (L - 5) = 35
2K + L - 12 = 35
Since Lucy has $7 less than Kristine (equation 1), we can substitute K - 7 for L in the above equation:
2K + (K - 7) - 12 = 35
3K - 19 = 35
Adding 19 to both sides:
3K = 54
Dividing both sides by 3:
K = 18
Now we can substitute the value of K into equation 1 to find L:
L = K - 7
L = 18 - 7
L = 11
Finally, we can find the value of N by substituting the values of K and L into equation 3:
K + L + N = 35
18 + 11 + N = 35
N = 35 - 18 - 11
N = 6
Therefore, Lucy has $11.
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3. A phone company set the following rate schedule for an m-minute
call from any of its pay phones.
c(m) =
=
0.70
0.70+ 0.24(m - 6)
0.70+ 0.24([m-6] + 1)
when m≤ 6
when m > 6 and m is an integer
when m> 6 and m is not an integer
a. What is the cost of a call that is under six minutes?
b. What is the cost of a 14-minute call?
c. What is the cost of a
1912-m
9-minute call?
Answers
The obtained answers for the given piecewise function are:
(a) The cost of a call that is under six minutes is 0.70 (m < 6)
(b) The cost of a 14-minute call is 2.62 (m > 6; m is an integer)
(c) The cost of a 9 1/2 minute call is 1.66 (m > 6; m is not an integer)
What is a piecewise function?A piecewise function is given by different functions at different intervals.
Calculation:It is given that,
phone company set the following rate schedule for an m-minute call from any of its pay phones.
C(m) = 0. 70 when m ≤ 6
= 0.70 + 0.24(m - 6) when m > 6 and m is an integer
= 0.70 + 0.24([m - 6] + 1) when m > 6 and m is not an integer
(a) The cost of a call that is under six minutes:
Since m < 6, the cost is C(m) = 0.76
Thus, the cost of a call that is under six minutes is 0.76
(b) The cost of a 14-minute call:
Since 14 > 6, the cost is C(m) = 0.70 + 0.24(m - 6) when m > 6 and m is an integer.
C(14) = 0.70 + 0.24(14 - 6)
= 0.70 + 0.24(8)
= 0.70 + 1.92
= 2.62
Thus, the cost of a 14-minute call is 2.62.
(c) The cost of a 9 1/2 minute call:
9 1/2 = 19/2 = 9.5
Since 9.5 > 6, the cost is C(m) = 0.70 + 0.24([m - 6] + 1) when m > 6 and m is not an integer.
C(9.5) = 0.70 + 0.24([9.5 - 6] + 1)
= 0.70 + 0.24([3.5] + 1)
Since we know that if [x] is a function then its domain is R and the range is Z(integer)
So, [3.5] = 3(is an integer)
Then,
C(9.5) = 0.70 + 0.24(3 + 1)
= 0.70 + 0.96
= 1.66
Therefore, the cost of a 9 1/2 minute call is 1.66.
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______ has at least one solution, and an inconsistent system has no solution.
Answers
The statement "Consistent system of equations has at least one solution, and an inconsistent system has no solution" is true.
In the context of systems of linear equations, a consistent system refers to a system where there exists at least one solution that satisfies all the equations in the system. This means that the equations can be simultaneously satisfied by a set of values for the variables.
On the other hand, an inconsistent system refers to a system of equations that has no solution. This occurs when the equations are contradictory or cannot be satisfied simultaneously by any values for the variables.
Therefore, a consistent system guarantees the existence of at least one solution, while an inconsistent system does not have any solution.
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Whats the slope?
Hurryyyyyyyyy
Answers
Answer: 3/4
Step-by-step explanation:
When you rise from the first point , it’s three spaces to get in the same line as the second point, then when you run to the right , you are moving four spaces to the right therefore the answer is 3/4
what is the equation in slope intercept form 3 y - 9= 12x
Please help I need to turn it in.
Answers
Answer:
y=4x+3
Step-by-step explanation:
3y-9=12x
+9 +9
3y=12x+9
/3 /3
y=4x+3
Explanation:
3y = 12x + 9 (i moved the constant to the right-hand side and change its sign.)
y = 4x + 3 (i divided both sides of the equation by 3 and got y = 4x + 3)
Explain it too and is it x method?
Answers
So Iam not sure either what the correct answer is but that’s what I got
In whitch number dose one digit 6 have a value that is 1,100 of value of the other difit 6?
Answers
6,702 = 6 thousands and 7 hundreds and 0 tens and 2 ones
\(= 6 \times 1000 + 7 \times 100 + 0 \times 10 + 2 \times 1\)
\(= 6000 + 700 + 2\).
Above, we have written the number 6,702 in expanded form, or as a SUM of its different parts according to place value. The digit 6 in the number 6,702 actually has the value 6,000 and the digit 7 actually signifies the value 700. This is why our number system is also called a place value system, because the value of a digit (like 6 or 7 in our example) depends on its placement within the number. In other words, the digit 6 in 6702 does not mean six but six thousand, because the six is placed in the thousands' place. The place of a digit determines its value. I'll go for 66.04 that's the closest.
Complete Question-
In which number does one digit 6 have the value of 1/100 of the other digit 6? The answers given are 66.04, 56.60, 46.06, and 40.66, which is the correct answer?
please view the image and answer the questions.
Answers
The values of a and b for the given equation are 25,-25
What is Quadratic equation ?
Quadratic equation can be defined as the equation which is in the form of ax^2+bx+c = 0 .
Given ,
equation x^3 - 625 x = 0
x^3 - 625x = 0
taking x common
x(x^2 - 625 ) = 0
x^2 - 625 = 0
(x+25 ) (x-25) = 0
It is in the form of a2-b2
hence it is equals to a+b * a-b
x = 25,-25 .
Hence, The values of a and b are 25,-25 respectively for the given equation.
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!!HELP ASAP!! No Links.
The domain (input values) of the cosine function is:
A. all negative and positive angle measures.
B. angle measures less than 2 π π radians.
C. angle measures less than 90°.
D. angle measures between 0 and π π radians.
* I can’t miss anymore please help*
Answers
Answer:
all negative and positive angle measures.
Step-by-step explanation:
The domain of the cosine function is: all negative and positive angle measures.
What is domain of a function?"It is a set of all possible input values for which a function is well defined."
We know,
A cosine function i.e., f(x) = cos(x) is defined for any real value of x.
This means, the domain of the cosine function is, all negative and positive angle measures.
Therefore, the correct answer is option (A).
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Anyone at least 48 inches may ride the ferris wheel. Represent this statement with an inequality.
Answers
Answer:
x ≥ 48
Step-by-step explanation:
PLEASE PLEASE PLEASE HELP
The midpoint of CD is M(-3,-7). If the of C is (-2,-10), what is the of D??
x=
y=
Answers
Answer:
D is (-4, -4)
Step-by-step explanation:
M = (x1 + x2)/2
-3 = (-2 + x2)/2
-6 = -2 + x2
x2 = -4
M = (y1 + y2)/2
-7 = (-10 + y2)/2
-14 = -10 + y2
y = -4
3 bags of food cost 17.25$. How much would marco spend on 6 of cat food?
Answers
Answer:
$34.5
Step-by-step explanation:
3 x2=6
17.25x2=34.5
Answer: $34.50
Step-by-step explanation:
Since 3 bags cost 17.50, 6 bags would just be 2 times that.
Latisha hired 4 babysitters in the last month. She paid a total of $170 in babysitting fees. If each babysitter worked a total of 5 hours and is paid the same amount, how much did each babysitter earn per hour?
Answers
8.5Step-by-step explanation:
Suppose a business records the following values each day the total number of customers that day (X) Revenue for that day (Y) A summary of X and Y in the previous days is mean of X: 600 Standard deviation of X: 10 Mean of Y: $5000, Standard deviation of Y: 1000 Correlation r= 0.9 Calculate the values A,B,C and D (1 mark) Future value of X Z score of X Predicted y average of y+ r* (Z score of X)* standard deviation of y 595 A B 600 0 $5000 D 615 IC You will get marks for each correct answer but note you are encouraged to show working. If the working is correct but the answer is wrong you will be given partial marks
Answers
The predicted values of A, B, C, and D are: A = 595B = -0.5C = 600D = $6350, therefore, the correct option is IC.
Given,
Mean of X = 600
Standard deviation of X = 10
Mean of Y = $5000
Standard deviation of Y = 1000
Correlation r= 0.9
Future value of X = 595
Z score of X = (X- Mean of X) / Standard deviation of X= (595-600) / 10 = -0.5
Using the formula, Predicted y = average of y+ r* (Z score of X)* standard deviation of y
Predicted y = $5000 + 0.9 * (-0.5) * 1000 = $4750
The predicted value of Y for X = 595 is $4750.
Now, to find the values of A, B, C, and D; we need to calculate the Z score of X = 615 and find the corresponding predicted value of Y.
Z score of X = (X- Mean of X) / Standard deviation of X= (615-600) / 10 = 1.5
Predicted y = average of y+ r* (Z score of X)* standard deviation of y
Predicted y = $5000 + 0.9 * (1.5) * 1000 = $6350
The predicted value of Y for X = 615 is $6350.
Hence, the values of A, B, C, and D are: A = 595B = -0.5C = 600D = $6350
Therefore, the correct option is IC.
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H. :P - 0.65 and H.: p > 0.65 where p = the proportion of students who were quarantined at some point during the Fall Semester of 2020. Identify the correct explanation for a Type II error. Conclude the percent was higher than 65%, but it was not higher. Conclude the percent was higher than 65% and it was higher. Did not conclude the percent was higher than 65%, but it was higher. Did not conclude the percent was higher than 65% and it was not higher.
Answers
A Type II error occurs when we fail to reject a null hypothesis that is actually false. In this case, the null hypothesis is that the proportion of students who were quarantined at some point during the Fall Semester of 2020 is equal to or less than 0.65.
The alternative hypothesis is that the proportion is greater than 0.65. If we make a Type II error, we fail to reject the null hypothesis when it is actually false, meaning we do not conclude that the proportion is higher than 0.65 even though it actually is higher.
Therefore, the correct explanation for a Type II error, in this case, we would be: "Did not conclude the percent was higher than 65%, but it was higher."
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The step by step process to answer one of these
Answers
Given:
The highest point on the graph of y =f(x) is (-3, 6)
The highest point of the graph of :
\(y\text{ = }\frac{1}{2}f(x-1)\text{ + 5}\)The new function is translated to the right by 1 unit and translated upwards by 5 units.
Applying this to the highest point of the original function y = f(x), we have:
\(\begin{gathered} =\text{ (-3 + 1, 6 + 5}) \\ =\text{ (-2, 11)} \end{gathered}\)Answer:
(-2, 11)
pls help asap!!!!!!!!!!!!!
Answers
Answer:
2ebervhjebhvbrv
Step-by-step explanation:
vhehifhfkj2hf2euihfwuhvruihgr
Given f(x)=(x+7)a) What is the domain of f(x) in interval notation?b) Find f-1(x)c) Find the range of f(x).
Answers
Given f(x) = (x + 7)a) Domain of f(x) in interval notation is [-7, ∞)The notation of the domain of f(x) is [-7, ∞).Explanation:Given f(x) = (x + 7).Since it's a polynomial function it's defined for all real numbers.
Rules to find the domain of any function:Denominator of the fraction can not be zero.
In case of even root, the radicand (expression under the root) must be greater than or equal to zero.
In case of the logarithmic function, the argument (expression under the logarithm) must be greater than zero.
Therefore, the domain of the function is [-7, ∞).b) f-1(x)f(x) = (x + 7)We need to find the inverse of the function f(x) to get f-1(x).y = (x + 7)y - 7 = xOrf-1(x) = x - 7c) Range of f(x)Range of f(x) is the set of all possible values of y that the function can take.
We see that there is no value of x for which y can be less than -7.Therefore, the range of f(x) is (-∞, ∞).
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The domain of the function f(x) in interval notation is (-∞, ∞).
The inverse function of f(x) is f-1(x) = x-7.
The range of the function f(x) is (-∞, ∞).
a) The domain of a function is the set of all possible input values (usually x).
Since x can take on any real number value, the domain of f(x) is (-∞, ∞) or (-infinity, infinity).
The domain of the function f(x) in interval notation is (-∞, ∞).
b) The inverse function of f(x) can be found by solving for x in terms of y, replacing f(x) with y, and swapping the variables.
Here's how to solve for f-1(x):
y = (x+7)
Swap x and y:
x = (y+7)
Solve for y:
y = x-7
Therefore, the inverse function of f(x) is f-1(x) = x-7.
c) The range of a function is the set of all possible output values (usually y).
Since a can take on any real number value, f(x) can take on any real number value shifted down by 7 units.
The range of the function f(x) is (-∞, ∞), with all values shifted down by 7 units.
The range of the function f(x) is (-∞, ∞).
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3/8 ÷ 2/3 and express the answer in simplest form
Answers
Answer: 9/16
Step-by-step explanation:
maya drove 693 miles in 11 hours how long would it take her to drive 819 miles
Answers
Answer:
13
Step-by-step explanation:
693/11 = 63 miles per hour
819/63 = 13
Edgar us using computer graphics to build the background images for a new animated film. He is using linear modeling, the process of using linear equations to describe real-world objects. Edgar had identified the functions needed to build an image in the graphics program.
Answers
A field of mathematics called linear equations is essential to computer graphics. It investigates matrices, linear transformations, and vectors. These subjects were covered in Subsection 2.3. 8 in a two-dimensional setting.
What is a linear model?A continuous response variable is described by a linear model as a function of one or more predictor variables. They can assist you in analyzing experimental, monetary, and biological data or in understanding and predicting the behavior of complex systems. A statistical technique used to build a linear model is called linear regression.
Depending on the context, the phrase "linear model" is used differently in statistics. The word is frequently used interchangeably with a linear regression model since it occurs most frequently in relation to regression models. The phrase has a different connotation when employed in time series analysis, though.
By using a linear combination of predictor variables, linear models can be used to describe a response variable. A continuous variable with a response that is at the very least roughly regularly distributed is required.
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