find the linear approximation l(x) of the function f(x)=3x3 4x2 2x−2 at a=−2
Answers
the linear approximation L(x) of the function f(x) = 3x³ - 4x² + 2x - 2 at a = -2 is L(x) = 46x + 82.
To find the linear approximation L(x) of the function f(x) = 3x³ - 4x² + 2x - 2 at a = -2, we can use the formula:
L(x) = f(a) + f'(a)(x - a), Where f(a) is the value of the function at a, f'(a) is the value of the derivative at a, and x is the input value for which we want to find the approximation.
In this case, a = -2, so we need to find f(-2) and f'(-2) . f(-2) = 3(-2)³ - 4(-2)² + 2(-2) - 2
= -32f'(x) = 9x² - 8x + 2f'(-2)
= 9(-2)² - 8(-2) + 2
= 46
Now we can plug in these values into the formula to get:
L(x) = -32 + 46(x + 2)
Simplifying this expression, we get:
L(x) = 46x + 82
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Related Questions
On Monday, 6 out of 10 people who entered the store purchased something. If 1,000 people entered the store on Monday how many people purchased something?
PLEASE IM IN CLASS RIGHT NOWWW
Answers
Answer:
600
Step-by-step explanation:
Hope this helps you bro.
We can set this up as a proportion.
\(\frac{6}{10}=\frac{x}{1000}\) so 10x=6000 and x=600.
600 out of the 1000 people who went into the store, bought something.
One number is 2 less than 3 times another. If the sum of the two number is 14, find the numbers.
Answers
Solution:
Given:
A word problem.
To solve the question, we develop the statements into mathematical equations.
Hence,
Let the two numbers be represented by x and y
where;
x is one number
y is another number
\(\begin{gathered} \text{One number is 2 less than 3 times another.} \\ \text{Mathematically means;} \\ x=3y-2 \\ R\text{earranging, th}e\text{ equation becomes; }x-3y=-2\ldots\ldots\ldots\ldots.(1) \\ \text{The sum of the two numbers is 14.} \\ \text{Mathematically means;} \\ x+y=14\ldots\ldots\ldots\ldots\ldots(2) \end{gathered}\)
Solving both equations generated simultaneously, using the elimination method, we subtract equation (1) from equation (2).
That is equation (2) - equation (1);
\(\begin{gathered} x-3y=-2\ldots\ldots\ldots\ldots\text{.}\mathrm{}(1) \\ x+y=14\ldots\ldots\ldots\ldots\ldots\text{.}(2) \\ \text{equation (2)-(1);} \\ x-x+y-(-3y)=14-(-2)_{} \\ y+3y=14+2 \\ 4y=16 \\ \text{Dividing both sides by 4,} \\ y=\frac{16}{4} \\ y=4 \end{gathered}\)
Substituting the value of y gotten into equation (2) to solve for x,
\(\begin{gathered} x+y=14 \\ x+4=14 \\ x=14-4 \\ x=10 \end{gathered}\)
Hence, the solution to the equations is;
\((x,y)=(10,4)\)Therefore, the numbers are 10 and 4.
A ball is chosen at random from a bag containing 150 balls that are either red or blue and either dull or shiny. There are 36 red shiny balls and 54 blue balls. What is the probability of the chosen ball being shiny conditional on it being red
Answers
Answer:
The probability of the chosen ball being shiny conditional on it being red is; 0.375
Step-by-step explanation:
Let A be the event that a red ball has been chosen
Let B be the event that a shiny ball has been chosen
Let S be the total outcomes = 150 balls
Thus;
P(A ∩ B ) = 36/150
A ∩ B' = 150 - 36 - 54
A ∩ B' = 60
Thus; P(A ∩ B') = 60/150
P(A') = 54/150
P(A) = (150 - 54)/150 = 96/150
Thus, probability of the chosen ball being shiny conditional on it being red is;
P(B | A) = P(B ∩ A)/P(A)
Thus; P(B | A) = (36/150)/(96/150)
P(B | A) = 0.375
What is the slope of this line? (5 points)
Show all work.
Answers
Answer:
-2,2
Step-by-step explanation:
At what ordered pair is "Parking Lot B" located at?
Question 1 options:
(-4, 1)
(-3, 4)
(7, -3)
(4, -3)
Answers
If the simple interest on $5000 for 4 years is $800, what is the interest rate?
Answers
Answer: I = $ 160,000.00
Step-by-step explanation:
if a = b, then does ax = bx and ay = by?
Answers
Answer:
My answer to your question is a "No".
We can know that a and b are the same numbers. If we multiply the same number on each side, the answer will be the same. However, x and y have different values. So, it will show differently.
Let's have an example:
It we say a = 5, x = 6, y = 7.
We know a and b are the same number so, both a and b will be 5. If we multiply a by x, it will be 5 x 6 which is 30. It will show the same answer on multiplying b because as you said a and b are the same. The equation will be 5(a) x 6(x) = 5(b) x 6(x) Let's look at multiplying y. If we multiply a by y, it will be 5 x 7 which is 35. As you said it will show the same answer on multiplying b because a and b are the same. The equation for this will be 5(a) x 7(y) = 5(b) = 7(y). Finally, let's compare the two equations.
5(a) x 6(x) = 5(b) x 6(x) -> 30 = 30
5(a) x 7(y) = 5(b) = 7(y) -> 35 = 35
You can see it more clearly when we compare those to the equations that I made.
Thank you
Yes, if a = b, then ax = bx and ay = by for any value of x.
This is because the equation a = b implies that a and b are equal in value, so any expression involving a can be replaced with an equivalent expression involving b. In other words, any operation performed on a can be performed on b and produce the same result.
For example, if a = b, then multiplying both sides of the equation by x yields ax = bx, and multiplying both sides of the equation by y yields ay = by. This means that any power, root, logarithm, or other mathematical operation performed on a can also be performed on b and produce the same result.
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good luck on finals week :)
Answers
you too ty :)
ilysm and you matter <3
In a triangle, the measure of the largest angle is 114°. The measure
of a second angle is 26°. What is the measure of the remaining
Answers
Answer:
40 degrees
Step-by-step explanation:
There are always 180 degrees in a triangle, so add up the two known angles
114+26=140
then subtract this amount from 180 to get the last remaining angle
180-140=40 degrees
Describe how to write 7,594,000,000 in scientific notation. Complete the description. First move the decimal point places to the left to find , a number that is greater than or equal to 1 and less than 10. Then multiply by 10 , using an exponent on 10 that equals the number of places you moved the decimal.
Answers
Step-by-step explanation:
The given number is 7,594,000,000.
To convert it into scientific notation,
First move the decimal point places to the left to find a number that is greater than or equal to 1 and less than 10. Then multiply by 10 , using an exponent on 10 that equals the number of places you moved the decimal. The exponent is negative if the original no was <1 and the exponent is positive, if the original number was > 1.
In 7,594,000,000, we move the decimal point places to the left before 5. It means we have moved 9 digits left.
Hence, \(7,594,000,000=7.59\times 10^9\) is the scientific notation.
The length of a rectangle i 2cm greater than the width of the rectangle. The perimeter of the rectangle i 24cm
Answers
The length of the rectangle is 7 cm and the width is 5 cm.
Perimeter of a rectangle:The whole distance covered by the rectangle's borders or its sides is known as its perimeter. As we know the rectangle will have 4 sides then the perimeter of the rectangle will be equal to the total of its four sides. And the unit will be in meters, centimeters, inches, feet, etc.
The formula for the Perimeter of the rectangle is given by
Perimeter = 2( Length + Width )Here we have
The length of a rectangle is 2cm greater than the width of the rectangle
And perimeter of the rectangle = 24 cm
Let x be the width of the rectangle
From the given data,
Length of the rectangle = (x + 2) cm
As we know Perimeter of rectangle = 2(Length+width)
=> Perimeter of rectangle = 2(x+2 + x) = 2(2x +2)
From the given data,
Perimeter of rectangle = 24cm
=> 2(2x +2) = 24 cm
=> (2x +2) = 12 [ Divided by 2 into both sides ]
=> 2x = 12 - 2
=> 2x = 10
=> x = 5 [ divided by 2 into both sides ]
Length of rectangle, (x+2) = 5 + 2 = 7 cm
Therefore,
The length of the rectangle is 7 cm and the width is 5 cm.
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The radius of a circle is 17 inches. What is the circle's area?
Use 3.14 for л.
Answers
Answer:
Step-by-step explanation:
The formula for the area of a circle is:
A = πr^2
where A is the area, π (pi) is approximately 3.14, and r is the radius.
Substituting the given radius of 17 inches into the formula, we get:
A = 3.14 × 17^2
A = 3.14 × 289
A = 907.06
Therefore, the area of the circle is approximately 907.06 square inches.
Answer:
907.46
Step-by-step explanation:
Area of a circle formula is πr^2
It says the radius is 17
**Simplify**
(3.14)(17)^2=907.46
Alejandro can run 54 miles in 112 hour. At this rate, how far can he run in 1 hour?
Answers
Answer:
0.482 miles per hour
Step-by-step explanation:
54÷112
=0.482142
Three consecutive integers have a sum of 42. Find the integers.
Answers
Answer:
13, 14, 15
Step-by-step explanation:
Three consecutive integers have a sum of 42 means which 3 numbers in a row add up to 42
We can call the lowest integer x,
the next integer x+1 (since our integers need to be even)
the third integer x+2
algebraic equation: 42 = x + (x+1) + (x+2).
Combine like terms on the right side,
42 = 3x + 3
Subtract 3 from each side
39 = 3x
Divide each side by 3
x=13, which is our lowest integer.
The next two integers we find with 13 + 1 =.14 and 13 + 2 = 15
13 + 14 + 15 = 42.
a survey of 130 college graduates was conducted. students were asked whether they were employed and if they were looking for a job. the following table shows the results. job searching no job searching total employed 28 61 89 not employed 18 23 41 total 46 84 130 according to the table, what is the probability that a randomly chosen student is not employed given that they are job searching? give your answer as a fraction in simplest form.
Answers
The probability that a randomly chosen student is not employed given that they are job searching is 9/23.
What is the probability that a randomly chosen person is not employed despite job searching
The probability of a student not being employed given that they are job searching is given by the conditional probability:
P(not employed | job searching) = P(not employed and job searching) / P(job searching)
We can find the probabilities for the numerator and denominator from the table:
P(not employed and job searching) = 18
P(job searching) = 46
Therefore, the conditional probability is:
P(not employed | job searching) = 18 / 46
We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which is 2:
P(not employed | job searching) = 9 / 23
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What is antiderivative of sin?
Answers
The antiderivative of sin is -cos(x) + C.
The antiderivative of a function is the inverse operation of differentiation which is is also known as its indefinite integral.
So, the integral of sin
∫sin(x) = -cos(x) + C
where C = constant of integration.
This can be verified by differentiating -cos(x) + C with respect to x, which gives sin(x).
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Use the formula to solve the equation x^2 + 9x + 8 = 0.
Answers
Answer:
\(x=-8, -1\)
Step-by-step explanation:
Given the equation \(x^{2} +9x+8=0\\\),
By the quadratic formula,
\(x=\frac{-b+-\sqrt{b^{2}-4ac } }{2a}\),
\(x=\frac{-(9)+-\sqrt{(9)^{2}-4(1)(8) } }{2(1)}=\frac{-9+-\sqrt{49 } }{2}=\frac{-9+-7 }{2}\)
We have two different solutions for x where \(x=\frac{-9-7 }{2}\) and \(x=\frac{-9+7 }{2}\)
So, x = \(-16/2=-8\) and \(x=-2/2=-1\)
Therefore, the solutions to this quadratic equation is x = -8, -1, by the quadratic formula.
17. Differentiate
X^2/(2x+1)
with respect to x
Answers
Answer:
cheese is cheese
PLEASE HELP!!
The method 100 students use to get to school and their grade level is shown below.
Find the probability a student walks, given that they are a senior.
P(walk | senior) = [?]
Answers
The probability of being a senior is the total number of seniors divided by the total number of students.
The probability of a student walking given that they are seniors can be calculated using Bayes' theorem. Bayes' theorem is a formula that relates conditional probabilities to their inverses. The formula is: P(A|B) = P(B|A) P(A) / P(B)where P(A|B) is the probability of event A given that event B has occurred. In this case, A is "walking" and B is "senior." P(B|A) is the probability of being a senior given that the student is walking, P(A) is the probability of walking, and P(B) is the probability of being a senior. We can also represent the above formula in the form of a tree diagram, where P(walk | senior) is one branch of the tree.
The probability of being a senior is represented by the root of the tree, while the probability of walking is represented by a branch from the root. The probability of walking given that the student is a senior is calculated by dividing the probability of a senior walking by the probability of being a senior. The probability of walking can be calculated by adding up the probabilities of walking for each grade level and dividing by the total number of students.
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Maggies brother is 7 years younger than twice here. The sum of their ages i 32
How old is Maggie
Maggie is
Years old
Answers
Then,
According to the question
Maggies brother is 7yrs younger than twice of her so, the equation will be ,
2x-7=y………eqn 1
And the sum of their ages is 32 so,
x + y = 32 ………..eqn 2
Now,
Putting the value of y in equation 2 we get,
x + y= 32
x + (2x-7) =32
x + 2x-7 =32
3x = 32+7
x = 39/3
x = 13
Here,
Taking eqn 2 and putting the value of x we get,
x + y = 32
13 + y = 32
Y = 32-13
y = 19
Hence,
The age of maggies is 13 years
Answer:
Maggie is 13years old
Step-by-step explanation:
Let the age of Maggie be = x
Let her brothers age be = y
Given:
Brother is 7 years younger than twice her age , y = 2x - 7 --------- ( 1 )
[ Twice her age = 2x
7 years younger than twice her age = 2x - 7 ]
Sum of their ages , x + y = 32 -------- ( 2 )
Substitute ( 1 ) in ( 2 ) :
x + ( 2x - 7 ) = 32
x + 2x - 7 = 32
3x = 32 + 7
3x = 39
x = 13
Maggie's age = 13 years
Substitute x in ( 1 ) :
y = 2x - 7
= 2 ( 13 ) - 7
= 26 - 7
= 19
Brother's age = 19 years
21 divided by 13,280 
Answers
Answer: 0.0015813253
Step-by-step explanation:
is you ment to say 14,280 divided by 21 then it would be 632.380952381
A tank can hold 40,000 gallons of water. If 500 gallons of water are
used each day, write the equation that represents the amount of water
in the tank x days after it is full.
Answers
Answer:
25
Step-by-step explanation:
1) 40,000-500(x)
this is the equation you could use
or
2) the tank will be empty after 80 days
this is to solve the problem
to check your work
40,000=500(80)
40,000=40,000
this way it checks out
How do I solve this question 5x - [7 - (2x - 1)] = 3(x - 5) + 4(x + 3)
Answers
Answer:
x = 6/4, or x = 3/2, OR x = 1 1/2
Step-by-step explanation:
5x - [7 - (2x-1)] = 3(x-5) + 4(x+3)
Pick one side to work on first, I will chose the right side,
Distribute on the right side.
5x - [7 - (2x-1)] = 3x - 15 + 4x + 3
Now, add like terms on the right side.
5x - [7 - (2x-1)] = 7x - 12
Now, to isolate 7 - (2x -1), subtract 5x from both sides.
so now,
-7 - (2x-1) = 2x - 12
Now, we can add 7 to both sides of the equation to isolate -(2x-1)
we add instead of subtract because the seven is a negative.
-(2x-1) = 2x - 5
Now, there is still a negative sign in front of the (2x-1), so we distribute the - to the equation.
-2x + 1 = 2x - 5
Now, we can isolate the variable and numbers bu adding five to both sides, and adding 2 to both sides. This is to make the equation easier by removing any negative terms.
6 = 4x
Divide both sides by 4
x = 6/4, or x = 3/2, OR x = 1 1/2
What is the equation in point-slope form of the line passing through (0,5) and (-2, 11)?
Oy-5=-3(x + 2)
Oy-5= 3(x + 2)
Oy - 11 = -3(x - 2)
Oy - 11 = -3(x + 2)
Answers
Answer: y-11 = -3(x+2)
What assumption do we need to make to find a valid 99% confidence interval for the mean number of all workplace homicides per year
Answers
We have to assume that the sample mean is given , distribution is normal and sample size is also given.
Given confidence level 99%.
We have to answer the assumptions that are needed to make a valid 99% confidence interval.
Confidence interval can be made by formula of margin of error.
Margin of error is the difference between actual values and the calculated values.
Upper level of confidence interval=Mean+ margin of error
Lower level of confidence interval= Mean - margin of error.
Margin of error=z*σ/\(\sqrt{n}\)
where z is the corresponding z value for the confidence level given ,
σ is population mean and n is sample size.
Hence to calculate the confidence interval we need population mean, sample size.
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Please help me with this. Method included please
Answers
Answer:
a) 9.135
b) 392.79
Step-by-step explanation:
Hope my answers are helpful
f(x) = -3 |x-1| +5; Find f(3)
Answers
Answer: f(3) = -1
Step-by-step explanation:
f(x) = -3 |x-1| +5
f(3), we just need to put 3 in for both the x
f(3) = -3 |3-1| +5
f(3) = -9 + 3 +5
f(3) = -1
by observing a set of data values, thomas used a calculator for the weight (in pounds) and predicted the number of calories burned per minute to get an equation for the least-squares line: ŷ
Answers
The correct option is c.) A person weighing 134 pounds can burn 8.9 calories per minute.
We will keep in the weight of each person in the equation to find the number of calories burnt per minute.
a) Å = 2.2 + 0.05 × 125
Å = 8.45 calories burnt per minute. Since these are more than stated amount of 8.3 calories, the stated option is wrong.
b) Å = 2.2 + 0.05 × 149
Å = 9.65 calories burnt per minute. Since these are less than stated amount of 9.8 calories, the stated option is wrong.
c) Å = 2.2 + 0.05 × 134
Å = 8.9 calories burnt per minute. Since these are same as the stated amount of 8.9 calories, the stated option is true.
d) Å = 2.2 + 0.05 × 173
Å = 10.85 calories burnt per minute. Since these are more than stated amount of 10.7 calories, the stated option is wrong.
Hence, the correct option is c.
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The complete Ques is -
By observing a set of data values, Thomas used a calculator for the weight (in pounds) and predicted the number of calories burned per minute to get an equation for the least-squares line: Å· = 2.2 + 0.05x. Based on the information gathered by Thomas, select the statement that is TRUE. a.) A person weighing 125 pounds can burn 8.3 calories per minute. b.) A person weighing 149 pounds can burn 9.8 calories per minute. c.) A person weighing 134 pounds can burn 8.9 calories per minute. d.) A person weighing 173 pounds can burn 10.7 calories per minute.
Expression that is equivalent to 5^6
Answers
Answer:
5^6 = 5*5*5*5*5*5 = 15625
Step-by-step explanation:
definition of exponents
Answer:
5 to the 6th power is 5*5*5*5*5*5
Step-by-step explanation:
Given vector u = (1, 2) and v = (1, -4), determine the value of 4u + 3v. Click
and drag copies of the dotted vectors as many times as needed, lining them up head
to tail, in order to find the result graphically. You may have to negate the direction of
one of the vectors by pressing the link.
Answers
Let u and v be a vectors. Then u can be broken up into two components, r and s such that r is parallel to v and s is perpendicular to v.
How do you find vector U and V?The component of u perpendicular to v is referred to as s, while r is referred to as the projection of u onto v. Then, u v = u1v1 + u2v2 + + unvn is the dot product of u with v.
Keep in mind that u v is defined when u and v have the same number of components and that the dot product of two vectors is a scalar. Though the dot product is a union of two vectors, the outcome is not a vector, which is an intriguing observation.
In particular, u (v w) makes no sense if u, v, and w are vectors because v w is a scalar. Before confirming that the dot product has the desired geometric characteristics, we'll mention.
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When given vector u = (1, 2) and v = (1, -4), Then the value of 4u + 3v = ⟨7, -4⟩, graph in attachment.
How do you find vector U and V?The component of u perpendicular to v is referred to as s, while r is referred to as the projection of u onto v. Then, u v = u1v1 + u2v2 + + unvn is the dot product of u with v.
Keep in mind that u v is defined when u and v have the same number of components and that the dot product of two vectors is a scalar. Though the dot product is a union of two vectors, the outcome is not a vector, which is an intriguing observation.
Given u = (1, 2) and v = (1, -4),
4u + 3v = 4(1, 2) + 3(1, -4)
= (4, 8) + (3, -12)
= ⟨4 + 3, 8 + (-12)⟩
= ⟨7, -4⟩
Thus, 4u + 3v = ⟨7, -4⟩
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