Answers
Answer:
f’(2) = -21/128
f’(-1) = -42
Step-by-step explanation:
We are given a function:
[tex]\displaystyle \large{f(x)=\frac{6}{x^7}}[/tex]
We want to evaluate f’(2) and f’(-1). Keep in mind that f’(x) denotes or means the derivative of f(x). So what we are going to do first is to find the derivative of given function.
Derive the function, there are two ways to derive it, either using power rules or quotient rules. For this, I’ll demonstrate two methods.
Power Rules
If [tex]\displaystyle \large{f(x)=x^n}[/tex] then [tex]\displaystyle \large{f\prime (x)=nx^{n-1}}[/tex] where n is any real numbers.
Since the function is written in a fraction form, we’ll have to convert it to the x^n form using law of exponent.
[tex]\displaystyle \large{f(x)=\frac{6}{x^7} \to f(x)=6\cdot \frac{1}{x^7}}[/tex]
Law of Exponent I
[tex]\displaystyle \large{\frac{1}{a^n} = a^{-n}}[/tex]
Therefore:
[tex]\displaystyle \large{f(x)=6x^{-7}}[/tex]
Then derive the function using power rules:
Property of Differentiation I
[tex]\displaystyle \large{y=kf(x) \to y\prime = kf\prime (x)}[/tex] where k is a constant.
[tex]\displaystyle \large{f\prime (x)=6\cdot -7x^{-7-1}}\\\displaystyle \large{f\prime (x)=6\cdot -7x^{-8}}\\\displaystyle \large{f\prime (x)=-42x^{-8}}[/tex]
Quotient Rules
[tex]\displaystyle \large{y=\frac{f(x)}{g(x)} \to y\prime = \frac{f\prime (x)g(x)-f(x)g\prime (x)}{[g(x)]^2}}[/tex]
If f(x) = k or a constant then:
Property of Differentiation II
[tex]\displaystyle \large{y=k \to y\prime = 0}[/tex] for k is a constant.
[tex]\displaystyle \large{y=\frac{k}{g(x)} \to y\prime = \frac{0\cdot g(x)-kg\prime (x)}{[g(x)]^2}}\\\displaystyle \large{y\prime = \frac{-kg\prime (x)}{[g(x)]^2}}[/tex]
Therefore:
[tex]\displaystyle \large{f\prime (x)=\frac{-6\cdot 7x^{7-1}}{[x^7]^2}}\\\displaystyle \large{f\prime (x)=\frac{-42x^6}{x^{14}}}\\\displaystyle \large{f\prime (x)=-42x^{6-14}}\\\displaystyle \large{f\prime (x)=-42x^{-8}}[/tex]
Laws of Exponent used above:
[tex]\displaystyle \large{(a^n)^m = a^{nm}}\\\displaystyle \large{\frac{a^n}{a^m} = a^{n-m}}[/tex]
Therefore the derivative of function is:
[tex]\displaystyle \large{f\prime (x) = -42x^{-8}}[/tex] or [tex]\displaystyle \large{f\prime (x)=-\frac{42}{x^8}}[/tex]
Next is to substitute x = 2 and x = -1 in the derivative.
[tex]\displaystyle \large{f\prime (2)=-\frac{42}{2^8}}\\\displaystyle \large{f\prime (2) = -\frac{42}{256}}\\\displaystyle \large{f\prime (2)= -\frac{21}{128}}[/tex]
And:
[tex]\displaystyle \large{f\prime (-1)=-\frac{42}{(-1)^8}}\\\displaystyle \large{f\prime (-1) = -\frac{42}{1}}\\\displaystyle \large{f \prime (-1) = -42}[/tex]
Therefore, f’(2) = -21/128 and f’(-1) = -42.
Related Questions
Divide and simplify.
- 8/15 divided by - 3/5
A) - 3/25
B) - 4/5
C) 13/15
D) 8/9
Answers
Answer:
8/9
Step-by-step explanation:
Evaluate the algebraic expression 4y + x - w, when w = 12, x = 10, y = 5 and z = 9.
Answers
Answer:
Step-by-step explanation:
simply plug in the given values for the letter and do the math.
4(5) + 10 - 12 = 20+10-12 = 18.
Answer:
18
Step-by-step explanation:
w=12
x=10
y=5
z=9
4 (5)+10-12
20+10-12
BODMAS
addtition then subtraction
20+10=30
30-12
=18
Brainiest please
Solve for X and Y
1. y = 2x
6x + 3y = 12
2. y = -4x + 2
y = 6x - 8
3. y = x - 4
-4x - 6y = -16
4. x = 3y + 1
2x + 4y = 12
Answers
Answer:
What do you mean?
Step-by-step explanation:
A piece of wire 20 m long is cut into two pieces. One piece is bent into a square and the other is bent into a circle.
Answers
The length of the wire is the perimeter of the wire
The radius of the circle is 1.59 meters
How to determine the radius of the circle?The length of the wire is given as:
L = 20m
When cut into two pieces, we have:
Perimeter of square = 10 mCircumference of circle = 10mThe circumference of the circle is calculated using:
C = 2πr
So, we have:
2πr = 10
Make r the subject
r = 10/2π
Evaluate the quotient
r = 1.59
Hence, the radius of the circle is 1.59 meters
Read more about radius at:
https://brainly.com/question/9554871
please I need help with this question
Answers
Dave pays 15 * (1+0.08) = $16.2
So the difference is:
$21.6-$16.2 = $5.4
Answer:
$5.40
Step-by-step explanation:
First, find Dave's purchase. To do this, you multiply 15 by the tax percent and add that to the original.
So:
15 x 8% = 15 x 0.08 = 1.2
15 + 1.2 = 16.2
Next, do the same for Mel's purchase:
20 x 8% = 20 x 0.08 = 1.6
20 + 1.6 = 21.6
Then, you subtract Dave's purchase from Mel's:
21.6 - 16.2 = 5.4
This comes out to $5.40
Help please! How many cups for white paint on 1 then white paint on 10!
Answers
Answer:
1 is .83 or .80 if your rounding and 10 is 8.3 but if your rounding its just 8
Step-by-step explanation:
Its because 5/6 is .83 so for every 1 white there .83 red
How do you solve this?
Answers
Answer:
22
Step-by-step explanation:
5x + 8 = 118
5x = 110
x = 22
What is the area of the figure below ?
A. 12
B. 15
C. 18
D. None of these
Answers
Step 1: Find the area of the larger rectangle
Area of a rectangle = base x height
Area = 4 x 3 = 12
Step 2: Find the area of the other rectangle
The tricky part about this one is that we aren't given the length of this rectangle. We do know, however, that the whole base of the figure is 6 and 3 units are taken up by the first rectangle. Therefore, the length of this rectangle is 3.
Area = 2 x 3 = 6
Step 3: Find the area of the figure
Now that we know the area of both rectangles by themselves, all that's left to do is add them up.
6 + 12 = 18
Answer: 18
Hope this helps!
Answer:
18
Step-by-step explanation:
A=bh
A=3x4 A=3x2
12+6=18.
Which function should be used when evaluating the function at x = -1?
S -x2 + 8x if x < -1
p(x) =
*x? - 4 if x 2-1
O p (x) = {x? - 4
O p(x) = -x2 + 8x
Answers
When a system contains the equations of two parabolas, there can only be one solution.
True or False
Answers
A circular "No Parking" road sign has a diameter of 26 inches. Which measurement is closest to the area of the sign in square inches? 81.64 in.² 163.28 in.² 530.66 in.² 2,122.64 in.²
Answers
Answer:
530.66 in²
area of circle: πr²
diameter: 26 inradius : diameter/2 = 26/2 = 13 inarea: πr² ⇒ π(13)² ⇒ 530.66 in²
Answer:
pretty sure its 530.66 in.²
Step-by-step explanation:
In the polynomial below, what number should replace the question mark to produce a difference of squares?
x^2 + ?x - 36
A. 12
B. 36
C. 6
D. 0
Answers
Answer:
Step-by-step explanation:
c
Find the derivative of the image below
Answers
[tex]~~~\dfrac{d}{dx} f(x) \\ \\=\dfrac{d}{dx} \left(x^3 \cdot \log_6 x \right)\\\\=x^3\dfrac{d}{dx} \left(\log_6 x\right) + \log_6 (x)\dfrac d{dx} x^3 \\\\=x^3 \cdot \dfrac 1{x \ln 6} + \log _6 (x) \cdot 3x^2\\\\=\dfrac{x^2}{\ln 6} + \log_6(x) \cdot 3x^2\\\\\\=x^2 \left(\dfrac 1{\ln 6} + 3\log_6 x \right)[/tex]
[tex]\text{The derivative is now in a form of}~ x^A (B + C \log_D (x))[/tex]
answer the questions.
Answers
By analyzing the data tables given, we will see that:
1) The range is 28.
2) The graph can be seen at the end.
3) There are clusters at 16 and 17, and 25 is an outlier.
4) The range decreases almost by 50%.
How to get the range for the data?
The range is defined by the difference between the largest and smallest values from the data set.
In this case, the largest is: 95The smallest is: 67So the range is: R = 95 - 67 = 28
The correct option is D.
How to make a line plot?For each time that a number appears, you need to make a dot above the correspondent value.
The graph can be seen below.
3) we have clusters on 16 and 17, and as you can see, the value 25 is really away of the rest of the values, so we have a gap, and 25 is an outlier.
4) With the 25, the range is:
25 - 16 = 9
If we remove it, the range is:
21 - 16 = 5
So the range decreases almost by a 50%.
If you want to learn more about data sets, you can read:
https://brainly.com/question/3514929
jack had m math problems to complete during his vacation. he solved the same number of problems every day and finished them all in 5 days. how many problems did jack solve per day.
Answers
If Jack finish them all in 5 days, then he can solve m/5 math problem in just one day.
Word problems leading to quadratic equationFrom the given question, jack can only solve m math problems in 5 days, this can be expressed as:
m problems = 5 days
The number of questions he can solve per day is expressed as:
x = 1 day
Take the ratio
m/x = 5/1
5x = m
x = m/5 math problems
This shows that jack can solve m/5 math problem in just one day
Learn more on ratio here: https://brainly.com/question/2328454
PLEASE HELP!
The scatter plot shows the number of years of experience, x, and the
amount charged per hour, y, for each of 25 dog sitters in Texas.
(a) Write an approximate equation of the line of best fit for the data. It doesn't have to be the exact line of best fit.
(b) Using your equation from part (a), predict the amount charged per hour by a dog sitter with 18 years of experience.
Answers
Answer:
(a) [tex]\sf y=\dfrac{11}{20}x+7[/tex]
(b) $16.90
Step-by-step explanation:
Part (a)
Add a line of best fit (see attached).
Find two points on the line: (7, 0) and (20, 18)
Use these points to find the slope of the line:
[tex]\sf slope\:(m)=\dfrac{change\:in\:y}{change\:in\:x}=\dfrac{18-7}{20-0}=\dfrac{11}{20}[/tex]
Use the found slope and one of the points in the point-slope form of the linear equation to find an equation for the line of best fit:
[tex]\sf\implies y-y_1=m(x-x_1)[/tex]
[tex]\sf\implies y-7=\dfrac{11}{20}(x-0)[/tex]
[tex]\sf\implies y=\dfrac{11}{20}x+7[/tex]
Part (b)
Substitute x = 18 into the equation and solve for y:
[tex]\sf\implies y=\dfrac{11}{20}(18)+7=\$16.90[/tex]
Please find 2/3 minus 3/5
Answers
I am not sure how to do for this question! Pls help
Answers
Answer:
wheres the question
Step-by-step explanation:
??????
Eight striped ties and 6 polka dot ties are on a
rack in a dark closet. What is the probability
of drawing out one polka dot tie? Write your
answer as a decimal rounded to two decimal
places.
Answers
Answer: 6 out of 14 or 3 out of 7
Step-by-step explanation: just add up all the ties and put polka dot ties out of the total and
Find Rate of change and y intercept in a graph and table y=3x-3
Answers
Answer:
x=6?
Step-by-step explanation:
I think it's this answer im not sure
Two cars, one traveling north and
one traveling east leave a city.
The car traveling north goes X
miles while the car traveling east
has gone ×+4 miles. If the
distance between the cars at this
moment is 20 miles find the
distance the car traveling east has
traveled.
Answers
5 2⁄5 - 3 7⁄10 = What is the correct answer if the answer is wrong I will come and haunt you
Answers
[tex] \mathsf\red{♧ANSWER♧}[/tex]
[tex] \mathsf \blue{5 \frac{2}{5} - 3 \frac{7}{10} }[/tex]
[tex] \blue \implies \mathsf \green{ \frac{27}{5} - \frac{37}{10} }[/tex]
[tex] \blue \implies \mathsf \green{2( \frac{27}{5} ) - \frac{37}{10} }[/tex]
[tex] \blue \implies \mathsf \green{ \frac{54}{10} - \frac{37}{10} }[/tex]
[tex] \blue \implies \mathsf \green{ \frac{17}{10} = 1 \frac{7}{10} = 1.7}[/tex]
What is the value of the unknown?
4x?+ ?= -2x?
Answers
Answer:
If the whole transaction is written separately from the beginning, an algebraic equation is obtained
Step-by-step explanation:
[tex]4x = s[/tex]
[tex] - 2x = w[/tex]
[tex]w \times s = - 8 {x}^{2} [/tex]
[tex]w = s = s \times s = 16 {x}^{2} [/tex]
[tex] - 8 {x}^{2} + 16 {x}^{2} = 8 {x}^{2} [/tex]
This is the way to get the answer
Two old RSM students were standing ten feet apart when they ran in opposite directions with speeds of 180 feet per minute and 160 feet per minute respectively, how many minutes would pass before they were 1870 feet apart?
Answers
The number of minutes that would pass before they were 1870 feet apart is 5.47 minutes
Since one student runs at a speed of 180 feet per minutes, in time t minutes, he moves a distance of d = 180t.Also, the second student runs at a speed of 160 feet per minute, in time t minutes, he moves a distance of d' = 160t.
Since they are initially 10 feet apart, their total distance apart after t minutes is D = d + 10 + d'
D = 180t + 10 + 160t
D = 340t + 10
Number of minutes before they are 1870 feetMaking t subject of the formula, we have
t = (D - 10)/340
Since they are 1870 feet apart after t minutes, D = 1870 feet.
t = (D - 10)/340
t = (1870 - 10)/340
t = 1860/340
t = 5.47 minutes
So, the number of minutes that would pass before they were 1870 feet apart is 5.47 minutes
Learn more about minutes of distance apart here
https://brainly.com/question/8783264
Find the equation of the line through the points (0, –3) and (4, 5)
Answers
Answer:
y=2x-3
Step-by-step explanation:
Hi there!
We are given the points (0, –3) and (4, 5)
We want to find the equation of the line between these points
There are 3 ways to write the equation of the line, yet the most common way is slope-intercept form, which is y=mx+b, where m is the slope and b is the y intercept
To write the equation of the line in this way, we need to first find the slope of the line
The slope can be found using the formula [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are points
We already have 2 points, but let's label their values to avoid confusion and mistakes when calculating.
m=[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
m=[tex]\frac{5--3}{4-0}[/tex]
Simplify
m=[tex]\frac{5+3}{4-0}[/tex]
m=[tex]\frac{8}{4}[/tex]
Divide
m=2
We found the slope of the line.
Here is the equation of the line so far:
y=2x+b
Now let's find b
As stated before, b is the y intercept of the line, which is the point where the line passes through the y axis; the value of x at the y intercept is 0
One of the points we were given (0, -3) is actually the y intercept of the line!
The value of b is the value of y at the y intercept; in this case, b is equal to -3
Now substitute -3 as b in the equation.
y=2x-3
Hope this helps!
See more on this topic here: https://brainly.com/question/27172025
multiply the two plynomials
(x + 3)( + 9)
(x + 2)(x + 9)
(x - 8)(x - 6)
im really looking for ways to solve it rather than the solution because it would make my hw alot easier. thanks!
Answers
Answer:
1. x² + 12x + 27
2. x² + 11x + 18
3. x² + -14x + 48
Step-by-step explanation:
When you multiply polynomials, you use FOIL.
First
Outer
Inner
Last
For example, to solve the first polynomial (x + 3)(x + 9), you would multiply the first term in each parenthesis to each other. In this case, it would be x · x, which would be equal to x². The next step would be to multiply the first term in the first parenthesis to the last term in the second parenthesis, which are the outer terms. You get 9x when you multiply x by 9. Then, you multiply the inner terms of the polynomial, which is the last term of the first parenthesis and the first term of the second parenthesis. You get 3x. The last part of FOIL is to multiply the last term in each parenthesis to each other. You would multiply 9 and 3 and get 27. Your answer would be x² + 9x + 3x + 27. Simplify the equation to get x² + 12x + 27. That is your final answer. Do the same thing to the other equations to find the answer. (MAKE SURE TO CHECK THE SIGN OF THE TERMS YOU ARE MULTIPLYING FIRST. )
I hope this helped and please mark me as brainliest!
A rule for creating a pattern is given below.
Rule: Subtract 7 from x to get y.
Which ordered pair, (x, y), works for the rule?
Choose 1 answer:
(Choice A)
(10, 17)
(Choice B)
(7, 0)
(Choice C)
(14, 2)
Answers
Answer:
(Choice B)
Step-by-step explanation:
(7, 0)
7 - 7 = 0
Here, we can see that when 7 is subtracted from x, we get 0 (our y)
Hope this helps!
third time posting this question pls help. it's 7 grade maths.pls help i need it I give brainlist
Answers
Answer:
Step-by-step explanation:
7) m + 6 > 17
m > 17- 6
8. 500 + p > 1500
9. Let cost of pencil be 'x' and it is 5 less than y
x < y -5
Cost of pencil and ruler is less than $ 30.
x + y < 30
10. r + 5 > 17
r > 17 - 5
r > 12
12.She is spending $ x. So, we have to subtract from $10.
10 -x < 5
PLS HELP ME !! I REALLT NEED HELP
Answers
Step-by-step explanation:
it clearly says (and also shows it by specifying 4cm × 4cm side lengths) : a square base.
so, all net diagrams not having a square in the middle (but a rectangle or a triangle) are out.
and in fact, all 3 that have a square in the middle, are valid nets that would fold up to the pyramid : the 2nd, 4th and 6th.
pls help me i will mark as brilliant
Answers
The question is not clear.