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
NO LINKS!!
Part 1: Figure A is a dilated image of Figure B. Find the scale factor. #1 and 2
Answers
Take one side
B=3unitsA=9unitsScale factor (A to B)
[tex]\\ \rm\rightarrowtail \dfrac{3}{9}=\dfrac{1}{3}[/tex]
Scale factor (B to A)=3#2
B=6unitsA=4unitsScale factor Bto A:-
4/6=2/3Scale factor (Ato B)=3/2
Answer:
The scale factor can either increase or decrease the size of an object. To find the scale factor of dilation:
[tex]\textsf{Scale factor} = \dfrac{\textsf{Dimension of the new shape}}{\textsf{Dimension of the original shape}}[/tex]
For these questions:
new shape = Figure Aoriginal shape = Figure BQuestion 1
Top edge of Figure A = 9 unitsTop edge of Figure B = 3 units[tex]\sf \implies scale \ factor=\dfrac{9}{3}=3[/tex]
Question 2
Width of Figure A = 4 unitsWidth of Figure B = 6 units[tex]\sf \implies scale \ factor=\dfrac46=\dfrac23[/tex]
Solve each pair of simultaneous equations giving both solutions. You need to multiply both equations by suitable numbers before adding \subtracting to eliminate.
a) 6x - 7y = 9
3x + 2y = 54
b) 4x - 5y = 12
2x - 3y = 8
c) 4x - 2y = 28
3x + 3y = 12
please work it out and clear. who ever answer give them brainlest answer
Answers
Answer:
a) x = 12 y = 9
b) x = -2 y = -4
c) x = 6 y = -2
Step-by-step explanation:
a)
Equation 1: 6x - 7y = 9
Equation 2: 3x + 2y = 54
Multiply Equation 2 by 2:
⇒ 6x + 4y = 108
Subtract equations:
6x + 4y = 108
- 6x - 7y = 9
11y = 99
Divide both sides by 11:
⇒ y = 9
Substitute found value of y into Equation 1 and solve for x:
⇒ 6x - 7(9) = 9
⇒ 6x - 63 = 9
⇒ 6x = 72
⇒ x = 12
---------------------------------------------------------------------------------------------------
b)
Equation 1: 4x - 5y = 12
Equation 2: 2x - 3y = 8
Multiply Equation 2 by 2:
⇒ 4x - 6y = 16
Subtract equations:
4x - 6y = 16
- 4x - 5y = 12
-y = 4
Divide both sides by -1:
⇒ y = -4
Substitute found value of y into Equation 1 and solve for x:
⇒ 4x - 5(-4) = 12
⇒ 4x + 20 = 12
⇒ 4x = -8
⇒ x = -2
---------------------------------------------------------------------------------------------------
c)
Equation 1: 4x - 2y = 28
Equation 2: 3x + 3y = 12
Multiply Equation 1 by 3:
⇒ 12x - 6y = 84
Multiply Equation 2 by 4:
⇒ 12x + 12y = 48
Subtract equations:
12x - 6y = 84
- 12x + 12y = 48
-18y = 36
Divide both sides by -18:
⇒ y = -2
Substitute found value of y into Equation 1 and solve for x:
⇒ 4x - 2(-2) = 28
⇒ 4x + 4 = 28
⇒ 4x = 24
⇒ x = 6
Need help with these geometric questions
Answers
Check the picture below.
a)
notice, since lines KP and NL are parallel, they make up the same angle in purple when they hit line MK, and both triangles share the green angle at M.
b)
notice, LP = LK = 14, and in an isosceles twin sides stemming from a vertex make twin angles.
Help picture below problem 12
Answers
Answer:
78°
Step-by-step explanation:
Angles on a straight line = 180°
AD is the straight line
Angle BFA = 48
Angle CFD = 54
54 + 48 = 102
180 - 102 = 78
Therefore, Angle BFC = 78°
In the figure; Triangle ABC is isosceles with BC=AC . If ∠A = 70, find the values of x and y . Give reasons for your answer.
Captionless Image
Answers
Answer:
∠B = 70 and ∠C = 40
Step-by-step explanation:
The image is not loading for me but with isosceles triangles there will two angles that are the same and one different angle.
All the angles will add up to equal 180 degrees.
In this case the different angle would angle C as the two same lines meet at that point.
From this you can that angle A and B are the same, both 70, so angle C would be:
180 (all the angles of a triangle added together) - 70 - 70 = 40
I'm assuming that x and y are angles B and C as they are not stated so they would be: ∠B = 70 and ∠C = 40.
Here is a diagram to demonstrate this:
{(4x+2y=6),(-2x+2y=18):} Solve by using the elimination method
Please help and show me how you did it
Answers
Answer:
[tex]\displaystyle [-2, 7][/tex]
Step-by-step explanation:
You want to eradicate one pair of variables so they are set to zero. It does not matter which pair is selected:
[tex]\displaystyle \left \{ {{4x + 2y = 6} \atop {-2x + 2y = 18}} \right.[/tex]
{½[4x + 2y = 6]
{−2x + 2y = 18
>> [tex]\displaystyle \left \{ {{2x + y = 3} \atop {-2x + 2y = 18}} \right. \\ \\ \frac{3y}{3} = \frac{21}{3} \\ \\ \\ y = 7[/tex]
Plug this back into the system to get the x-value of [tex]\displaystyle -2.[/tex]
I am joyous to assist you at any time.
construct the exponential function that contains the points (0,2) and (3,54)
Answers
The exponential function that passes through (0,2) and (3,54) is a growth function
The exponetial function is y = 2 * 3^x
How to construct the exponential function?The points are given as:
(x,y) = (0,2) and (3,54)
An exponential function is represented as:
y = ab^x
Substitute the points in the equation
2 = ab^0 and 54 = ab^3
Solve 2 = ab^0
a = 2
Substitute 2 for a in 54 = ab^3
54 = 2b^3
Divide by 2
27 = b^3
Take the cube roots of both sides
b = 3
So, we have:
y = ab^x
This becomes
y = 2 * 3^x
Hence, the exponetial function is y = 2 * 3^x
Read more about exponential functions at:
https://brainly.com/question/24077767
solve for X 3.5x/9= 4.2/5 Please help me
Answers
Answer:
x=2.16
Step-by-step explanation:
1. Cross multiply. 3.5x(5) = 9(4.2)
2. Simplify. 17.5x=37.8
3. Divide both sides by 17.5. x=2.16
Sort all of the following triangle side lengths into if each set would form a right, acute, or obtuse triangle.
Answers
Answer:
acute, acute, obtuse*, right, obtuse
Step-by-step explanation:
The Pythagorean theorem is used as a reference for classifying triangles from their side lengths. If the sum of the squares of the short sides is equal to the square of the long side, then the triangle is a right triangle. If the long side is too short, then triangle is acute. If the long side is too long, the triangle is obtuse.
__
The math can be tedious, so it is convenient to let a spreadsheet do it. The results are attached.
The first two triangles are acute; the 4th one is a right triangle, and the remaining two are obtuse.
_____
Additional comment
* Note that triangle #3, with side lengths 2, 4, 6, is classified as "obtuse" because the largest angle is greater than 90°. In fact, with those side lengths, the largest angle is 180°. Some would argue it isn't a triangle at all because its area is 0 and it looks like a line segment.
(Our spreadsheet doesn't care if the triangle inequality is not satisifed. It is only concerned with the Pythagorean theorem.)
find the equation (in terms of x) of the line through the points (-2,1) and(2,9)
Y=
Answers
Answer:
2
Step-by-step explanation:
gradient =y² -y¹ /x²-x¹
=9-1/2--2
=8/4
=2
Answer:
y = 2x + 5
Step-by-step explanation:
There are 2 ways to find this equation:
The first way: We have: y = ax + b (this is the line, right?)
The line is through the point (-2, 1) so we have:
1 = (-2)a + b (1)
The line is also through the point (2, 9) so we have:
9 = 2a + b. (2)
From (1) and (2) we get a equals 2, b equals 5. Then:
y = 2x + 5
The second way:
Let A(-2, 1) and B(2, 9), then AB = (4, 8).
=> The normal vector of this line is n = (-2, 1).
The line that is through the points A(-2, 1) and B(2, 9), and has the normal vector n=(-2, 1) has the equation:
[tex]-2(x - 2) + 1(y - 9) = 0[/tex]
[tex]-2x + y - 5 =0\\ < = > y = 2x + 5[/tex]
7/8m+9/10-2m-53 answer
Answers
Answer:
− (45m+2084)/40
Step-by-step explanation:
I do not have one sorry,
area of the base= 75square inches and heigh = 15 inches
Answers
75 ÷ 15 = 5
the width is 5 inches
One person is selected at random from a class of 15 males and 14 females. Find the odds against selecting
a) a female.
b) a male.
Answers
Answer:
48% chance to be female and 52% chance to be male.
Step-by-step explanation:
14 female + 15 males = 29 total people
a) 14 females/29 total = 0.48... * 100 = 48%
b) 15 males/29 total = 0.57.... * 100 = 52%
HELPPPP big brains I need this urgently
Answers
Answer:
9 or 9 months (if you have to add units)
Step-by-step explanation:
Subtract 15 from his savings:
420-15 = $405
This is the amount left he has to pay the monthly membership
405/45 = 9
9 is the number of months
Answer:
9 months
Step-by-step explanation:
Set up and solve the equation 15 + 45x = 420. Begin by subtracting 15 from both sides. After paying 15 dollars for the deposit, He will have $405 dollars left. Divide both sides of the equation by 45. When you divide 405 by 45 that will tell you how many months the membership can be paid.
Which expression represents 25 times the sum of m and 3?
Answers
Answer:
25(m+3)
Step-by-step explanation:
25 is multiplied by (m+3)
'the sum of m and 3' is a quantity which must be indicated using parentheses
Hello!
The sum of means we add:
m+3
Multiply it times 25:
25(m+3)
The answer is Option C.
Now, the option you selected is wrong for the following reasons:
If you translate it into a verbal phrase, this is what it means:
25 plus the product of m and 3
Hence, Option C is correct.
Hope everything is clear.
Let me know if you have any questions!
Always remember: Knowledge is power! :-)
If 14 is added to a number, the result is 40 less than twice the number. Find the number.
Answers
Answer:
Asher should be 61
Step-by-step explanation:
.......................................
Answers
Answer:
what is your question??????
Step-by-step explanation:
What is the slope-intercept equation for this line?
y = [?]x+ []
Answers
Answer:
y=3x+1
Step-by-step explanation:
Find the mean median and range of the data 0,1,1,2,2,3,3,3,4,4,4,4,5,5,5,5,6,6,7,7,7,8,8,9,9,17
Answers
Answer:
Mean: 5.19 or 5.2
Median: 5
Range: 17
Step-by-step explanation:
Range: Q3 - Q1
0, 1, 1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 7, 7, 7, 8, 8, 9, 9, 17
Here, we have 26 numbers
Minimum: 0
Maximum: 17
Median: 5 + 5 = 10/2 = 5
Lower quartile (Q1): 3
Upper quartile (Q3): 7
Range (biggest # - the smallest #): 17 - 0 = 17
Mean (add up all the numbers, and divide it by 26): 135/26 = 5.19 or 5.2
Hope this helps!
trigonometric formulas
Answers
Answer:
all shown in the picture !
Step-by-step explanation:
also shown in the picture
En un estadio 6/8 de los asistentes son mayores edad y de estos 2/4 son mujeres ¿que fraccion de los asistentes mayores de edad son mujeres?
Answers
Answer: 3/8
Step-by-step explanation: 6/8 x 2/4 = 3/8
The fraction of attendees of legal age who are women are 3/8
What is Equation Modelling?Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
We have in a stadium, 6/8 of the attendees are older and of these 2/4 are women.
The fraction of attendees of legal age who are women are -
2/4 of 6/8
2/4 x 6/8
12/32
3/8
Therefore, the fraction of attendees of legal age who are women are 3/8
To solve more questions on equation modelling, visit the link below-
brainly.com/question/9144182
#SPJ2
[English translation of question -
In a stadium, 6/8 of the attendees are older and of these 2/4 are women, what fraction of the attendees of legal age are women?
Spanish translation of answer -
Tenemos en un estadio, 6/8 de los asistentes son mayores y de estos 2/4 son mujeres.
La fracción de asistentes mayores de edad que son mujeres son:
2/4 de 6/8
2/4 x 6/8
32/12
3/8
Por tanto, la fracción de asistentes mayores de edad que son mujeres son 3/8
]I really need help with the answers
Answers
Answer:
Part A: 512 ft²
Part B: 3 cans
Step-by-step explanation:
Part A:
We can divide the shape into 2 areas or rectangles.
The top rectangle's area: 20 x 12 =240
The bottom: 34 x 8 = 272
add these 2 up, 240 +272, and you get 512, the area of this figure.
Part B:
We have to divide the number of feet covered by the area:
512/200 = 2.56
However, we half to round up, cause we cant buy part of a can, we have to buy a whole one.
So, we get 3 cans.
nine times a number p plus two
Can someone plss translate this into a algebraic expression.
Answers
Answer:
9n + 2
Step-by-step explanation:
Answer:
[tex]9p+2[/tex]
Hope This Helps! Please give Brainliest!
Simplify the expression. (x)^2(2xy^3)^5
Answers
Answer:
32x^7y^15
Step-by-step explanation:
x^2(2xy^3)^5
can be simplified by adding up the x and y values.
can someone please tell me the answer to this I can’t figure it out!!
Answers
Answer:
the answer is (0, 0) trust me
In circle O. AD and BE are diameters. The measure of arc AB is 55° and the measure of arc CD is 25° B с F D E What is the measure of BC ? 090 O 110 O 100 O 80
Answers
Answer:
100°
Step-by-step explanation:
the total of all angles around O on one side of AD is 180° (as that would represent a half-circle).
and the sum of the arc angles AB + BC + CD covers the whole 180°.
so, we have
180 = 55 + BC + 25
180 = 80 + BC
BC = 100°
Question 1
Let f(x) = 2x^2 - 3x - 4 and g(x) = x + 5. Find (fg)(x).
Answers
The function (fg)(x) is a composite function
The value of the function (fg)(x) is 2x^3 + 7x^2 - 19x - 20
How to determine the function (fg)(x)?The functions are given as:
f(x) = 2x^2 - 3x - 4 and g(x) = x + 5.
To calculate (fg)(x), we make use of
(fg)(x) = f(x) * g(x)
So, we have:
(fg)(x) = (2x^2 - 3x - 4) * (x + 5)
Expand
(fg)(x) = 2x^3 - 3x^2 - 4x + 10x^2 - 15x - 20
Collect like terms
(fg)(x) = 2x^3 - 3x^2 + 10x^2 - 4x - 15x - 20
Evaluate
(fg)(x) = 2x^3 + 7x^2 - 19x - 20
Hence, the function (fg)(x) is 2x^3 + 7x^2 - 19x - 20
Read more about composite function at:
https://brainly.com/question/10687170
A={ 0,1,3,5,6}; B={1,2,3,7} draw the venn diagram of AUB Writ
Answers
Answer:
Here,
n(A)={0,1,3,5,6}
n(B)={1,2,3,7}
n(AUB)=?
we know that,
AUB={0,1,2,3,5,6,7}
Step-by-step explanation:
is it okay ?
hopefully it works <3 ❣️
Arkansas is __________ of Oklahoma?
Answers
Answer:
East
Step-by-step explanation:
Arkansas is East of Oklahoma.
Refer to the image below:
Answer: East
Step-by-step explanation:
Which of the following numbers is the sum of 82.545 and 128.580 written with the correct number of significant digits? A. 211.1225 B. 211.125 C. 211.13 D. 211.130
Answers
When we add 82.545 and 128.580 we get a total of 211.125, now the closest number to the answer is B. 211.125Addition of Numbers
Mathematical OperationsGiven Data
Number one = 82.545Number two = 128.580Apart from addition of numbers there are other mathematical operations we can perform on integer numbers like in our example above
they are
SubtractionMultiplicationDivisionModulus ---This will return the remainder of the numbers when dividedTotal Number = 82.545 + 128.580Total Number = 211.125
Learn more about Mathematical Operations of numbers here:https://brainly.com/question/10679598
Answer:
B
Step-by-step explanation:
Took the test, have a good day.