Answer:
Lf(x) = Lg(x) = Lh(x) = 1 - 2x
value of the functions and their derivative are the same at x = 0
Step-by-step explanation:
Given :
f(x) = (x − 1)^2,
g(x) = e^−2x ,
h(x) = 1 + ln(1 − 2x).
a) Determine Linearization of f, g and h at a = 0
L(x) = f (a) + f'(a) (x-a) ( linearization of f at a )
for f(x) = (x − 1)^2
f'(x ) = 2( x - 1 )
at x = 0
f' = -2
hence the Linearization at a = 0
Lf (x) = f(0) + f'(0) ( x - 0 )
Lf (x) = 1 -2 ( x - 0 ) = 1 - 2x
For g(x) = e^−2x
g'(x) = -2e^-2x
at x = 0
g(0) = 1
g'(0) = -2e^0 = -2
hence linearization at a = 0
Lg(x) = g ( 0 ) + g' (0) (x - 0 )
Lg(x) = 1 - 2x
For h(x) = 1 + ln(1 − 2x).
h'(x) = -2 / ( 1 - 2x )
at x = 0
h(0) = 1
h'(0) = -2
hence linearization at a = 0
Lh(x) = h(0) + h'(0) (x-0)
= 1 - 2x
Observation and reason
The Linearization is the same in every function i.e. Lf(x) = Lg(x) = Lh(x) this is because the value of the functions and their derivative are the same at x = 0
7 women can bake 100 cookies in 14 days. How many would it take for 4 women to bake 240 cookies?
Answer:
it would take 30 and a half days to make 240 cookies
!PLEASE HELP WILL GIVE BRAINLIEST!
An internet service charges $34 per month for internet access. Write an equation to represent the total cost based on the number of months of internet access.
Answer:
34m = c
Step-by-step explanation:
For every month (m) you pay 34 dollars. However many months youu use that service time 34 equals your total cost (c).
Answer:
[tex]let \: cost \: be \: { \bf{c}} \: and \: months \: be \: { \bf{n}} \\ { \bf{c \: \alpha \: n}} \\ { \bf{c = kn}} \\ 34 = (k \times 1) \\ k = 34 \: dollars \\ \\ { \boxed{ \bf{c = 34n}}}[/tex]
The proportion of brown M&M's in a milk chocolate packet is approximately 14% (Madison, 2013). Suppose a package of M&M's typically contains 52 M&M's
Answer:
7 brown M&Ms.
Step-by-step explanation:
This question is not complete, but I will assume that the final question is how many brown M&Ms will be in this package.
0.14 × 52 is our equation.
The answer is 7.28. We cannot have .28 of a brown M&M in a package (unless you count the broken ones) so there will be, on average, 7 brown M&Ms in a package.
(again, the question is incomplete, so this may not be the answer)
what is the perimeter of a triangle?
Answer:
P = side a + side b + side c
Step-by-step explanation:
The perimeter of any polygon is all sides added together.
Answer:
3 X sides please mark me brainlist
pls help with all the questions
Answer:
Step-by-step explanation:
Since, CD is an altitude, ∠CDB will be a right angle.
m∠CDB = m∠CDA = 90°
By applying triangle sum theorem in ΔABC,
m∠CAB + m∠CBA + m∠ACB = 180°
20° + m∠CBA + 90° = 180°
m∠CBA = 180° - 110°
= 70°
Therefore, m∠CBD = 70°
By applying triangle sum theorem in ΔBCD,
m∠BCD + m∠CDB + m∠DBC = 180°
m∠BCD + 90° + 70° = 180°
m∠BCD + 160° = 180°
m∠BCD = 20°
m∠CAD = m∠A = 20°
m∠ACD = 90° - m∠BCD
= 90° - 20°
m∠ACD = 70°
prove the identity sin3x=3sinx-4sin³x
Hi
we know that sin(A+B)=Sin(A)Cos(B)-Cos(A) Sin (B)
cos(2x)=1-2sin²(x)
sin(2x)=2sin(x)cos(x)
Exp:- Sin(3x)=Sin(x+2x)
Sin(x)cos(2x)+cos(x)sin(2x)
sin(x){1-2sin²(x)}+2cos²(x)sin(x)
sin(x)-2sin³(x)+2sin(x){1-sin²(x)}
sin(x)-2sin³(x)+2sin(x)-2sin³(x)
3sin(x)-4sin³(x)
Hope it helps....
Use a Maclaurin series to obtain the Maclaurin series for the given function.
f(x)= 14x cos(1/15x^2)
Answer:
[tex]14x cos(\frac{1}{15}x^{2})=14 \sum _{k=0} ^{\infty} \frac{(-1)^{k}x^{4k+1}}{(2k)!15^{2k}}[/tex]
Step-by-step explanation:
In order to find this Maclaurin series, we can start by using a known Maclaurin series and modify it according to our function. A pretty regular Maclaurin series is the cos series, where:
[tex]cos(x)=\sum _{k=0} ^{\infty} \frac{(-1)^{k}x^{2k}}{(2k)!}[/tex]
So all we need to do is include the additional modifications to the series, for example, the angle of our current function is: [tex]\frac{1}{15}x^{2}[/tex] so for
[tex]cos(\frac{1}{15}x^{2})[/tex]
the modified series will look like this:
[tex]cos(\frac{1}{15}x^{2})=\sum _{k=0} ^{\infty} \frac{(-1)^{k}(\frac{1}{15}x^{2})^{2k}}{(2k)!}[/tex]
So we can use some algebra to simplify the series:
[tex]cos(\frac{1}{15}x^{2})=\sum _{k=0} ^{\infty} \frac{(-1)^{k}(\frac{1}{15^{2k}}x^{4k})}{(2k)!}[/tex]
which can be rewritten like this:
[tex]cos(\frac{1}{15}x^{2})=\sum _{k=0} ^{\infty} \frac{(-1)^{k}x^{4k}}{(2k)!15^{2k}}[/tex]
So finally, we can multiply a 14x to the series so we get:
[tex]14xcos(\frac{1}{15}x^{2})=14x\sum _{k=0} ^{\infty} \frac{(-1)^{k}x^{4k}}{(2k)!15^{2k}}[/tex]
We can input the x into the series by using power rules so we get:
[tex]14xcos(\frac{1}{15}x^{2})=14\sum _{k=0} ^{\infty} \frac{(-1)^{k}x^{4k+1}}{(2k)!15^{2k}}[/tex]
And that will be our answer.
Determine the equation of the line that is parallel to the given line, through the given point.
3x+2y = 10; (8,-11)
Answer:
[tex]y=-\frac{3}{2}x+1[/tex]
Step-by-step explanation:
Hi there!
What we need to know:
Linear equations are typically organized in slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when x is 0)Parallel lines always have the same slope1) Determine the slope (m)
[tex]3x+2y = 10[/tex]
First, we must organize this given equation in slope-intercept form. This will help us identify its slope.
[tex]3x+2y = 10[/tex]
Subtract 3x from both sides
[tex]2y = -3x+10[/tex]
Divide both sides by 2
[tex]y = -\frac{3}{2} x+5[/tex]
Now, we can identify clearly that [tex]-\frac{3}{2}[/tex] is in the place of m in [tex]y=mx+b[/tex], making it the slope. Because parallel lines have the same slope, this makes the slope of the line we're currently solving for [tex]-\frac{3}{2}[/tex] as well. Plug this number into [tex]y=mx+b[/tex]:
[tex]y=-\frac{3}{2}x+b[/tex]
2) Determine the y-intercept (b)
[tex]y=-\frac{3}{2}x+b[/tex]
Plug in the given point (8,-11) and solve for b
[tex]-11=-\frac{3}{2}(8)+b\\-11=-\frac{24}{2}+b\\-11=-12+b[/tex]
Add 12 to both sides
[tex]1=b[/tex]
Therefore, the y-intercept of the line is 1. Plug this back into [tex]y=-\frac{3}{2}x+b[/tex]:
[tex]y=-\frac{3}{2}x+1[/tex]
I hope this helps!
Zach read a book for 10 minutes every weekend in the first month, 20 minutes in the second month, 40 minutes in the third month, and 80 minutes in the fourth month.
Victoria read a book for 35 minutes every weekend in the first month, 50 minutes in the second month, 65 minutes in the third month, and 80 minutes in the fourth month.
Which statement best describes the methods used by Zach and Victoria to increase the time they spent reading a book? (1 point)
Select one:
a. Zach's method is linear because the number of minutes increased by an equal factor every month.
b. Victoria's method is linear because the number of minutes increased by an equal number every month.
c. Both Victoria's and Zach's methods are exponential because the number of minutes increased by an equal factor every month.
d. Both Victoria's and Zach's methods are exponential because the number of minutes increased by an equal number every month.
9514 1404 393
Answer:
b. Victoria's method is linear because the number of minutes increased by an equal number every month
Step-by-step explanation:
Zach's reading doubled each month, a characteristic of an exponential function.
Victoria's reading increased by 15 minutes each month, characteristic of a linear function.
The only reasonable description among those offered is the one shown above: choice B.
a construction company built a scale
Answer:
There are no shortcuts to scaling successfully. It takes just as much — or more — work as it did to start the company in the first place. Take control of the transition. Get organized with tools that support your employees in their day-to-day roles, making it easier for them to get more done as the company grows.
Urgent help!!!
*Picture included
Answer:
3x+4
Step-by-step explanation:
When you factor 9x^2+24x+16, it factors to (3x+4)^2
Factoring 9x^2 - 16 factors to (3x+4)(3x-4)
Therefore the common factor is 3x+4
I hope this helps!
A bus started from Kathmandu and reached khanikhola,26km far from Kathmandu, in one hour. if the bus had uniform acceleration, calculate the final velocity of the bus and acceleration.
Answer:
a = 0.0040 m/s², v = 14.4 m/s.
Step-by-step explanation:
Given that,
The distance between Kathmandu and Khanikhola, d = 26 km = 26000 m
Time, t = 1 hour = 3600 seconds
Let a is the acceleration of the bus. Using second equation of motion,
[tex]d=ut+\dfrac{1}{2}at^2[/tex]
Where
u is the initial speed of the bus, u = 0
So,
[tex]d=\dfrac{1}{2}at^2\\\\a=\dfrac{2d}{t^2}\\\\a=\dfrac{2\times 26000}{(3600)^2}\\\\a=0.0040\ m/s^2[/tex]
Now using first equation of motion.
Final velocity, v = u +at
So,
v = 0+0.0040(3600)
v = 14.4 m/s
Hence, this is the required solution.
Which of these is an example of technology?
an idea for a story
the first wheel ever built
an engineer
Answer:
the first wheel ever built
Answer:
The first wheel ever built
Step-by-step explanation
(*) Sorry for my late answer but I hope this helps others that are looking for this.
100% in the test :)
Precision manufacturing: A process manufactures ball bearings with diameters that are normally distributed with mean 25.0 millimeters and standard deviation 0.07 millimeter. Round the answers to at least four decimal places. (a) Find the 60th percentile of the diameters. (b) Find the 67th percentile of the diameters. (c) A hole is to be designed so that 2% of the ball bearings will fit through it. The bearings that fit through the hole will be melted down and remade. What should the diameter of the hole be
Answer:
a) The 60th percentile of the diameters is of 25.0177 millimeters.
b) The 67th percentile of the diameters is of 25.0308 millimeters.
c) The diameter of the hole should be of 24.8562 millimeters.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Normally distributed with mean 25.0 millimeters and standard deviation 0.07 millimeter.
This means that [tex]\mu = 25, \sigma = 0.07[/tex]
(a) Find the 60th percentile of the diameters.
This is X when Z has a p-value of 0.6, so X when Z = 0.253.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0.253 = \frac{X - 25}{0.07}[/tex]
[tex]X - 25 = 0.253*0.07[/tex]
[tex]X = 25.0177[/tex]
The 60th percentile of the diameters is of 25.0177 millimeters.
(b) Find the 67th percentile of the diameters.
This is X when Z has a p-value of 0.67, so X when Z = 0.44.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0.44 = \frac{X - 25}{0.07}[/tex]
[tex]X - 25 = 0.44*0.07[/tex]
[tex]X = 25.0308[/tex]
The 67th percentile of the diameters is of 25.0308 millimeters.
(c) A hole is to be designed so that 2% of the ball bearings will fit through it. The bearings that fit through the hole will be melted down and remade. What should the diameter of the hole be.
This is the 2nd percentile, which is X when Z has a p-value of 0.08, so X when Z = -2.054.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-2.054 = \frac{X - 25}{0.07}[/tex]
[tex]X - 25 = -2.054*0.07[/tex]
[tex]X = 24.8562[/tex]
The diameter of the hole should be of 24.8562 millimeters.
Figure A
Figure B
Figure C
3 ft
3 ft
Sf
3 ft
3 ft
5 ft
5 ft
3 ft
3 ft
Sft
3 ft
3 ft
Х
?.
None of the figures
(a) Which figures are rectangles?
Mark all that apply.
Figure A Figure B Figure C
(b) Which figures are squares?
Mark all that apply.
Figure A Figure B Figure C
(c) Which figures are parallelograms?
Mark all that apply.
Figure A
Figure B
Figure C
None of the figures
None of the figures
Answer:
a) Figure B and Figure C
b) Figure C
c) Figure A, Figure B, and Figure C
Step-by-step explanation:
a) Rectangles are shapes that have four sides, and four right angels. Right angles are angles that are 90 degrees.
The only shapes with four sides AND four right angles are Figure C and Figure B.
b) Squares are shapes with four EQUAL sides and four right angles. The only shape with four equal sides and four right angles is Figure C.
c) Parallelograms are any shapes with four sides. All of these shapes have four sides.
Hope this helps!
The figure below shows two triangles on the coordinate grid: A coordinate grid is shown from positive 6 to negative 6 on the x axis and from positive 6 to negative 6 on the y axis. A triangle ABC is shown with vertex A on ordered pair negative 4, negative 1, vertex B on ordered pair negative 3, negative 1 and vertex C on ordered pair negative 4, negative 4. Another triangle A prime B prime C prime is shown with vertex A prime on ordered pair negative 1, 1, vertex B prime on ordered pair negative 2, 1, and vertex C prime on ordered pair negative 1, 4. What set of transformations is performed on triangle ABC to form triangle A′B′C′? A translation 5 units up, followed by a 270-degree counterclockwise rotation about the origin A 270-degree counterclockwise rotation about the origin, followed by a translation 5 units up A 180-degree counterclockwise rotation about the origin, followed by a translation 5 units to the right A translation 5 units to the right, followed by a 180-degree counterclockwise rotation about the origin
Option D. The set of transformation that is performed on this triangle (ABCD)' is A translation 5 units to the right, followed by a 180-degree counterclockwise rotation about the origin
How to solve for the transformationThe answer choices have been shown to have all solutions to be rotated around their origin.
To shift the triangle, It has to be done through the connection the points ABC ' to the origin in such a way that the line is extended as we can seen in the diagram.
Read more on reflection here:
https://brainly.com/question/1908648
#SPJ1
help with this please !!
Answer:
B
Step-by-step explanation:
The coeffecients (I totally didn't spell that right) and variables match up.
A student-faculty government committee of 4 people is to be formed from 20 student
volunteers and 5 faculty volunteers.
a. If one person from the group of volunteers is chosen at random to draw the names
out of a hat, what is the probability that the person drawing the names is a student?
b. How many ways can the committee of four be formed if there are no restrictions on
composition.
C. How many ways can two of the students be chosen?
d. How many ways can 2 faculty be chosen?
e. What is the probability that the random selection of the four-person committee will
result in two students and two faculty?
the answer is c i just had this question your welcome
Which of the following expressions would represent a class of 42 students divided equally into 7 groups?
Answer: [tex]7\sqrt{42}[/tex]
Step-by-step explanation:
42 students divided equally into 7 groups means 42 divided by 7, and [tex]7\sqrt{42}[/tex] is the only choice that shows that.
7√42. is the expressions would represent a class of 42 students divided equally into 7 groups
What is Division?A division is a process of splitting a specific amount into equal parts.
Given,
A class of forty two Forty two students divided equally into 7 groups.
Forty two students divided equally into seven groups means forty two divided by seven, and
this can be done by using 7√42.
42 students divided equally into 7 groups means forty two divided by seven
Hence 7√42. is the expressions would represent a class of 42 students divided equally into 7 groups
To learn more on Division click:
https://brainly.com/question/21416852
#SPJ2
Gieo 120 hạt giống của một loại cây thấy có 15 hạt nảy mầm. Với độ tin cậy 95% hãy tìm ước lượng khoảng cho tỷ lệ nảy mầm của loại hạt giống đó.
Mn giúp mình với ạ
Answer:
sorry can't understand the language
For the problem I tried dividing but my answers were not correct. How can I solve this problem then? Can someone help me out here please?
Answer:
8
Step-by-step explanation:
5 = 40
1 = x
Then we multiply by the rule of crisscrossing
5 x X = 40 x 1
5x = 40 then divide both by 5
X = 8
The graph below represents the following system of inequalities.
Answer:
(2,3)
Step-by-step explanation:
how to solve these questions?!
Answer:
1. x + 4 = 9
Hint: the word 'sum' generally refers to addition.
2. 10a = 70
3. [tex]\frac{3}{4} t[/tex] = 15
4. [tex]\frac{1}{4} x[/tex] - 4 = 4
Which number produce a rational number when multiples by 1/5
Answer:
-2/3
Step-by-step explanation:
A rational number is a number that can be expressed by a fraction so when y add to fractions it’s a rational number.
Find the limit of f as or show that the limit does not exist. Consider converting the function to polar coordinates to make finding the limit easier. f(x,y)
Answer:
[tex]\lim_{(x,y) \to (0,0)} \frac{x^2 \sin^2y}{x^2+2y^2} = 0[/tex]
Step-by-step explanation:
Given
[tex]f(x,y) = \frac{x^2 \sin^2y}{x^2+2y^2}[/tex]
Required
[tex]\lim_{(x,y) \to (0,0)} f(x,y)[/tex]
[tex]\lim_{(x,y) \to (0,0)} f(x,y)[/tex] becomes
[tex]\lim_{(x,y) \to (0,0)} \frac{x^2 \sin^2y}{x^2+2y^2}[/tex]
Multiply by 1
[tex]\lim_{(x,y) \to (0,0)} \frac{x^2 \sin^2y}{x^2+2y^2}\cdot 1[/tex]
Express 1 as
[tex]\frac{y^2}{y^2} = 1[/tex]
So, the expression becomes:
[tex]\lim_{(x,y) \to (0,0)} \frac{x^2 \sin^2y}{x^2+2y^2} \cdot \frac{y^2}{y^2}[/tex]
Rewrite as:
[tex]\lim_{(x,y) \to (0,0)} \frac{x^2 y^2}{x^2+2y^2} \cdot \frac{\sin^2y}{y^2}[/tex]
In limits:
[tex]\lim_{(x,y) \to (0,0)} \frac{\sin^2y}{y^2} \to 1[/tex]
So, we have:
[tex]\lim_{(x,y) \to (0,0)} \frac{x^2 y^2}{x^2+2y^2} *1[/tex]
[tex]\lim_{(x,y) \to (0,0)} \frac{x^2 y^2}{x^2+2y^2}[/tex]
Convert to polar coordinates; such that:
[tex]x = r\cos\theta;\ \ y = r\sin\theta;[/tex]
So, we have:
[tex]\lim_{(x,y) \to (0,0)} \frac{(r\cos\theta)^2 (r\sin\theta;)^2}{(r\cos\theta)^2+2(r\sin\theta;)^2}[/tex]
Expand
[tex]\lim_{(x,y) \to (0,0)} \frac{r^4\cos^2\theta\sin^2\theta}{r^2\cos^2\theta+2r^2\sin^2\theta}[/tex]
Factor out [tex]r^2[/tex]
[tex]\lim_{(x,y) \to (0,0)} \frac{r^4\cos^2\theta\sin^2\theta}{r^2(\cos^2\theta+2\sin^2\theta)}[/tex]
Cancel out [tex]r^2[/tex]
[tex]\lim_{(x,y) \to (0,0)} \frac{r^2\cos^2\theta\sin^2\theta}{\cos^2\theta+2\sin^2\theta}[/tex]
[tex]\lim_{(x,y) \to (0,0)} \frac{r^2\cos^2\theta\sin^2\theta}{\cos^2\theta+2\sin^2\theta}[/tex]
Express [tex]2\sin^2 \theta[/tex] as [tex]\sin^2\theta+\sin^2\theta[/tex]
So:
[tex]\lim_{(x,y) \to (0,0)} \frac{r^2\cos^2\theta\sin^2\theta}{\cos^2\theta+\sin^2\theta+\sin^2\theta}[/tex]
In trigonometry:
[tex]\cos^2\theta + \sin^2\theta = 1[/tex]
So, we have:
[tex]\lim_{(x,y) \to (0,0)} \frac{r^2\cos^2\theta\sin^2\theta}{1+\sin^2\theta}[/tex]
Evaluate the limits by substituting 0 for r
[tex]\frac{0^2 \cdot \cos^2\theta\sin^2\theta}{1+\sin^2\theta}[/tex]
[tex]\frac{0 \cdot \cos^2\theta\sin^2\theta}{1+\sin^2\theta}[/tex]
[tex]\frac{0}{1+\sin^2\theta}[/tex]
Since the denominator is non-zero; Then, the expression becomes 0 i.e.
[tex]\frac{0}{1+\sin^2\theta} = 0[/tex]
So,
[tex]\lim_{(x,y) \to (0,0)} \frac{x^2 \sin^2y}{x^2+2y^2} = 0[/tex]
Which ordered pair makes both inequalities true?
y < 3x – 1
y > –x + 4
Answer:
SECOND ONE
Step-by-step explanation:
Is this right?? If not please tell me the answers
Answer:
TAMA PO
Step-by-step explanation:
Paki brainliest nadin po
What is the depth of water in a tank with 300,000 gallons of water at 70F when the pressure gauge at the bottom of the tank reads 23 psig?
Answer:
53.08 ft
Step-by-step explanation:
The pressure at the bottom of the tank, P = ρgh where ρ = density of water = 1000 kg/m³, g = acceleration due to gravity = 9.8 m/s² and h = depth of water in tank.
Since the pressure at the bottom of the tank, P = ρgh, making h subject of the formula, we have
h = P/ρg
Since P = 23 psig = 23 × 1 psig = 23 × 6894.76 Pa = 158579.48 Pa
Substituting the values of the other variables into h, we have
h = P/ρg
h = 158579.48 Pa/(1000 kg/m³ × 9.8 m/s²)
h = 158579.48 Pa/(9800 kg/m²s²)
h = 16.18 m
h = 16.18 × 1 m
h = 16.18 × 3.28 ft
h = 53.08 ft
Which problem has a greater (bigger) answer? Solve both, choose the one that has the bigger answer and explain (1-2 sentences) how you found your
answer.
1) (2 + 3) (5 + 5)
2)2 + 3 x 5 + 5 =
I need help pleaseeee
Answer:
1) has bigger answer
Step-by-step explanation:
1)
solving parenthesis first we get
5 × 10
so, the answer = 50
2)
solving 3 × 5 first as we have to see multiplication first then addition
2 + 15 + 5
22
comparing both
50 > 22
so problem 1 has a bigger answer
What is the sum of the 14th square number and the 3rd square number?
Answer:23
Step-by-step explanation:
