Answer:
x ∈ [-0.369, 0.678]
Step-by-step explanation:
To prove - [tex]\sqrt[4]{1 + 2x}[/tex] ≈ 1 + [tex]\frac{1}{2}[/tex] x
As given , f(x) = [tex]\sqrt[4]{1 + 2x}[/tex]
As we know that the linear approximation can be defined as :
L(x) = f(a) + f'(a)(x-a) .........(1)
Now,
We have to show that at a = 0 , equation (1) satisfies
Now,
f(0) = [tex]\sqrt[4]{1 + 0}[/tex] = 1
Also,
f'(x) =
[tex]\frac{d}{dx} (\sqrt[4]{1 + 2x} ) = \frac{1}{4}(1 + 2x)^{\frac{1}{4} - 1}\frac{d}{dx}(1 + 2x) ) \\ = \frac{1}{4}(1 + 2x)^{\frac{-3}{4} } (2)\\ = \frac{1}{2}(1 + 2x)^{\frac{-3}{4} }\\[/tex]
∴ we get
f'(x) = [tex]\frac{1}{2}(1 + 2x)^{-\frac{3}{4} }[/tex]
⇒f'(0) = [tex]\frac{1}{2}[/tex]
Now, equation (1) becomes
L(x) = f(0) + f'(0)(x-0)
= 1 + [tex]\frac{1}{2}[/tex] (x)
⇒ [tex]\sqrt[4]{1 + 2x}[/tex] ≈ 1 + [tex]\frac{1}{2}[/tex] x
Hence verified.
Now,
|[tex]\sqrt[4]{1 + 2x}[/tex] - (1 + [tex]\frac{1}{2}[/tex] x ) | ≤ 0.1
⇒ -0.36893 ≤ x ≤ 0.67766
⇒x ∈ [-0.369, 0.678]
PLEASE HELP, Will give brainliest if u help and 38 points.
You are deciding between two laptops to purchase. The first laptop has an initial value
of $2000 but loses 14% of its value every year. The second laptop has an initial value
of $1200 but loses 11% of its value every year.
a. Write functions that represent the values (in dollars) of the laptops after t years.
Then graph the functions in the same coordinate plane.
b. Find the approximate monthly percent decrease in value for each laptop.
C. Which laptop should you buy if you plan on selling the laptop in 5 years? Explain
your reasoning
Step-by-step explanation:
a)
The first laptop
Initial value- $2000Value loss - 14% every yearFunction for value- V(t) = 2000*0.86^tThe second laptop
Initial value- $1200Value loss - 11% every yearFunction- V(t) = 1200*0.89^tb)
Monthly percent decrease
The first laptop:
14%/12 = 1.16%The second laptop:
11%/12 = 0.92%c)
The second laptop will lose less value in 5 years hence is better choice
See the graph attached
Find the values of x and y.
Answer:
x = 20 (degrees)
y = 70 (degrees)
Step-by-step explanation:
The angle adjacent to the one labeled 40° is supplementary, so it would measure 140°. And the obtuse triangle is an isosceles, which means that x is half of 180° - 140°, so x = 1/2(40°) = 20°
To find y, subtract 90° and x from 180°
y = 180° - 90° - 20°
y = 70°
Answer:
x = 20 and y = 70
Step-by-step explanation:
x = 20 and y = 70
If a pound of turkey costs $0.82, how much will n pounds cost?
The value of a professional basketball player's autographed basketball rose 20% in the last year. It is now worth $264. What was it worth a year ago? and here is 100 points thx
Answer:
$211.20
Step-by-step explanation:
20% of $264 is 52.8
264 - 52.8 = $211.20
Answer:
220
Step-by-step explanation:
What is the slope of the line? question 3
Answer:
slope =1
Step-by-step explanation:
hope it help you
Answer:
Undefined.
Step-by-step explanation:
The x-coordinates of the points along the straight line are always 1.
slope = change in y-coordinate/change in x-coordinate.
Since the change in x-coordinate is 0 (1-1=0), the denominator in the above will be 0 and the fraction (i.e. the slope) would be undefined.
Bebe's Bakery can bake 175 loaves of bread in 5 hours as shown on the double number line diagram below. 5 Number of Hours Loaves of Bread 175 At that rate, how many loaves of bread can Bebe's Bakery bake in 8 hours? A. 35 loaves B. 240 loaves C. 280 loaves D. 350 loaves
Answer:
double number line diagram below. 5 Number of Hours Loaves of Bread 175 At Bakery bake in 8 hours? A. 35 loaves B. 240 loaves
Step-by-step explanation:
What is the decimal Expansion of the following fraction?
Answer:
B
Step-by-step explanation:
1/25 = 0.04 only. this is surely the anwer
What is 50 x 79 x 27 + 69
106,719
Answer:
[tex]50 \times 79 \times 27 + 69 \\ \\ = 106,650 + 69 \\ \\ = 106,719[/tex]
Answer:
173790.07374
Step-by-step explanation:
if u apply DMAS rule it will give u same answer if u simply do this it will again give u same answer for sure!
first multiply each then add 60
pls mark this brainliest
n thanks
how many 1/5's are there in 9
1/5 9 = _____
Answer:
45
Step-by-step explanation:
1
1/5 X 5 times 9
Answer:
45 times is the correct answer
If s= 6 inches, and the altitude, h, is 21 inches, what is the volume of the pyramid?
Answer: 42 inches
Step-by-step explanation:
To find the volume you multiply 1/3 of the base which is 6 then with 1/3 is 2 them multiply the altitude which is 21. So 2 times 21 is 42 inches
Answer:
The volume of the pyramid is 42 inches³.
Step-by-step explanation:
The formula is V = ⅓ A H. 6x21=126, 126x1/3=42.
PLZZZZ HELPP ASAP!!! In a board game, you must roll two 6-sided number cubes. You can only start the game if you roll a 3 on at least one of the number cubes. Make a list of all the different possible outcomes when two number cubes are rolled. What fraction of the possible outcomes is favorable? Suppose you rolled the two number cubes 100 times, would you expect at least one 3 more or less than 34 times? Explain. Answer:
Hey there!
You should not expect more than 34 times to be favorable, because favorable outcomes are about 28% of outcomes, and 28% of 100 is 28, which is less than 34.
6/21 outcomes will be favorable.
Here is a list of all possible out comes:
1 - 1
1 - 2
1 - 3
1 - 4
1 - 5
1 - 6
2 - 2
2 - 3
2 - 4
2 - 5
2 - 6
3 - 3
3 - 4
3 - 5
3 - 6
4 - 4
4 - 5
4 - 6
5 - 5
5 - 6
6 - 6
The underlined ones have one or two 3's in their outcome. There are 21 outcomes total, and 6 of them have 3's in them. We will find the percentage by doing 6/21 = .286, or 28.6%. This means that for every 100 outcomes, you should expect about 29 of them to be favorable.
I hope it helps and have an amazing day! You've got this!
need help asap please !!
Answer:
17
Step-by-step explanation:
As we know that when diagonals bisect each other it gets divided into two equal parts so
CG = CE
6z - 85 = z
6z - z = 85
5z = 85
z = 85 / 5
Therefore z = 17
Hope it will help :)
Answer:
[tex]\displaystyle 17[/tex]
Step-by-step explanation:
[tex]\displaystyle 6z - 85 = z → 85 = 5z; 17 = z[/tex]
I am joyous to assist you at any time.
2 people work together take 5 hours to lay floors. How many hours does it take for 6 people to lay floors
Answer:
It takes ( hours for 6 people to lay floors
Step-by-step explanation:
2=5 divide it and for one person it would take 1 1/2 so then times 1 1/2 by 6.
С
a
Find all the missing elements:
B
A = 40°
a = 8
А
b = 7
b
B = [?]° C = [ ]° c = [ ]
Round to the nearest tenth.
C С
Answer:
B=34.2
C=105.8
c=12.0
Step-by-step explanation:
find B using the sine rule
(sin40÷8)=(sinB÷7)
rearrange
sin B= (sin40x7)÷8
sin B=0.562
make sure to use your calculator
then press shift sin to find B
B= 34.2°
to the nearest tenth means to 1 decimal place
sum of angles in a triangle is 180
so 180-(40+34.2)=105.8°=C
use sine rule again to find c
(sin105.8÷c)=(sin40÷8)
rearrange
c= (sin 105.8x8)÷sin40
c=12.0
a ferry boat leaves the dock once per hour your waiting time for the next ferry will follow a uniform distribution from 0 to 60 minutes
37 people showed up to the party. There were 9 less men than women present. How many women were there?
Answer:
23
Step-by-step explanation:
tbh, i just guessed around the numbers until i got the right one xD
The number of women present in the party will be 23.
What is expression ?Expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
We have,
Total persons in party = 37
Let,
Number of men = m
Number of women = w
So,
Total number of persons in party ,
m + w = 37 .....(i)
Now,
According to the question,
m = w - 9
Now
Substituting m = w - 9 in equation (i),
i.e.
w - 9 + w = 37
We get,
2w = 37 + 9
2w = 46
We get,
w = 23
So, number of women are 23.
Hence, we can say that the number of women present in the party were 23.
To know more about expression click here
https://brainly.com/question/14083225
#SPJ2
The equation of line j is y=5/7x-9. Line k, which is parallel to line j, includes the point (-7, 1 ). What is the equation of line k ?
Answer:
math waaayys can help you
Step-by-step explanation:
Mei runs 93.24 miles in 3 weeks. If she runs 6 days each week, what is the average distance she runs each day?
Answer:
5.18 miles each day
Step-by-step explanation:
3 weeks × 6 days = 18 days
93.24 miles in 18 days gives an average of 93.24 ÷ 18 = 5.18 miles per day
Each bill at a restaurant includes an 18% tip. Which of the following bill amounts and tips could be from this restaurant? Select Yes or No.
Answer:
1. Yes
2. No
3. No
4. Yes
Natalie has 16 close friends. How many ways can she choose 5 to E
bridesmaids in her wedding?
Answer:
80 ways
Step-by-step explanation:
You just miltiply 16 by 5 and you get your answer. Hope this helps!!!!!
Ryan has two jobs. He earns $9 per hour for x hours babysitting his cousins and he earns $18 per hour for y hours working at the coffee shop. Ryan will work both jobs. He is able to work no more than 10 hours a week, due to school commitments. Ryan wants to earn at least $72 a week, working a combination of both jobs.
Answer:
Umm I don't think you wrote out the whole question...
Step-by-step explanation:
$18 nine hours, $9 one hour = $177
$18 eight hours, $9 two hours = $162
$18 seven hours, $9 three hours = $153
$18 six hours, $9 four hours = $144
$18 five hours, $9 five hours = $135
$18 four hours, $9 six hours = $126
$18 three hours, $9 seven hours = $117
$18 two hours, $9 eight hours = $108
$18 one hour, $9 nine hours = $99
Scenario: Multiplying Polynomials
Instructions:
View the video found on page 1 of this Journal activity.
Using the information provided in the video, answer the questions below.
Show your work for all calculations.
The Students' Conjectures
Emily and Zach have two different polynomials to multiply:
Polynomial product A:
(4x2 – 4x)(x2 – 4) Polynomial product B:
(x2 + x – 2)(4x2 – 8x)
They are trying to determine if the products of the two polynomials are the same. But they disagree about how to solve this problem.
1. Complete the table to summarize each student's conjecture about how to solve the problem. (2 points: 1 point for each row of the chart)
Classmate Conjecture
Emily
Zach
Evaluating the Conjectures
Who do you think is correct? (1 point)
Analyzing the Data
Table Method:
2. Use the table to find the products of the two polynomials. Write your answer in descending order. (4 points: 2 points for each product)
A) (4x2 – 4x)(x2 – 4)
4x2 –4x
x2
–4
B) (x2 + x – 2)(4x2 – 8x)
there's another part on my profile, can u do it to please!!
Answer: there's one more screen shot but the limit is 5... so ill type it out!
7. Are the two products the same when you multiply them vertically? (1 point)
Yes they are
Making a Decision:
8. Who was right, Emily or Zach? Are the products the same with the three different methods of multiplication? (1 point)
They were both correct
9. Which of these three methods is your preferred method for multiplying polynomials? Why? (1 point)
I prefer the first one, Table method. To me it is easier and the fastest out of them all.
Serena is flying to Paris. The plane travels 3,654 miles in 72 1/4 hours from New York to Paris. What
was her
average rate of speed in miles per hour?
Answer:
Step-by-step explanation:
d = 3654 miles
t = 72 1/4 hours = 72.25 hours
r = d / t
r = 3654/72.25
r = 50.57 miles / hour
A new car is purchased for 20000 dollars.The value of the cat depreciates at 12.5% per year.What will the value of the car be, to the nearest cent, after 11 years?
Answer:
$460.38
Step-by-step explanation:
Use the exponential decay formula, y = C(1 - r)^t
Plug in the original price, depreciation rate, and amount of time:
y = 20000(0.875)^11
y = 460.38
So, the car's value after 11 years will be $460.38
Which expression is NOT equivalent to
2^3•5•7
A 2•2•2•5•7
B 2^3•35
C 2•3•5•7
D 8•5•7
Answer:
its c or a
Step-by-step explanation:
Plz help. I rally need it
Answer:
8
Step-by-step explanation:
Guys i actually need help
Answer:
Rotation
Step-by-step explanation:
Answer:
That is just rotation.
Step-by-step explanation:
It is rotation because if you were to spin it to the right on a 57 degree it will be that angle.
It also not the others because if you were to put reflection that would it would the opposite.
integers between -9 and -2
Answer:
Step-by-step explanation:
the integers are -8,-7,-6,-5,-4,-3,
The cost to the store is $45. They will use a 35% markup. What is the selling price?
.25 x .22
what is the answer
Answer:
.055
Step-by-step explanation: