[tex]\Large \boxed{\sf \bf \ \ \lim_{x\rightarrow0} \ {\dfrac{sin(4x)-4sin(x)}{x^3}}=-10 \ \ }[/tex]
Step-by-step explanation:
Hello, please consider the following.
Using Maclaurin series expansion, we can find an equivalent of sin(x) in the neighbourhood of 0.
[tex]sin(x) \sim \left(x-\dfrac{x^3}{3!}\right)\\\\\text{So, in the neighbourhood of 0}\\\\\begin{aligned}(sin(4x)-4sin(x)) &\sim \left( 4x-\dfrac{(4x)^3}{3!}-4x+\dfrac{4x^3}{3!}\right)\\\\&\sim \left(\dfrac{x^3*4*(1-4^2)}{3*2}\right)\\\\&\sim \left(\dfrac{x^3*2*(-15)}{3}\right)\\\\&\sim \left(x^3*2*(-5)\right)\\\\&\sim \left(x^3*(-10)\right)\\\end{aligned}[/tex]
Then,
[tex]\displaystyle \lim_{x\rightarrow0} \ {\dfrac{sin(4x)-4sin(x)}{x^3}}\\\\= \lim_{x\rightarrow0} \ {\dfrac{-10*x^3}{x^3}}\\\\=-10[/tex]
Thank you
Answer:
-10
Step-by-step explanation:
L' Hopital's rule can be used to solve it.
We search for lim (f(x)/g(x))
this is the same as lim (f' (x)/g' (x))
this is the same as lim f'' (x)/g'' (x)
so here we have f(x) =sin(4x)-4sin(x)
g(x)=x^3
g'' (x)= 6x
f'' (x)=-16sin(4x)+4sin(x)
so lim f'' (x) / g ''(x) = -16/6 lim sin(4x)/x + 4/6 lim (sin(x)/x)
= -16*4/6+4/6
=(-64+4)/6=-60/6=-10
Lizbeth runs from 14:40 until 15:30 pm at an
average speed of 7 km/h. How far did she go?
Answer:
5.83333333333 km
Step-by-step explanation:
14.40 until 15.30 is a total of 20 Minutes to 15:00 and andother 30 Minutes to 15:30 hr, so, she has been running for 50 Minutes.
Now solve for distance when 1 hr (60 min) = 7 km
So, simply (7/60)*50 = 5.83333333333 km
please help me!!
find the variables!
1) 8x -44= -3x
2) 1w- 9= 4w
3) 5n- 16=1n
4) 8h+ 36=2
Answer:
Step-by-step explanation:
1. 11x = 44
x = 4
2. 3w = -9
w = -3
3. -4n = -16
n = 4
4. 6h = 36
h= 6
the measure of one angle of a triangle is three times the measure of a second angle. the measure of the third angle is 12 less than the sum of the other two. what are the measures of the 3 angles
PLEASEEEE HELP<333
Answer:
24, 72, and 84
Step-by-step explanation:
Let the first, second, and third angles be A, B, and C, respectively.
So, first of all, since the figure is a triangle, the three angles must total 180. Thus:
[tex]A+B+C=180[/tex]
Now, we are told that the measure of one angle (let's use A) is 3 times the measure of a second angle (B). So:
[tex]A=3B[/tex]
And the measure of the third angle (C) is 12 less than the sum of the other two (A&B). Therefore:
[tex]C=(A+B)-12[/tex]
For this equation substitute A for 3B:
[tex]C=(3B+B)-12[/tex]
Combine like terms:
[tex]C=4B-12[/tex]
So we have the following equations thus far:
[tex]A+B+C=180[/tex]
[tex]A=3B[/tex]
[tex]C=4B-12[/tex]
So, substitute A and C in for the first equation:
[tex]A+B+C=180\\(3B)+B+(4B-12)=180[/tex]
Combine like terms:
[tex]8B-12=180[/tex]
Add 12 to both sides:
[tex]8B=192[/tex]
Divide by 8:
[tex]B=24[/tex]
So, the second angle B is 24 degrees.
The first angle A is three times B. Thus, A is 3(24)=72 degrees.
And C is 12 less than the sum of them. Thus:
[tex]C=(72+24)-12\\C=96-12\\C=84[/tex]
So, our angles are:
24, 72, and 84
And we are done :)
Edit: Typo
11. The second of two numbers is 5 more than twice the first. The sum of the numbers is 44. Find the numbers by writing and
solving a system of equations.
O A. (11, 33)
O B. (22, 22)
O C. (20, 24)
O D. (17, 22)
O E. (13,31)
O F. (17, 27)
explain too please
Answer:
E
Step-by-step explanation:
So the equation is y= 5+2x
and x+y=44
So we use the substitution method and says that y=44-x
So 44-x=5+2x
simplify
44-5=3x
x=13
there's only one option with x=13
Answer: E. (13, 31)
Step-by-step explanation:
Let x= first number
Let y= Second number
----------------------------------
y-5=2x
x+y=44
--------------------------------
y=2x+5
x+y=44
----------------------------
x+(2x+5)=44 ⇔ substitute y value in terms of x
x+2x+5=44
3x+5=44
3x=39
x=13
44-13=31
Hope this helps!! :)
Please let me know if you have any question or need further explanation
The distance that a jogger travels at a constant speed of 6.5 miles per hour can be modeled by the linear function f(x)=6.5x, where x is the time in hours the jogger runs. What is the domain of this function? How would a graph of this function show it?
The domain of the function f(x) = 6.5x will be a positive real number.
What are domain and range?The domain means all the possible values of x and the range means all the possible values of y.
The distance that a jogger travels at a constant speed of 6.5 miles per hour can be modeled by the linear function f(x) = 6.5x, where x is the time in hours the jogger runs.
We know that time is a scalar quantity. Then the value of the time is always greater than equal to zero.
x ≥ 0
The domain of the function f(x) = 6.5x will be a positive real number.
More about the domain and range link is given below.
https://brainly.com/question/12208715
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Samantha is building a miniature maze for a science experiment. she determines that she needs 6 yards of wood for the exterior walls. how many feet of wood must she by in order to build her maze?
Answer:
18 ft
Step-by-step explanation:
Convert yards to feet:
6 yds 3 ft
------------ * ------------ = 18 ft
1 1 yd
if a right cylinder have the same radius and height as the oblique cylinder shown here, what is the volume of the right cylinder? Use 3.14 for pi. Round to the nearest whole number.
Answer:
[tex]\displaystyle V_\text{right} \approx 1696\text{ units}^3[/tex]
Step-by-step explanation:
Recall that the volume for an oblique cylinder is the same for the volume of a right cylinder. That is:
[tex]\displaystyle V_\text{right} = V_\text{oblique} = \pi r^2h[/tex]
Hence, find the volume of the oblique cylinder:
[tex]\displaystyle \begin{aligned} V_\text{oblique} & = (3.14)(6)^2(15) \\ \\ & = 1695.6 \text{ units}^3 \\ \\ &\approx 1696\text{ units}^3\end{aligned}[/tex]
Therefore:
[tex]\displaystyle V_\text{right} \approx 1696\text{ units}^3[/tex]
In conclusion, the volume of the right cylinder is about 1696 units³.
= neage Check Find the distance between the polnts (6,-5) and (-3,-5).
Answer:
The answer is
9 unitsStep-by-step explanation:
The distance between two points can be found by using the formula
[tex]d = \sqrt{ ({x1 - x2})^{2} + ({y1 - y2})^{2} } \\ [/tex]where
(x1 , y1) and (x2 , y2) are the points
From the question the points are
(6,-5) and (-3,-5)
The distance between them is
[tex]d = \sqrt{ ({6 + 3})^{2} + ( { - 5 + 5})^{2} } \\ = \sqrt{ {9}^{2} + 0 } \\ = \sqrt{81} [/tex]We have the final answer as
9 unitsHope this helps you
Freida’s credit card has an APR of 13.73%, and it calculates her finance charge by using the daily balance method and a 30-day billing cycle. On September 1st, Freida had a balance of $449.22. During the month of September, she made a payment of $85.33 and a purchase of $60.99. How much greater will her September finance charge be if the purchase occurred on September 7th and the payment occurred on September 20th than it would be if the payment occurred on September 7th and the purchase occurred on September 20th? a. $0.13 b. $0.41 c. $0.72 d. $0.28
Answer:
$0.72 C
Step-by-step explanation:
ON E2020 THE ANSWER IS CCC
Freida's ffinance charge on credit card if the purchase of $60.99 and payment of $85.33 occured between September 7th and 20th is $0.72 C which is option C.
What is APR 13.73% mean?
The interest on the credit amount for one year on the credit card.
Freida’s credit card has an APR is 13.73%
One month iinterest 0.1373÷12
⇒0.0115
APR for credit cards is charged on purchased amount =$60.99
⇒Interest on $60.99 for 00ne month is= $60.99×0.0115
=$0.72
According to the given option:-
a. $0.13
b. $0.41
c. $0.72
d. $0.28
the answer will be option C $0.72.
Learn more about APR here: brainly.com/question/2772156
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What is the sum of the first four composte numbers?
19
20
27
28
Answer:
27
Step-by-step explanation:
The first four composite numbers are - 4, 6, 8, 9.
Add these all together and you get 27. Hope it helps!
Answer:
is 19
Step-by-step explanation:
A freezer was sold during a clearance sale sale for $387.50. If the freezer was sold at a discount of 50/3%, what was the list price?
Answer:
$465
Step-by-step explanation:
100 - 50/3 = 250/3
250/3 ÷ 100 = 5/6
$387.50 ÷ 5/6 = $465
List all number sets that apply to 38
Answer:
Natural numbers whole numbers integers and Rational numbers
Refer to the following distribution:Cost of Textbooks Frequency $25 up to $35 2 S35 up to $45 5$45 up to $55 7$55 up to $65 20 S65 up to $75 16What is the relative class frequency for the $25 up to $35 class? A) 0.10 B) 0.05 C) 0.02 D) 0.04
Answer:
[tex]Relative\ Frequency = 0.04[/tex]
Step-by-step explanation:
Given
Cost of Textbooks ---- Frequency
$25 up to $35 ----- 2
$35 up to $45 ------- 5
$45 up to $55 ------- 7
$55 up to $65 ------ 20
$65 up to $75 ---- -- 16
Required
Determine the relative class frequency for the $25 up to $35 class
First, we need to get the total frequency
[tex]Total = 2 + 5 + 7 + 20 + 16[/tex]
[tex]Total = 50[/tex]
Next, is to write out the frequency of $25 up to $35 class
[tex]Frequency = 2[/tex]
Divide this frequency by the total frequency; This gives the relative frequency
[tex]Relative\ Frequency = \frac{Frequency}{Total}[/tex]
[tex]Relative\ Frequency = \frac{2}{50}[/tex]
[tex]Relative\ Frequency = 0.04[/tex]
Hence;
Option D answers the question
A student rides his bike to school with an average velocity of 10 miles per hour. It takes him 12 minutes to get to school. Write a function that models the student's distance from home. Use t for time in hours and d for distance. Then identify the domain and range of this situation using interval notation--label each one!
Answer:
The function is [tex]d=10t[/tex]
domain is 0 to 0.2 hour.
range is 0 to 2 miles.
Step-by-step explanation:
Given that,
Average velocity = 10 miles/hour
Time = 12 min = 0.2 hour
We need to write a function that models the student's distance from home
Using formula of distance
[tex]d=v\times t[/tex]
Where, v = velocity
t = time
d = distance
Put the value into the formula
[tex]d=10t[/tex]
This is a function.
We know that,
Domain :
Domain shows the time.
So, domain = 0 to 0.2 hour
Range :
Range shows the distance.
The range at t =0,
Put the value of t in the function
[tex]d = 10\times0=0[/tex]
The range at t =0.2 hour
[tex]d = 10\times0=0[/tex]
[tex]d=2\ miles[/tex]
So. range = 0 to 2 miles
Hence, The function is [tex]d=10t[/tex]
domain is 0 to 0.2 hour
range is 0 to 2 miles
What is the end behavior of the polynomial function? Drag the choices into the boxes to correctly describe the end behavior of the function. f(x)=−3x^4−3x^3−8x+2 f(x)=3x^3−8x^2−x+1
Answer:
f(x) = -3x⁴ - 3x³ - 8x + 2
As x -> ∞, f(x) -> -∞
As x -> -∞, f(x) -> -∞
f(x) = 3x³ - 8x² - x + 1
As x -> ∞, f(x) -> ∞
As x -> -∞, f(x) -> -∞
Step-by-step explanation:
Graph both functions.
End behavior is what happens to the y-values when x-values approach either +∞ or -∞.
Another florist has 16 yellow mums and 40 white carnations. Which question can be answered by finding the GCF of 16 and 40? How many different combinations of yellow mums and white carnations can the florist make? What is the greatest number of identical groups that can be made with a number of mums and carnations in each group? How many total number of flowers will be in each group of mums and carnations? What is the greatest number of white carnations that can be in each group?
Answer:
B
Step-by-step explanation: I got correct on ed2020!
Hope this helps!~ :>
Answer:
B
Step-by-step explanation:
it's correct
What is [−7,−5)∩[−5,0]?
Answer:
[−7,−5)∩[−5,0] = [-5]
Step-by-step explanation:
A = A1 ∩ A2 means that A contains the intersected elements (shared elements) of A1 and A2
Is "What is the area of the floor in this classroom?" a statistical question?
The answer is No
Explanation:
All statistical questions involve collecting numerical data (usually from a group of people) and then analyzing it to draw conclusions about the opinions of people of a certain phenomenon as the data varies depending on the response of each person. This process is not required to determine the area of the floor because this has a unique answer and can simply be found by measuring the height and width of the classroom and then multiplying both numbers. Also, this does not imply gathering a lot of data and the data does not vary.
Gasoline was $2.629 per gallon one week and $2.849 per gallon the next. By how much did the price change?
The price of the gasoline changed by $1.
Simplify (5x^2 + 3x + 4) + (2x^2 − 6x + 3).
Answer:
7x² - 3x + 7
Step-by-step explanation:
Step 1: Write out expression
5x² + 3x + 4 + 2x² - 6x + 3
Step 2: Combine like terms (x²)
7x² + 3x + 4 - 6x + 3
Step 3: Combine like terms (x)
7x² - 3x + 4 + 3
Step 4: Combine like terms (constants)
7x² - 3x + 7
Answer:
[tex]\Large \boxed{7x^2-3x+ 7}[/tex]
Step-by-step explanation:
[tex](5x^2 + 3x + 4) + (2x^2 -6x + 3)[/tex]
Removing brackets.
[tex]5x^2 + 3x + 4 + 2x^2 -6x + 3[/tex]
Grouping like terms.
[tex](5x^2 + 2x^2) + (3x -6x)+ (4 + 3)[/tex]
Combining like terms.
[tex](7x^2) + (-3x)+ (7)[/tex]
On a recent road trip, Johnny was able to drive 360 miles on 12 gallons of gas. a. What is the average gas mileage for Johnny’s car?
Answer:
1/30 gallon per mile
12/360=1/30
Answer:
Step-by-step explanation:
The answer is 1/30 of a gallon
12/360=1/30
Of the 13,955,000 Asians age 25 and over in the U.S.,8,107,000have completed at least a bachelors degree. What percentage is this?
Answer:
Step-by-step explanation:
You just need to divide the number of people with degrees (about 8 million) by the total number of Asians (about 14 million) and multiply by 100
8107000
======== * 100 = 0.58094 * 100 = 58.094%
13955000
Which is a very high %
A line passes through the point (6, 7) and has a slope of
دیا یہ
3
2
Write an equation in slope-intercept form for this line.
Answer:
hi
Step-by-step explanation:
hi
Fill in the missing entries for the following form.
Date
Interest Deposit
Withdrawal
Balance
08-01
$389.42
$
08-01 $2.12
V
08-08
$
$293.59
08-14
$109.16
$
v
08-16
$
$491.52
08-26
$202.27
$
Answer:
Step-by-step explanation:
389.49 + 2.12=391.54
391.54-97.95= 293.59
293.59+109.16= 402.75
402.75 +88.75=491.52
491.52-202.27= 289.25
hope this helps!
As per linear equation, the missing values are $391.54, $97.95, $402.75, 88.75, $289.25.
What is a linear equation?"A linear equation is an equation in which the highest power of the variable is always 1."
Date: 08/01
Balance = $389.49
Interest = $2.12
Balance = $(389.49 + 2.12) = $391.54
Date: 08/08
Balance = $391.54
Withdraw = $97.95
Balance = $(391.54 - 97.95) = $293.59
Date: 08/14
Balance = $293.59
Deposit = $109.16
Balance = $(293.59 + 109.16)= $402.75
Date: 08/16
Balance = $402.75
Deposit = $88.75
Balance = $(402.75 + 88.75) = $491.52
Date: 08/26
Balance = $491.52
Withdraw = $202.27
Balance = $(491.52 - 202.27) = $289.25
Learn more about a linear equation here: https://brainly.com/question/2203023
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Determine the Next three terms in the following sequence -1 1/2 -1/4 1/8
Answer:
-1/16 1/32 -1/64
Step-by-step explanation:
They are dividing by -2 each time; therefore, they multiply (1/4) x (-1/2), (-1/16) x (-1/2), (1/32) x (-1/2) because of the keep change flip rule.
Answer:
-
[tex] - \frac{1}{16} \\ \frac{1}{32} \\ \frac{ - 1}{64} [/tex]
Step-by-step explanation:
It's a geometric sequence with the common ratio r = -1/2
1st: -1
2nd: (-1)x(-1/2) = 1/2
3rd: (1/2) x (-1/2) = -1/4
4th: (-1/4) x (-1/2) = 1/8
so:
5th: (1/8) x (-1/2) = -1/16
6th: (-1/16) x (-1/2) = 1/32
7th: (1/32) x (-1/2) = -1/64
endent Practice
1. National Geographic is reporting on the migration patterns of Canadian Geese. One of
the birds they are tracking traveled from Ottawa, Canada to Jackson, Mississippi
Part A: What units would be best to describe this situation
Part B: While writing the article for the next edition of National Geographic, the reporter
estimates that this goose flew 2,552,000 yards. How many significant digits does
the reporter's estimate have?
Part C: The Editor in Chief decided that the reporter chose the incorrect units. The editor
wants the reporter to convert the distance to miles. Complete this conversion.
Part D: Your younger brother determined that the distance from Jackson to Tucson
Arizona is 7,159,680 feet. He claims that this is further than the distance to
Ottawa. Is he correctJustify your answer using mathematical evidence.
Answer:
Part A: The unit that would be best to describes the situations is to the mile
Part B: 4 significant figures
Part C: 1,450 miles
Part D: He is not correct
Step-by-step explanation:
Part A: By unit conversion, we have;
1 mile = 1,760 yards
Given that the distance from Ottawa, Canada to Jackson Mississippi is 2,552,000 yards it would best simplified into miles
Part B: The number of significant digits in the reporters estimate are the non-zero digits before the zeros in the number figure which are 2, 5, 5, and 2 or 4 significant figures
Part C: 2,552,000 yards = 2,552,000 yards/(1,760 yards/mile) = 1,450 miles
Part D: Given that the distance from Jackson to Tucson = 7,159,680 feet, we have;
1 mile = 5,280 feet
Therefore;
7,159,680 feet = 7,159,680 feet/(5,280 feet/mile) = 1,356 miles
Therefore, the claim that the distance from Jackson to Tucson which is 1,356 miles is further than the distance from Ottawa, Canada to Jackson Mississippi which is 1,450 miles is not correct because;
The distance from Jackson to Tucson 1,356 miles [tex]\ngtr[/tex] 1,450 miles which is the distance from Jackson to Ottawa
Find the four second partial derivatives. Observe that the second mixed partials are equal z=x^2+8xy+3y^2
Answer:2,8,8,6
Step-by-step explanation:
[tex]f_x=2x+8y\\f_y=8x+6y\\f_{xx}= 2\\f_{xy}= f_{yx}= 8\\f_{yy}=6[/tex]
According to Clairaut's theorem, for most cases, the mixed partial derivatives are equal. In this case, it is.
Trig: Solve Quadratic Equations by Factoring help with 3c and 3d
Answer:
3c) x = 1/4, x = 6
3d) t = 0, t = 4
Step-by-step explanation:
3c).....................................
6x² - 15x + 2 = 2x² + 10x - 44x² -25x + 6 = 04x² - 24x - (x - 6) = 04x(x -6) - (x - 6) = 0(4x - 1)(x - 6) =04x - 1 = 0 ⇒ 4x = 1 ⇒ x = 1/4x - 6 = 0 ⇒ x = 6==============================
3d).....................................
- 16t² + 76t + 5 = 12t + 5-16t² + 64t = 0t² - 4t = 0t(t - 4) = 0t = 0t - 4 = 0 ⇒ t = 4The length of a person's hand compared with the
length of the same person's foot
O line graph
scatter plot
bar graph
histogram
DONE
Answer:scatter plot
Step-by-step explanation:
Answer:
B) scatter plot
Step-by-step explanation:
edge 2023
HEEELP ME WITH THIS PROBLEM PLEASEEW
(The problem is in a picture)
Answer:
x < 6
Step-by-step explanation:
2 x -9 < 3
+9 . +9
2x < 3 + 9
2x < 12
__ . __
2 . 2
x < 6