Expand the limand as
[tex]\dfrac{e^{x^3} - (1 - x^3)^{1/3} + \left((1-x^2)^{1/2} - 1\right) \sin(x)}{x \sin^2(x)} \\\\ ~~~~~~~~ = \dfrac{e^{x^3} - (1-x^3)^{1/3}}{x^3} \cdot \dfrac{x^2}{\sin^2(x)} + \dfrac{(1-x^2)^{1/2} - 1}{x^2} \cdot \dfrac{x}{\sin(x)}[/tex]
Recall that for [tex]a\neq0[/tex],
[tex]\displaystyle \lim_{x\to0} \frac{\sin(ax)}{ax} = 1[/tex]
Then
[tex]\displaystyle \beta = \lim_{x\to0} \left( \dfrac{e^{x^3} - (1-x^3)^{1/3}}{x^3} + \dfrac{(1-x^2)^{1/2} - 1}{x^2}\right)[/tex]
Rationalize the numerators.
[tex]\dfrac{e^{x^3} - (1-x^3)^{1/3}}{x^3} = \dfrac{e^{3x^3} - (1 - x^3)}{x^3 \left(e^{2x^3} + e^{x^3} (1-x^3)^{1/3} + (1-x^3)^{2/3}\right)} \\\\ ~~~~~~~~~~~ = \left(\dfrac{e^{3x^3} - 1}{x^3} + 1\right) \cdot\dfrac1{e^{2x^3} + e^{x^3} (1-x^3)^{1/3} + (1-x^3)^{2/3}}[/tex]
and observe that
[tex]\dfrac1{e^{2x^3} + e^{x^3} (1-x^3)^{1/3} + (1-x^3)^{2/3}} \to \dfrac13[/tex]
[tex]\dfrac{(1-x^2)^{1/2}-1}{x^2} = \dfrac{(1-x^2) - 1}{x^2 \left((1-x^2)^{1/2} + 1\right)} \\\\ ~~~~~~~~ = -\dfrac1{(1-x^2)^{1/2} + 1} \to -\dfrac12[/tex]
This leaves us with
[tex]\displaystyle \beta = \lim_{x\to0} \frac{e^{3x^3} - 1}{3x^3} - \frac16[/tex]
The remaining limit is the derivative of [tex]e^{3x^3}[/tex] at [tex]x=0[/tex], so its value is 1, and we find
[tex]\beta = 1 - \dfrac16 = \dfrac56 \implies 6\beta = \boxed{5}[/tex]
5. Consider the statement “There are no simple solutions to life’s problems”. Write an informal negation for the statement, and then write the statement formally using quantifiers and variables.
The informal negation for the statement is that there are simple solutions to life’s problems.
∀ x ∈ X, x is not a solution to life's problems.
How to illustrate the information?A statement is any sentence that can be determined as true or false. A statement can be written as P(x) or Q(x) .
A negation to a statement is the opposite to that statement.
The negation of “There are no simple solutions to life’s problems” is “There are simple solutions to life’s problems.”
To write the statement formally using quantifiers.
1. For all, denotes as ∀
2. There exists, denoted as ∃
Let us define a domain and a Set. A Set is simply a collection of objects.
Let X be the set of all simple solutions to all problems.
∀ x ∈ X, x is not a solution to life's problems.
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Determine ratio of A to B. Round as indicated.
A = 18 and B = 3 (Do not round.)
Select one:
a. 1|2
b. 6
с. 1/6
d. 2
Please answer correctly, my grade depends on it also i'd help if you asnwer my other questions but only if you want to.
The domain are the independent variables for which an expression or equation exists. The domain of the graph in interval notation will be [-9,7]
Domain of a graph.The domain are the independent variables for which an expression or equation exists.
The given graph is described as a piecewise function since there are several lines that make up the graph.
The domain of the function are the value that lies along the x-axis of the line graph while the range are values of the function along the y-axis of the line graph.
The domain of the graph in interval notation will be [-9,7]. Note that both brackets are closed since the circles are shaded.
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6 in. 5 in. 4 in. 1 in. 2 in. 3 in. 5 in. 4 in. what is the volume
Answer:
Step-by-step explanation:
Do 6 +5=11+4=15+1+2+18+3=21+5=26+4=30 theres ur answer:D
The 100th term of 1, 7, 13, 19, … is
[tex]Consider \: the \: sequence \: u_{n} \\ u_{n} \: appears \: to \: be \: arithmtic[/tex]
Quick Proof:[tex]u_{4}-u_{3}=u_{3}-u_{2}=... \\ 19 - 13 = 13 - 7 = .. \\ 6 = 6 = ...[/tex]
[tex]u_{n} \: is \: arithmetic \: with \: d = 6 \:and \: u_{1} = 1 \\ [/tex]
[tex]u_{n} = u_{1}+(n-1)d \\ u_{100} = 1 + (100 - 1)6 \\ u_{100} = 595[/tex]
The product of the ages of Sally
and Joey now is 175 more than
the product of their ages 5 years
prior. If Sally is 20 years older
than Joey, what are their current
ages?
The product of the ages of
Current age of Sally is 25
Current age of Joey is 5
Let age of Sally 5 years prior be x
age of Joey 5 years prior be y
Now the age of Sally is x+5
Now the age of Joey is y+5
product of the ages of Sally and Joey now is 175 more than the product of their ages 5 years prior.
(x+5)(y+5)=175+xy
x y + 5x +5y +25 = 175 + x y
5x+5y = 175-25 = 150
x+ y = 30 .. .. ..1
Sally is 20 years older than Joey
x=20+y
Substitute x=20+y in .. . 1
20+y + y = 30
2y=10
y=5
x=20+y=20+5=25
Current age of Sally is 25
Current age of Joey is 5
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Under his cell phone plan, Mason pays a flat cost of $51.50 per month and $4 per gigabyte, or part of a gigabyte. (For example, if he used 2.3 gigabytes, he would have to pay for 3 whole gigabytes.) He wants to keep his bill under $65 per month. What is the maximum whole number of gigabytes of data he can use while staying within his budget?
The maximum whole number of gigabytes of data he can use while staying within his budget is 3 gigabytes
What is straight-line equation?
The straight-line equation which comprises of the fixed charge that Mason would have to pay for data usage every month and the variable charge which is based on the number of gigabytes used is as shown below:
y=a+bx
y=total cos65
a=fixed charge=51.50
b=cost per gigabyte=4
x=number of gigabytes he has to use to stay within his budget=unknown
65=51.50+4x
65-51.50=4x
13.5=4x
x=13.5/4
x=3.38( 3 gigabytes so as not to pay for 4 gigabytes)
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A country with a population of 2.1 million experiences 4310 fatalities as a result of a virus. What is the fatality rate per 100,000?
The fatality rate per 100,000 is 205.23.
In mathematics, a rate of something is simply the ratio between two related quantities which are expressed different units. While expressing the units of any rate, the word "per" is used to distinguish the units of the two measurements used to calculate the rate.
Here, we are given that a country has a population of 2.1 million.
2.1 million can be written as- 2,100,000
The number of fatalities experienced by the country = 4,310
This means that there where 4,310 fatalities per 2.1 million of the population.
The number of fatalities per 100,000 will be given as-
4,310/ 2,100,000 × 100,000
expanding it further we get-
4,310/ 21
= 205.23
Thus, the fatality rate per 100,000 is 205.23.
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Crystal has 25 lollipops. Angie has 12 more lollipops than Crystal.
How many lollipops do the girls have all together?
Answer:
Both the girls have 62 lollipops
Step-by-step explanation:
25+25=50
50+12=62
Answer:
62 lollipops
Step-by-step explanation:
If Angie has 12 more lollipops than Crystal...
25 + 12 = 37 lollipops
Angie has 37 lollipops and Crystal has 25 lollipops. In total, that is...
37 + 25 = 62 lollipops
Cadence baked 45 cupcakes on Tuesday. This was 3 more than twice the number of cupcakes she baked on Monday. How many cupcakes did Cadence bake on Monday?
Please give an explanation/step-by-step process on how to solve this. Do not just answer and take points or you will get reported.
Thank you :)
The sum of 3 times a number and -8 added to 7 times the number
Answer:
(3x+-8) + 7x
Pls mark brainliest
Solve and put your final answer in the box
2 1/3 × -4/5
A patient is to receive 0.25 mg of Medication A per kg of body weight per day. If the patient is a 157 lb man, how much medication A will he need?
The patient needs 17.66 mg of medication A .
Unitary method is "A way of finding a single-unit value from a multi-unit value, and then finding a multi-unit value from a single-unit value."For simplicity, always write what you calculate on the right and what you know on the left.In order to do that, we must first find the value of one thing by division and then find the value of more or fewer things by multiplication.It is given that a patient has weight 157 lbs.
We apply division because we need to find the cost of one item given the cost of many items. If you need to find the cost of many items from the cost of one item, apply the multiplication operation.
We need to convert this weight in kilogram using unitary method , we get 1 pound have = 0.45 kilogram
157 pound will have [tex]=157\times0.45[/tex]
[tex]=70.65[/tex] kilogram
A patient receive 0.25 mg of Medication A per kg
Using unitary method , we get
1 kg of body receives = 0.25 mg of medication A
70.65 kg of body receives [tex]=0.25\times 70.65[/tex]
[tex]=17.66[/tex] mg of medication A
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A cargo truck is traveling 70 miles per hour and plans to travel 840 miles, plus or minus 105 miles, depending on fuel levels. Fnd the minimum and maximum number of hours the truck will travel at that speed.
The minimum is 10.5 hours and the maximum is not 12.2 hours.
The minimum and a maximum number of hours the truck will travel at that speed are 10.5 and 13.5 hours respectively.
What is velocity?Velocity is the rate of distance covered per time. Velocity could be average or instantaneous.
Average velocity = total distance / total time taken
Units of velocity are given by ⇒ meter/second
Speed of truck = 70 miles/hour
Maximum distance = 840 + 105 = 945 miles.
Minimum distance = 840 - 105 = 735 miles.
Now,
Time = distance / velocity
Minimum time = minimum distance / velocity
So,
Minimum time = 735 / 70 = 10.5 hour.
Maximum time = maximum distance / velocity.
Maximum time = 945 / 70 = 13.5 hour.
Hence "The minimum and a maximum number of hours the truck will travel at that speed are 10.5 and 13.5 hours respectively".
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Find the value of the power.
89⁰
Answer: 1
Step-by-step explanation:
Anything to the power of zero is one
Answer:
0.999847695
Step-by-step explanation:
1 for short ig :^
solve the quadratic equation 3×2-16+5=0
Answer:
3×2-16+5=0
-5=0
Step-by-step explanation:
Step-by-step explanation:
(3)(2)−16+5=0
−5=0
The price of an item has been reduced by $2.89.the new sale price is $80.05. What was the original price
Answer: 82.94
Step-by-step explanation:
Math
in the following figure what is the value of y in terms of x?
a. x + 80
b. 80 - x
c. x + 100
d. x - 100
f. 100 - x
Customer in Event 4 returned $4,200 worth of goods that had a cost of $2,150 .
The discussion is shown below:
What is data?In computing, data is information that has been translated into a form that is efficient for movement or processing.
According to the data
Transaction Cost
Event 1 NA
Event 2 Product
Event 3 Product
Event 4 Product
Event 5 Period
Event 6 Product
Event 7 NA
Event 8 NA
Event 9 Period
Event 10 Period
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The question you have uploaded is incomplete.
The complete question is:
5.Award: 1.00 point Problems? Adjust credit for all students. The Pet Store experienced the following events for the Year 1 accounting period:
1. Acquired $60,000 cash from the issue of common stock.
2. Purchased $65,000 of inventory on account.
3. Received goods purchased in Event 2 FOB shipping point; freight cost of $900 paid in cash.
4. Sold inventory on account that cost $38,000 for $71,000.
5. Freight cost on the goods sold in Event 4 was $620. The goods were shipped FOB destination. Cash was paid for the freight cost.
6. Customer in Event 4 returned $4,200 worth of goods that had a cost of $2,150.
7. Collected $58,300 cash from accounts receivable.
8. Paid $59,200 cash on accounts payable.
9. Paid $2,600 for advertising expense.
10. Paid $3,100 cash for insurance expense.
Requireda. Which of these events affect period (selling and administrative) costs? Which result in product costs? If neither, label the transaction NA.
guys what is 100+5617538...
Answer:
5617638
Step-by-step explanation:
You can use a calculator or just change the second 5 in the number to 6 because we are adding 100.
Answer: 5617638
Step-by-step explanation:
100+5617538=
5617538+100=
5617000+538+100=
5617000+638=5617638
What is the equation of the linear function in slope-intercept form described by this table?
f(x)= _____x + __________
The equation of line in slope intercept form described from given table will be equal to y = -2x + 1
What is the slope intercept form of a line ?
The equation of a line that can be written as y = mx + c, where m is the slope and c is the line's y-intercept, is known as a slope intercept form.
From the given figure we can find out that the points are (x1.y1) = (-2 , 5) and (x2 , y2) = ( -1 , 3).
The equation of line in slope intercept form
y = mx + c
Where m is the slope, and c is the y-intercept.
We have points (-2, 5) and (-1,3). Thus , the slope (m) will be :
m = ( [tex]y_{2} - y_{1}[/tex] ) /( [tex]x_{2} - x_{1}[/tex] )
m = ( 3 - 5 ) / ( -1 + 2)
m = -2
Using this value to find out the equation of line we get :
y = -2x + c
Point (-2,5) means that when x = -2 then y = 5 , and we use this data to find value of c , which is the y- intercept ;
5 = -2 × -2 + c
c = 5 - 4
c = 1
So , in slope intercept form the equation of line will be ;
y = -2x + 1
Therefore , the equation of line in slope intercept form will be y = -2x + 1.
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The function y = 2.5x + 3 can be used to determine the cost in dollars for a taxi ride of x miles.
What is the rate of change of the cost in dollars with respect to the number of miles?
$5.50/mile
$1/mile
$3/mile
$2.50/mile
Answer:
C. $2.50
Step-by-step explanation:
x=1 y=5.5
x=2 y=2.5
John and Sam have a lawn mowing service. At one home, John can mow the lawn by himself in 2 hours, but it takes Sam 2.5 hours. How many hours twill it take them to mow the same lawn
together? Give the answer correct to one decimal place.
Answer:
3/5 hours or 36 minutes
Step-by-step explanation:
John could mow three of these lawns in three hours (3/1 = three), while Sam could only mow two in three hours (3/1.5 = two). Therefore, the two of them could cut 5 lawns in 3 hours (3+2). Together, they can cut the same lawn in three and a half hours, or 36 minutes.
who travels the fastest explain why If two people answer and I see who is correct I will mark them brainlest
Answer: The jellyfish is faster
5,6 and 10 have a common multiple of 30 so make the denominator 30.
JF ->3/5=18/30
1/6=5/30
WR->5/6=25/30
3/10=9/30
9h-> 25 miles
1h->2.8 miles
5h->18 miles
1h->3.6 miles
Need help with this question. Dropped a picture down below.
The statements that complete the figure parameters are
CEH and HEB are complementary angles and CEH = 70 degreesAEH and HEB are supplementary angles and AEH = 160 degreesHow to complete the sentences?The given parameters are:
Angle HEB = 20 degrees
From the figure, we can see that
Line CE is perpendicular to line AB
This means that
HEB + CEH = 90 degrees ---- complementary angles
HEB + AEH = 180 degrees ---- supplementary angles
So, we have
20 + CEH = 90 degrees
20 + AEH = 180 degrees
Evaluate
CEH = 70 degrees
AEH = 160 degrees
Hence, the complete statements are
CEH and HEB are complementary angles and CEH = 70 degrees
AEH and HEB are supplementary angles and AEH = 160 degrees
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A sequence is defined recursively using the formula f(n+1)=-0.5f(n). If the first term of the sequence is 120, what is f(5)
Answer:
The sequence's fifth term is equal to 7.5.
Step-by-step explanation:
It is given in the question that A sequence is defined recursively using the formula f(n+1)=-0.5f(n) and we need to calculate f(5) if the first term of the sequence is 120.
Firstly,
The definition of a series is given by the formula f (n + 1) = -0.5 f. (n).
Now, what will be f(5) if the sequence's initial term is 120, let's calculate;
Recursively, a series is defined as follows;
=> f(n) = 120 if n = 1, otherwise.
Otherwise,
=> f(n) =-0.5f(n-1) if n > 1.
Now,
=> f(1) = 120
=> f(2) = -0.5f(1) = -0.5(120) = -60
=> f(3) = -0.5f(2) = -0.5(-60) = 30
=> f(4) = -0.5f(3) = -0.5(30) = -15
=> f(5) = -0.5f(4) = -0.5(-15) = 7.5
So, For n > 1, f(n) = (-0.5)(n-1) × 120
Therefore, the sequence's fifth term is equal to 7.5.
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A rolld of wool insulation is 114cm wide and 5.2m long. one roll costs £19.65. estimate the cost of the wool insulation required for a loft floor that is 4.5m by 10m
The cost of the wool insulation required for the loft floor is £149.16498
How to estimate the cost of the wool insulation required for the loft floor?The given parameters are
Roll of wool = 114 cm by 5.2 m
One roll = £19.65 per roll
The area of one roll is calculated as
Area = Length * Width
So, we have
Area = 114 cm x 5.2 m
Convert cm to m
Area = 1.14 m x 5.2 m
Evaluate the product
Area = 5.928 m^2
The cost of the required area of loft floor is
Total cost = Unit cost/Area of 1 roll x Area of floor
This gives
Total cost = £19.65/5.928 * 4.5 * 10
Evaluate the product
Total cost = £149.16498
Hence, the cost of the wool insulation required for the loft floor is £149.16498
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what affect does a outlier have on a mean
Answer: An outlier can affect the mean by being unusually small or unusually large
Step-by-step explanation: Outliers affect the mean value of the data but have little effect on the median or mode of a given set of data.
write ____ as a single power of 7
Answer:
[tex]7^{7/2}[/tex]
Step-by-step explanation:
[tex]7^3 \times \sqrt{7} \\ \\ =7^3 \times 7^{1/2} \\ \\ =7^{7/2}[/tex]
Alyssa works as a sales representative in an electronics store. She earns a fixed daily wage plus a commission on the sales she makes. The table shows her earnings based on the amount of sales she makes in a day.
Total Sales ($) Daily Earnings ($)
0 80
200 110
500 155
800 200
1,200 260
The equation that gives Alyssa's daily earnings based on her total sales is .
When this data is plotted on a graph with a line connecting all the points, the y-intercept of the line represents and the slope of the equation represents .
In this scenario, the y-intercept is .
The slope of the line relating Alyssa's sales to earnings is given by 0.15,the equation that gives Alyssa's daily earnings based on her total sales is y = 0.15x +80,the y-intercept of the line represents the part of Alyssa's earnings that doesn't depend on sales. It is Alyssa's fixed daily wage and the y-intercept is 80.
What is slope intercept form of line?The slope intercept form of a line is y=mx+c, where m is the slope of line.
a) The slope of the line relating Alyssa's sales to earnings is given by
slope = (change in earnings)/(change in sales)
Using the first two table entries, the slope is calculated as
slope = (110 -80)/(200 -10) = 30/200 = 0.15
The first entry in the table shows the y-intercept, the value of earnings (80) for zero sales. The slope-intercept form of the equation for a line is
y = slope*x + y-intercept
To answer the first question, we put the slope and intercept values in the appropriate spots in the equation.
The equation that gives Alyssa's daily earnings based on her total sales is y = 0.15x +80
b) The y-intercept of the line represents the part of Alyssa's earnings that doesn't depend on sales. It is Alyssa's fixed daily wage.
c) The slope of the equation represents Alyssa's commission rate.
d) The y-intercept is 80.
Therefore The slope of the line relating Alyssa's sales to earnings is given by 0.15,the equation that gives Alyssa's daily earnings based on her total sales is y = 0.15x +80,the y-intercept of the line represents the part of Alyssa's earnings that doesn't depend on sales. It is Alyssa's fixed daily wage and the y-intercept is 80.
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