Answers
Answer:
-x¹⁴ / 5040
-½ < x < ½
Step-by-step explanation:
f(x) = e^(-x²)
The Taylor series for eˣ centered at 0 is:
eˣ = ∑ (1/n!) xⁿ
Substitute -x²:
e^(-x²) = ∑ (1/n!) (-x²)ⁿ
e^(-x²) = ∑ (1/n!) (-1)ⁿ x²ⁿ
The 14th degree term occurs at n=7.
(1/7!) (-1)⁷ x¹⁴
-x¹⁴ / 5040
ln(1 + x) = ∑ₙ₌₁°° (-1)ⁿ⁺¹ xⁿ / n
If we substitute 4x²:
ln(1 + 4x²) = ∑ₙ₌₁°° (-1)ⁿ⁺¹ (4x²)ⁿ / n
Using ratio test:
lim(n→∞)│aₙ₊₁ / aₙ│< 1
lim(n→∞)│[(-1)ⁿ⁺² (4x²)ⁿ⁺¹ / (n+1)] / [(-1)ⁿ⁺¹ (4x²)ⁿ / n]│< 1
lim(n→∞)│-1 (4x²) n / (n+1)│< 1
4x² < 1
x² < ¼
-½ < x < ½
Related Questions
What is the quotient between 215÷9
Answers
215/9
= 23.888888........
It is written as shown in the picture
[PICTURE] please answer all questions 1-5 ASAP thanks! FOR 20 PTS!!
Answers
Answer:
bellnshaped i think
Step-by-step explanation:
∠10 and angle _____ are complementary angles.?
a.) ∠9 I
b.)∠11 O
Answers
Answer:
9
Step-by-step explanation:
they add up to 90 degrees
Answer: B
Step-by-step explanation:
HAVE A BLESSED DAY!!!!!!
Andrew is showing his work in simplifying −4.5 + 4.2 + 5.6 − 7.3. Identify any errors in his work or in his reasoning.
Step Work Reasoning
−4.5 + 4.2 + 5.6 − 7.3 Original problem
1 −4.5 + 4.2 + 5.6 + (−7.3) Additive inverse
2 −4.5 + (−7.3) + 4.2 + 5.6 Commutative property
3 [−4.5 + (−7.3)] + (4.2 + 5.6) Associative property
4 −11.8 + 9.8 Simplify
5 −21.6 Simplify
Step 1: He wrote −7.3 incorrectly as + (−7.3).
Step 2: He identified changing the order of the numbers as the commutative property, which is incorrect.
Step 3: He identified changing the grouping of the numbers as the associative property, which is incorrect.
Step 5: He simplified incorrectly.
Answers
Answer:
5.
Step-by-step explanation:
He simplified incorrectly:
-11.8 + 9.8 = -2, not -21.6.
Are the following 2x2 matrices inverses or not?
1 ㅔ
1 2 & 0 1
30
2 -1
Answers
Answer: A . Not all 2 × 2 matrices have an inverse matrix. If the determinant of the matrix is zero, then it will not have an inverse; the matrix is then said to be singular. Only non-singular matrices have inverses.
Step-by-step explanation:
Use the distributive property to remove the parentheses.
2x+(6x2-9)
Simplify your answer as much as possible.
Answers
After removing the parentheses using the distributive property, the expression [tex]2x^4 (6x^2 - 9)[/tex] simplifies to [tex]12x^6 - 18x^4.[/tex]
We have,
To remove the parentheses using the distributive property, we need to multiply each term inside the parentheses by the term outside the parentheses.
Applying the distributive property to the expression [tex]2x^4 (6x^2 - 9),[/tex] we have:
[tex]2x^4 * 6x^2 - 2x^4 * 9[/tex]
Multiplying the terms:
[tex]12x^6 - 18x^4[/tex]
Therefore,
After removing the parentheses using the distributive property, the expression [tex]2x^4 (6x^2 - 9)[/tex] simplifies to [tex]12x^6 - 18x^4.[/tex]
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Look at this coordinate plane
Which equation can be used to find the y-coordinate of point B?
y/1=23
y/2=56
y−1/2=4/6
y−1/2=y−5/4
Answers
Answer:
Hrmm
Step-by-step explanation:
Kara earned $136.75 last week working 16 hours. She earned $10.50 per hour at the fast food restaurant and $4.25 per hour helping her aunt clean her store.
How many hours did she work at the fastest food restaurant? How many hours did she help her aunt clean the store? In your response make sure to:
Create a model that can be used to determine the number of hours Kara worked at each job.
Define your variables.
Show all your work.
Answers
Answer:
First we are going to try to find how many hours she worked on the fast food restaurant so you multiply 4.25 time 16 and x
10.50x + 4.25(16-x) =136.75
10.50x + 68 - 4.25x= 136.75
Then, you subtract 68 from both sides and subtract 4.25x from 10.50x
6.25x=68.75
Divide
X=11 that is how many hours she worked at the FAST FOOD RESTAURANT
Then 16-11 and that gives us how many hours she helped her aunt.
ANSWER: she worked 11 hours at the fast food restaurant and 5 hours helping her aunt
Step-by-step explanation:
Here, we are required to determine how many hours Kara worked at the fastest food restaurant and how many hours did she help her aunt clean the store.
The number of hours worked by Kara in the restaurant is; 11hours.The number of hours worked by Kara in the restaurant is; 11hours.The number of hours worked by Kara in her aunt's store is; 5hours.First, we need to create a model for the work done and how much she earned.
Total earnings = $136.75Total hours worked = 16 hoursLet hours worked at the restaurant = xLet hours worked at the store = (16-x)Hourly rate at restaurant = $10.50Hourly rate at store = $4.25The model is therefore in the form;
$10.50(x) + $4.25(16-x) = $136.75
To determine the no. of hours worked at the fast food restaurant, we have to evaluate the value of x.
Therefore;
10.50x + 68 - 4.25x = 136.756.25x = 68.75x = 11
The number of hours worked by Kara in the restaurant is; 11hours.
The number of hours worked by Kara in her aunt's store is; (16 - 11) hours = 5hours.
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I didn't grasp this topic too well. can someone help me?
Answers
Answer:
2 hours
Step-by-step explanation:
I'm pretty sure its 2 hrs. If she did not take any breaks, she would have made it in 2 hrs due to her taking a 2 hr break. If its not 2 hours, its 3. But I am 99% sure its 2 hrs.
Select the story problem that this division problem represents. 3/4 / 1/5. Please help I will give brainliest, thanks!
Answers
Answer:
The answer is b
Step-by-step explanation:
To find the length of the mosaic, we need to use the area divided by width which is 3/4 / 1/3
70 POINTS Please answer the questions, it would help a lot.
Answers
You did not give 70 points, that was just 35 points
c. What is the major drawback of using the recursive rule?
Answers
Answer:
Use of recursion in an algorithm has both advantages and disadvantages. The main advantage is usually the simplicity of instructions. The main disadvantage is that the memory usage of recursive algorithms may grow very quickly, rendering them impractical for larger instances.
Answer:
uses more memory
recursion can be slow
Help, Ill give extra points too!
Answers
Answer:
(-6,-18) & (2,6) -----------> 3
(12,6) & (-4,-2) -----------> [tex]\frac{1}{2}[/tex]
(5,-19) & (6,-23) ----------> -4
(3,4) & (3,9) ---------------> unidentified
(1,-10) & (2,-15) -----------> -5
(-1,8) & (3,8) ---------------> 0
(0,0) & (21,14) -------------> [tex]\frac{2}{3}[/tex]
Step-by-step explanation:
Use this formula to find all of these slopes.
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Assessment
D. Fibonaces
2. The geometne sequences below has a common ratio of -2. except:
A32, 16, S. B*8. 16, 32 2. 4.-8.16 D. 3.-6. 12. 24
3. What is the common rate of the sequence 1000, 1000, 100, 10, 12
A
B 10
C 100
D. 1000
1.3,
4. Which of the following sequences illustrates arithmetic sequence?
-5. 0, 5, 10, 15.
3. 9. 27. 81.243,
IV. 4.1. -2.-5.-8.
AI and I
C II and III
B. I and IV
DI and IV
5. Which of the following does NOT belong to the group?
4.5. -10. 20.0
C 18. 15. 12.9
B-5. -10, -15, -20
D. 2. 4. 6,8
6. In the geometric sequence what is the next term?
A
B. 3
C.
D. 729
8
Answers
1). c
2). a
3). a **
4). d
5). a
6). c
** Question #3 has a typo (a typographical error, a misprint, an error, a mistake, a blunder, an oops, an owee) on the question sheet. The first number of the sequence should be 10,000 instead of 1000 .
1. If a sequence has a common ratio, it is called: C. Geometric Sequence
2. The sequence that does not have a common ratio of -2 is: A. -32, 16, -8, 4
3. The common ratio of 10,000, 1,000, 100, 10, 1 is: [tex]\mathbf{A. \frac{1}{10}}[/tex]
4. The sequences that are arithmetic sequence are:
D. I and IV.
5. The sequence that does not belong to the group is: A. 5, -10, 20, -40.
6. The next term of the geometric sequence is: C. [tex]\frac{1}{729}[/tex]
Recall:
In an ordered list of numbers, if each next term is found by multiplying the previous term by a constant known as the common ratio (r), the sequence is referred to as Geometric sequence.For an arithmetic sequence, the next term is found by adding a constant to the previous term. The constant added is referred to as the common difference.1. Therefore, if a sequence has a common ratio, it is called: C. Geometric Sequence
2. Common ratio = next term / previous term
The sequence, -32, 16, -8, 4 has the following common ratio which is not -2:
[tex]\frac{4}{-8} = \frac{-8}{16} = \frac{16}{-32} = -\frac{1}{2}[/tex]
The common ratio is: [tex]-\frac{1}{2}[/tex]
Therefore, the sequence that does not have a common ratio of -2 is: A. -32, 16, -8, 4
3. Find the common ratio of: 10,000, 1,000, 100, 10, 1
Common ratio = next term / previous term
Thus:
Common ratio = [tex]\frac{1}{10} = \frac{10}{100} = \frac{100}{1,000} = \frac{1,000}{10,000} = \frac{1}{10}[/tex]
Therefore, the common ratio of 10,000, 1,000, 100, 10, 1 is: [tex]\mathbf{A. \frac{1}{10}}[/tex]
4. An arithmetic sequence is an ordered list whereby the next term is gotten by adding a constant to the previous term.
Simply put, the ordered list of numbers has a difference between each terms.
To find the common difference, subtract the previous term from the next term.
Thus:
-5, 0, 5, 10, 15 would have the following common difference:
0 - (-5) = 5
5 - 0 = 5
10 - 5 = 5
15 - 10 = 5
Also:
4, 1, -2, -5, -8 would have the following common difference:
1 - 4 = -3
-2 - 1 = -3
-5 -(-2) = -3
-8 -(-5) = -3
Therefore, the sequences that are arithmetic sequence are:
D. I and IV.
5. The sequence, 5, -10, 20, -40, is a geometric sequence, that is it has a common ratio as shown below:
Common ratio = [tex]\frac{-40}{20} = \frac{20}{-10} = \frac{-10}{5} = -2[/tex]
The rest of the sequence in the answer choices have a common difference and are arithmetic sequences except 5, -10, 20, -40.
Therefore, the sequence that does not belong to the group is: A. 5, -10, 20, -40.
6. To find the next term in the geometric sequence, [tex]\frac{1}{9}, \frac{1}{27}, \frac{1}{81}, \frac{1}{243}[/tex], find the common ratio.
Then multiply it by the last term to get the next term in the sequence.
Common ratio = Next term / previous term
[tex]= \frac{1}{27} \div \frac{1}{9} \\\\= \frac{1}{27} \times \frac{9}{1} \\\\= \frac{1 \times 9}{27 \times 1}\\\\= \frac{9}{27} \\\\= \frac{1}{3}[/tex]
Multiply [tex]\frac{1}{3}[/tex] by [tex]\frac{1}{243}[/tex] to get the next term:
[tex]\frac{1}{243} \times \frac{1}{3} = \frac{1 \times 1}{243 \times 3} \\\\= \frac{1}{729}[/tex]
Therefore, the next term of the geometric sequence is: C. [tex]\frac{1}{729}[/tex]
In summary,
1. If a sequence has a common ratio, it is called: C. Geometric Sequence
2. The sequence that does not have a common ratio of -2 is: A. -32, 16, -8, 4
3. The common ratio of 10,000, 1,000, 100, 10, 1 is: [tex]\mathbf{A. \frac{1}{10}}[/tex]
4. The sequences that are arithmetic sequence are:
D. I and IV.
5. The sequence that does not belong to the group is: A. 5, -10, 20, -40.
6. The next term of the geometric sequence is: C. [tex]\frac{1}{729}[/tex]
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Graph a line with a slope of 4 that contains the point (3,0).
Answers
Hi there!
Recall that slope-intercept form is:
y = mx + b
Where m = slope
In this instance, we are given a slope of 4, therefore:
y = 4x + b
Substitute in the x and y coordinates of the point given:
0 = 4(3) + b
0 = 12 + b
Subtract 12 from both sides:
-12 = b
Therefore, the equation would be:
y = 4x - 12
Graph the equation by finding x and y values or using a calculator:
x = 0, y = 4(0) - 12 = 12 (0, 12)
x = 1, y = 4(1) - 12 = -8 (1, -8)
x = 2, y = 4(2) - 12 = -4 (2, -4)
x = 3, y = 4(3) - 12 = 0 (3, 0)
And so forth:
To graph a line passing through a point (3, 0) and slope 4, we will find the equation of the line first.
Since, equation of a line passing through a point (h, k) and slope 'm' is given by,
y - k = m(x - h)
Therefore, equation of a line passing through (3, 0) and slope 4 will be,
y - 0 = 4(x - 3)
y = 4x - 12
For y-intercept put x = 0 in the equation,
y = 4(0) - 12
y = -12
For x-intercept put y = 0 in the equation,
0 = 4x - 12
x = 3
Therefore, line will intersect x-axis at (3, 0) and y-axis at (0, -12).
By joining these points we can find the graph of the line passing through (3, 0) and having slope = 4.
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Given f(x)=2x+5 find f(3)
answer choices are:
1. ) 28
2.) -28
3.) 11
4.) 6x+5
5.) 5
Answers
Answer:
3.) 11
General Formulas and Concepts:
Pre-Alg
Order of Operations: BPEMDASStep-by-step explanation:
Step 1: Define
f(x) = 2x + 5
f(3) is x = 3
Step 2: Solve
Substitute: f(3) = 2(3) + 5Multiply: f(3) = 6 + 5Add: f(3) = 11The equations y = tan^2 (x) and y = 1 are graphed below. According to the graphwhich of the following is part the solution to the trigonometric inequality tan^2 (x) < 1 over the interval 0 <= x <= 2pi radians?
Answers
Answer: a
Step-by-step explanation:
just took test edg2020
The part of the solution of the equation that lies in the solution region of the inequality is x = π/6, the correct option is A.
What is an Inequality?An Inequality is a statement that is formed when two expressions are joined using an inequality operator.
The equation is
y = tan²x
y = 1
the inequalities are
tan²x < 1 ( 0≤ x ≤ 2π)
The graph of the system of equations and the inequality is plotted, and attached with the answer.
The answer can be seen as x = π/6.
To know more about Inequality
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A car traveled 480 miles in 4 hours. If its speed was 12 mph faster, what distance would it have traveled in 4 hours?
Answers
Answer:
528 miles
Step-by-step explanation:
First, we need to figure out how many miles it drives in 1 hour:
480 divided by 4 = 120
now, we add 12 to 120: 120 + 12 = 132
132 x 4 = 528
hope this helped have a great day/night!! :'')
what is the value of the digit in the tens place? 6,423
Answers
Answer: 20 :)
Step-by-step explanation:
helppp
i will mark the crown
please do all
Answers
Answer:
Answer is C
Step-by-step explanation:
Can someone pls help me this it’s due in an hour but I can’t figure it out
Answers
Answer: I do believe that it is that the smooth shape is the dominate and the wrinkled is the resistive.
Step-by-step explanation:
Evan's favourite hobby is origami. He plans to make 100 paper cranes to hang from the ceiling of his bedroom. Yesterday, he made 28 paper cranes in 4 hours. Today, he made 21 paper cranes at the same rate.
How long did Evan spend making paper cranes today?
Answers
Answer:
it took him 3 hours
Step-by-step explanation:
28 divideed by 4= 7
21divided by 7=3
Jane needs open-topped boxes to store her excess inventory at year's end. She purchases large
rectangles of thick cardboard with a length of 12 inches and width of 8 inches to make the boxes.
She is interested in maximizing the volume of the boxes and wants to know what size squares to
cut out at each corner of the cardboard (which will allow the corners to be folded up to form the
box) to do this. What is the maximum volume?
Answers
Answer:
x = 1,6 in ( the side of the corner squares )
V(max) = 67,58 in³
Step-by-step explanation:
The cardboard is:
L = 12 in w = 8 in
Let´s call "x" the side of the square from the corner:
Then the sides of the base of the open box are:
( L - 2*x ) and ( w - 2*x ) and x is the height
( 12 - 2*x ) and ( w - 2*x )
V(ob) = (L - 2*x ) * ( - 2*x ) * x
Wich is a function of x
V(x) = [( 12 - 2*x ) * ( 8 - 2*x ) ]*x
V(x) = ( 96 - 24*x - 16*x + 4*x²) * x
V(x) = 96*x - 40*x² + 4*x³
Tacking derivatives on both sides of the equation
V´(x) = 12*x² - 80*x + 96
V´(x) = 0 12*x² - 80*x + 96 = 0
Solving for x
x₁,₂ = 80 ± √ 6400 - 4608 / 24
x₁,₂ = 80 ± 42,33 / 24
x₁ = 5,10 We dismiss this solution since 2*x becomes 2*5,10 = 10,20
ant this value is bigger than 8 inches
x₂ = 1,60 in
Therefore dimensions of the box
a = 12 - 2*x ; a = 12 - 3,20 ; a = 8,8 in
b = 8 - 2*x ; b = 8 - 3,20 ; b = 4,80 in
And the volume of the open box is:
V(max) = 8,8*4,8*1,6
V(max) = 67,58 in³
How do we Know that is the maximun value for V?
We find V´´(x) = 24*x - 80 for x = 1,6 is negative ( V´´(x) = - 41,6 therefore V (x) has a local maximun for a value of x = 1,6
Raia purchases a new car for $32,000 and
finances it with a 6-year simple interest
loan at a rate of 4.25%. What are Raia’s
monthly car payments?
Answers
2. Which relation below is NOT a function?
A. {(-2, 4), (1,3), (0,4)}
B. {(5,5), (4,4), (3,3) }
C. {(-4,0), (-7,0), (11, 0)}
D. {(1,4), (2,5) (1,7)}
Answers
C is the answer to that question i think
Answer:
b
Step-by-step explanation:
The answer is B because different X values cannot have the same y values. For example in A the x values, -2 and 0, have the same y value 4. That's not possible.
Although C also has a similar problem ALL of the X values have the same y value meaning that the function is an undefined function which is still a type of function. Its basically a function where all the y values are the same.
Need help right now, big points
1, I thought of a two-digit number. The unit digit of my number is a prime number, and the tens digit is four times as big as the unit digit. What is my number?
2,I thought of a two-digit number. The digits of my number are different. The unit digit of my number is the tens digit raised to the third power. What is my number?
3,I thought of a two-digit number. The unit digit of my number is 7 more than the tens digit cubed. What is my number?
4. I thought of a three-digit number. Each digit to the left is the square of the previous digit. What is my number?
(Answer all the questions please, thank you very much!)
Answers
Answer:
1) 82
2) 28
3) 18
4) 111
Step-by-step explanation:
1) a two digit number can be written as:
N = b*10 + c*1
where b and c must be single digit numbers
in this case, c is a prime number, and b = 4*c
The prime numbers are:
2, 3, 5...
if c = 2, then:
b = 4*2 = 8
And the two digit number is: 82.
if c = 3, then:
b = 4*3 = 12, and this leads to a 3 digit number.
And for any large value of c, b will not be a single digit number, then the only option here is 82.
2) same as before:
N = b*10 + c
c = b^3.
c ≠ b
Let's give different values for b, and see what happens.
b can not be zero, because that will lead to a single digit number, then we start with one.
b = 1 ----> c = 1^3 = 1 ----> (c = b, then this is not our number)
b = 2 ----> c = 2^3 = 8, then:
N = 2*10 + 8 = 28.
if b = 3 ----> c = 3^3 = 28 (this is not a single digit number, then any value of b equal or larger than 3 does not work)
The only solution here is 28.
3) Same as before:
N = b*10 + c
c = b^2 + 7.
Same approach as before, let's give different values to b and see which one works:
b = 1 ----> c = 1^2 + 7 = 8
N = 1*10 + 8 = 18.
b = 2 ---> c = 2^2 + 7 = 4 + 7 = 11 (This is a two digit number, then any value of b equal or larger than 2 can be discarded)
The only option here is 18.
4) Now we have:
N = a*100 + b*10 + c.
where:
b = c^2
a = b^2.
Now let's give values to c. (here we can start with zero).
if c = 0 , then: b = 0^2 = 0, then: a = 0^2 = 0.
Then N = 0*100 + 0*10 + 0 = 0 (this is not a 3 digit number)
if c = 1, then: b = 1^2 = 1, then: a = 1^2
N = 1*100 + 1*10 + 1 = 111
If c = 2, then: b = 2^2 = 4, then: a= 4^2 = 16 (here a is not a single digit number, then values of c equal or larger than 2 can be discarded)
The only correct option here is 111.
X to the second power plus 3x - 4=6
Answers
Answer:
answer is 2
Step-by-step explanation:
Answer:
x^2+3x-4=6
Step-by-step explanation:
first you add the x
read the the following question
Answers
Answer:
11 (answer c)
Step-by-step explanation:
you need to find LCD and then combine
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[tex] \frac{7}{8} \div \frac{1}{8} + {2}^{2} = \\ [/tex]
[tex]( \frac{7}{8} \times 8) + {2}^{2} = \\ [/tex]
[tex]7 + 4 = 11[/tex]
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A sports ball has a diameter of 27 cm. Find the volume of the ball. cm.) Round your answer to the nearest tenth if necessary.
Answers
v=4/3pir^3
The radius (r) is half of the diameter
r=13.5
v=4/3pi13.5^3
v=10305.99
Therefore the volume of the sports ball is 10306cm^3 (to the nearest tenth)
Saleh can jog 2 3/7 miles in 6/11 hour. Find his average speed in miles per hour.
Answers
Answer:
3.73
Step-by-step explanation:
