Recall that
[tex]\sin(x) = \displaystyle \sum_{n=0}^\infty (-1)^n \frac{x^{2n+1}}{(2n+1)!}[/tex]
which converges for all real x. (One can show this with the ratio test, for instance.)
Then
[tex]\sin\left(x^4\right) = \displaystyle \sum_{n=0}^\infty (-1)^n \frac{\left(x^4\right)^{2n+1}}{(2n+1)!} = \boxed{\sum_{n=0}^\infty (-1)^n \frac{x^{8n+4}}{(2n+1)!}}[/tex]
By the ratio test,
[tex]\displaystyle \lim_{n\to\infty} \left|\frac{(-1)^{n+1} x^{8(n+1)+4}}{(2(n+1)+1)!} \times \frac{(2n+1)!}{(-1)^n x^{8n+4}}\right| \\\\ = x^8 \lim_{n\to\infty} \frac{(2n+1)!}{(2n+3)!} \\\\ = x^8 \lim_{n\to\infty} \frac1{(2n+3)(2n+2)} = 0[/tex]
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Answer:
what do you need help with
Step-by-step explanation:
Answer:
SAME
Step-by-step explanation:
I am so happy someone else goes through this! I'm SO happy I'm not alone.
Which of these ordered pairs is a solution to the inequality
y – 2x ≤ –3?
Question 3 options:
(2, 4)
(–2, 3)
(3, 4)
(1, –1)
The answer is: (1, –1)
Gavin invested $100 into a CD account. The account grow at a rate of 5%
each year. What type of equation do this scenario represent?
Answer: y=5x+100
Step-by-step explanation:
the y intercept is the 100$ invested into the account, and the rate of change is 5
If r(x) = 3x – 1 and s(x) = 2x 1, which expression is equivalent to (startfraction r over s endfraction) (6)? startfraction 3 (6) minus 1 over 2 (6) 1 endfraction startfraction (6) over 2 (6) 1 endfraction startfraction 36 minus 1 over 26 1 endfraction startfraction (6) minus 1 over (6) 1 endfraction
The expression which is equivalent to the given ratio of the two provided binary fraction is startfraction 3 (6) minus 1 over 2 (6) 1 endfraction.
What is the equivalent expression?Equivalent expressions are the expression whose result is equal to the original expression, but the way of representation is different.
The given binary functions are.
[tex]r(x) = 3x - 1[/tex]
[tex]s(x) = 2x +1[/tex]
The expression which has to be found out is,
[tex]\left(\dfrac{r}{s}\right)(6)=\left(\dfrac{3(6)-1}{2(6)+1}\right)\\\left(\dfrac{r}{s}\right)(6)=\left(\dfrac{18-1}{12+1}\right)\\\left(\dfrac{r}{s}\right)(6)=\left(\dfrac{17}{13}\right)[/tex]
Thus, the expression which is equivalent to the given ratio of the two provided binary fraction is startfraction 3 (6) minus 1 over 2 (6) 1 endfraction.
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Late night math for you guys to solve
A rectangle is 28 cm long and 9 cm wide what is thr perimeter of the rectangle pls hurry
Answer:
Perimeter of rectangle = 74 cmStep-by-step explanation:
In the question we are given with ,
Length of rectangle = 28 cmWidth of rectangle = 9 cmAnd we are asked to find the perimeter of rectangle . As we know that ,
[tex] \red {\boxed{\rm{Perimeter \: of \: rectangle = 2 ( L + W ) }}}[/tex]
Where ,
L = Length of rectangleW = Width of rectangleSubstituting values of length and width in formula :
[tex] \longmapsto \: 2(28 + 9)[/tex]
Step 1 : Solving the parenthesis :
[tex] \longmapsto \: 2(37)[/tex]
Step 2 : Multiplying 2 and 37 :
[tex] \longmapsto \: \red{ \boxed{74 \: cm}}[/tex]
Therefore , perimeter of rectangle having length 28 cm and width 9 cm is 74 cm .#Keep Learningfind the area of the equilateral triangle
Answer:
3.90 sq cm
Step-by-step explanation:
[tex]A_{equilateral\: \triangle} = \frac{ \sqrt{3} }{4} \times {(side)}^{2} \\ \\ = \frac{ \sqrt{3} }{4} \times {(3)}^{2} \\ \\ = \frac{9 \sqrt{3} }{4} \\ \\ = 3.89711432 \: {cm}^{2} \\ \\ \approx \: 3.90 \: {cm}^{2} [/tex]
Solve for X please answer
Answer:
x=1.082682
Step-by-step explanation:
What is the value of log subscript 0.5 baseline 16? –4.00 –0.25 1.51 2.41
Answer:
The correct option is a.
The given expression is,Use property of logarithm
The value of log(0.5) is -0.30103.
The value of given expression is -4.81648.
If the final answer appromatted to preceding integer, then the correct option is -4.00.Step-by-step explanation:
The value of the [tex]log_{0.5}[/tex] (16) will be -4.00 so the correct option will be (A).
What is a logarithm?The exponent indicates the power to which a base number is raised to produce a given number called a logarithm.
A logarithm is a power to which a number must be raised in order to get some other number.
A logarithm is useful to find out the values on which power has a variable.
In another word, a logarithm is a different way to denote any number.
If you want to write 1 in logarithm then it will be log(base).
[tex]log_{a}[/tex] (x) = b ⇒ [tex]a^{b}[/tex] = x.
Let's say the given number is x then
x = [tex]log_{0.5}[/tex] (16)
[tex]0.5^{x}[/tex] = 16
Take log by both sides
Log[tex]0.5^{x}[/tex] = log 16
By log property
x log 0.5 = log 16
x = -4.00 hence, the correct answer to the given question will be -4.00.
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what is the length of AD and find the measure of angle CAB
Answer:
AD = 44 and angle CAB = 90 degrees
Step-by-step explanation:
since the shape is a rectangle, all corner angles must be 90 degrees. so CAB is also 90 degrees.
the length of half of BC is 22, so the full length of BC is 44. using symmetry, AD should also be 44.
byebye!<3
What is the percent of increase from 2.5 to 4?
Answer:
60%
Step-by-step explanation:
(4-2.5):2.5*100 =
(4:2.5-1)*100 =
160-100 = 60
¿Alguien me ayuda con estas ecuaciones? :(
Answer:
see below
Step-by-step explanation:
7x-12=30
7x=30-+12
x=42/7
x=6
5x-18=77
5x=77+18
x=95/5
x=19
8x+12=36
8x=36-12
x=24/8
x=3
x+45=72
x=72-45
x=27
x+27=82
x=82-27
x=55
x-13=66
x=66+13
x=79
CAN u pls pls pls help its easy for yall not me im slow
Answer:
A
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
2.25/.5
You flip an unfairly weighted coin 4 times. If the probability of getting a tail is 0. 38.
What is the probability you will get at most 2 tails?
work needed
Answer:
0.84306608
Step-by-step explanation:
The probability of an event, e, occurring exactly r times over n trials follows the formula
(n combination r) * p^r * q ^ (n-r)
with p being the probability the event will occur and q being the probability the event will not occur.
I assume you have a calculator/can find one online that can do combinations.
Here, we want to figure out if you get:
- 0 tails
- 1 tail
- 2 tails
If you get 3 or 4 tails, we are getting more than the 2 tails desired
For 0 tails:
- p is the probability a tail will occur = 0.38
- we want it to occur 0 times, so r = 0
- q is (1-p) = 1- 0.38 = 0.62
- we have 4 trials, as we flip it 4 times
(n combination r) * p^r * q ^ (n-r) = (4 combination 0) * (0.38) ^0 * (0.62) ^(4-0) = 1 * (0.38) ^0 * (0.62) ^(4-0) = 0.14776336
For 1 tail:
- p = 0.38, q = 0.62 as with 0 tails
- r = 1, n = 4
(n combination r) * p^r * q ^ (n-r) = (4 combination 1) * (0.38) ^1 * (0.62) ^(4-1) = 4* (0.38) ^1 * (0.62) ^(4-1) = 0.36225856
For 2 tails:
- p = 0.38, q = 0.62 as with 0 tails
- r = 2, n = 4
(n combination r) * p^r * q ^ (n-r) = (4 combination 2) * (0.38) ^1 * (0.62) ^(4-2) = 6* (0.38) ^2 * (0.62) ^(4-2) = 0.33304416
add our 3 probabilities together
0.33304416 + 0.36225856 + 0.14776336 = 0.84306608 as our answer
Noah enjoys building towers in the shape of right rectangular prisms. Noah built a right rectangular prism, the area of
the base is __ square centimeters and the height is __ centimeters.
Answer:
do you have a picture so I can see more information
Jose is in 8th grade, and he is researching his favorite colleges. He notices that the current cost of tuition, books, and fees at one 4-year college is $14,500 per year. What will be the total cost of tuition, books, and fees for Jose if he eventually chooses to attend this college for four years?
Question 10 options:
A. $56,000
B. $29,000
C. $60,000
D. $58,000
The total cost of tuition, books, and fees for Jose if he eventually chooses to attend this college for four years is $58,000.
What is the total cost of attending the college for four years?
Multipiciation is the process of combining numbers or vectors together in order to determine their product. Multiplication is represented with this sign: x.
The total cost of attending the college for four years = cost per year x total number of years
$14,500 x 4 = $58,000
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The measure of angle C is 20.5 angles C and D are complementary angles Find m
Answer:
69.5 if C and D both add up to 90, M=90 if both angles C and D were complementary to combine to a supplementary.
Step-by-step explanation:
You're trying to find m which is a variable for measurement for the "D" angle.
Info Given:
20.5 for angle C
Unknown for angle D
Both angles are Complementary.
_____________________________________________
I have 2 answers for this (The question was stated unclearly so I have 2 interpretations of this)
1st Answer:
If you're asking to solve for M but the C and D angles add up to 90 then do
90 - 20.5 = 69.5
2nd Answer:
We know that both angles are complementary which are 90-degree angles.
If we combine them then the angles add up to 180.
So C and D add up to form a Supplementary Angle.
20.5+69.5 + m = 180
Then M could possibly be 90.
When f = 2 and g = 8, n = 4. if n varies jointly with f and g, what is the constant of variation? one-fourth one-half 4 64
The value of the constant of variation is one-fourth. Then the correct option is A.
What is the constant of variation?The term "constant of variation" refers to the fact that the relationship between variables remains constant.
The formula will be
y = kx
where k is the variation constant.
When f = 2 and g = 8, n = 4. if n varies jointly with f and g, then the equation will be
n = kgf
Then the value of k will be
4 = (2)(8)k
k = 1/4
More about the constant of variation link is given below.
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Answer:
Keep it simple. Answer: A
Step-by-step explanation:
Find the surface area of the cube shown below.
units 2 1/2
Answer:
Step-by-step explanation:
Answer: 37.5
Explanation: find the surface area of one side, which is 2.5*2.5=6.25 then multiply that product by six, since there’s six sides in a square, and you’ll get 37.5
-1.9y=2.47
rational equations!
please helP!
Answer: y = -1.3
Step-by-step explanation:
what is 3.20 divided by 5
Answer:
0.64
Step-by-step explanation:
...........................
Answer:
0.64
Step-by-step explanation:
3.20 divided by 5 is 0.64.
...................................
Since, the fundraiser only have three prices for books($2, $5 and $10), the number of $5 book that was sold is 12.
How to form equation and solve ?The fundraiser only have 3 prices for books which are $2, $5 and $10.
There were 6 more $5 books sold than $10 books sold.
Let
x = number of $10 book sold
Therefore,
number of $5 books sold = x + 6
There are 8 more $2 book sold than $10 book sold. Therefore,
number of $2 books sold = x + 8
A total of $250 was raised.
Therefore, the total amount sold forms the following equation:
10x + 5(x + 6) + 2(x + 8) = 250
10x + 5x + 30 + 2x + 16 = 250
17x = 250 - 30 - 16
17x = 204
x = 204 / 17
x = 12
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For what values of x is the inequality 2/3 + x/3 >1 true?
Answer:
B
Step-by-step explanation:
[tex]\frac{2}{3}[/tex] + [tex]\frac{x}{3}[/tex] > 1 ( multiply through by 3 to clear the fractions )
2 + x > 3 ( subtract 2 from both sides )
x > 1
The box plot below represents some data set. What is the interquartile range (IQR) of
the data?
-
42
45
48
51
54
57
60
Answer:
IQR = 5
Step-by-step explanation:
the IQR is the difference between the upper quartile Q₃ and the lower quartile Q₁
Q₃ is the value at the right side of the box plot , that is
Q₃ = 51
Q₁ is the value at the left side of the box plot , that is
Q₁ = 46
then
IQR = Q₃ - Q₁ = 51 - 46 = 5
9. What is the volume of the triangular prism
below?
5cm
3cm
4cm
3cm
Answer:
where is the prism? did u attach a photo of it
A quadratic equation of the form 0=ax2 bx c has a discriminant value of -16. how many real number solutions does the equation have?
The given quadratic equation has no real solutions.
Given quadratic equation is:
[tex]ax^2+bx+c=0[/tex]
What does the discriminant of a quadratic equation tell?The discriminant(D) of a quadratic equation tells about the nature of roots.
If [tex]D > 0[/tex], the roots of the quadratic equation will be real and distinct.
If [tex]D=0[/tex], the roots of the quadratic equation will be real and equal.
If [tex]D < 0[/tex], the roots of the quadratic equation will be imaginary.
Given that the quadratic [tex]ax^2+bx+c=0[/tex] has a discriminant value of -16.
[tex]D=-16 < 0[/tex]
So, the roots of the given quadratic equation will be imaginary.
So, the given quadratic equation has zero real solutions.
Hence, the given quadratic equation has no real solutions.
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Algebra Find the value of each variable.
pls help
The zeros of a quartic polynomial function are 2, -2, 4, and -4. Use the zeros to construct a possible sketch of the function on the set of axes
The sketch of the function on the set of axes is given below:
What are Zeros?The zero of any real-, complex-, or generally vector-valued function f, is a member x of the domain of function such that f(x)=0 at x; x is the solution to the equation f(x) = 0.
Finding the function:As we have the zeros 2,-2,4,-4
The function can be:
[tex]f(x)=(x-2)(x+2)(x-4)(x+4)\\f(x)=(x^2-4)(x^2-16)\\f(x)=x^4-20x^2+64[/tex]
The sketch using a graphing calculator:
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Reggie writes the expression m + 8 × (2/3). Which expression is equivalent to the one Reggie writes?
Answer:
A
Step-by-step explanation:
A)(m+8)(2 ÷3)
Because 2/3 is just 2 divided by 3
Brainliest please?
the sum of two integers always greater than the difference between them? Why or why not? Give examples
Answer:
Yes, because the gap is one less than the bigger of the two integers, plus you are adding a little bit more to the bigger integer so the sum will always be bigger than the difference.