Answer:
The answer is "0.9461"
Step-by-step explanation:
Given:
[tex]\int^1_0 \frac{sin(x)}{x} dx\\\\[/tex]
[tex]\int^1_0 \frac{sin(x)}{x} dx\\\\[/tex] ≈[tex]\sum^2_{n=0}\frac{(-1)^n x^{2n+1} (-1)^n (x-1)^n}{(2n + 1)!}[/tex]
[tex]\therefore[/tex]
[tex]\to \sin x = \sum^{\infty}_{n=0} (-1)^n\frac{x^{(2n+1)}}{(2n + 1)!}[/tex]
[tex]\because \\\\ \to \frac{\sin x}{x} =\sum^{\infty}_{n=0} (-1)^n \frac{x^{2n+1-1}}{(2n+1)!}\\[/tex]
[tex]=\sum^{\infty}_{n=0} (-1)^n \frac{x^{2n}}{(2n+1)!}[/tex]
The value is in between 0 and 1 then:
[tex]\to \int^1_0 \frac{sin(x)}{x} = =\sum^{2}_{n=0} \frac{(-1)^n}{ (2n+1) (2n+1)!}[/tex]
The above-given series is an alternative series, and it will give an error, when the nth term is bounded by its absolute value, that can be described as follows:
[tex]\to \frac{1}{(2n+3) (2n+3)!}< 0.0001\\\\\to (2n+3) (2n+3)!> 0.0001\\\\\to n\geq 2 \\[/tex]
So,
[tex]\int^1_0 \frac{sin(x)}{x} dx\\\\[/tex] ≈[tex]1 - \frac{1}{3 \cdot 3!}+\frac{1}{5 \cdot 5!}\\\\[/tex]
[tex]\approx 1 - \frac{1}{3 \cdot 6}+\frac{1}{5 \cdot 120}\\\\\approx 1 - \frac{1}{18}+\frac{1}{600}\\\\\approx 1 - \frac{1}{18}+\frac{1}{600}\\\\\approx \frac{18-1}{18}+\frac{1}{600}\\\\\approx \frac{17}{18}+\frac{1}{600}\\\\\approx \frac{1700+3}{1800}\\\\ \approx \frac{1703}{1800}\\\\\approx 0.9461[/tex]
The given series is an alternative series and will give an error when the nth term is bounded by its absolute value, then the approximation summation is equal to 0.9461.
What is a power series?The finite series can be used as a polynomial with an infinite number of the term.
[tex]\int_{0}^{1} \dfrac{\sin x}{x} dx = \sum_{n=0}^{2} \dfrac{(-1)^{n}x^{2n+1}(-1)^{n}x^{n}}{(2n+1)!}[/tex]
Then we have
[tex]\Rightarrow \sin x = \sum_{n=0}^{\infty} (-1)^{n} \dfrac{x^{2n+1}}{(2n+1)!} \\\\\\\Rightarrow \dfrac{\sin x}{x} = \sum_{n=0}^{\infty} (-1)^{n} \dfrac{x^{2n+1-1}}{(2n+1)!}\\\\\\\Rightarrow \dfrac{\sin x}{x} = \sum_{n=0}^{\infty} (-1)^{n} \dfrac{x^{2n}}{(2n+1)!}[/tex]
Then the value is between 0 and 1, will be
[tex]\Rightarrow \int_0^1 \dfrac{\sin x}{x} = \sum_{n=0}^{2} \dfrac{(-1)^{n} }{(2n+1)(2n+1)!}[/tex]
The given series is an alternative series and will give an error when the nth term is bounded by its absolute value, then which can be described as
[tex]\Rightarrow \dfrac{1}{(2n+3)(2n+3)!} < 0.0001\\\\\\\Rightarrow (2n+3)(2n+3)! = > 0.0001\\\\\\\Rightarrow n > 2[/tex]
So,
[tex]\int _0^1 \dfrac{\sin x }{x} dx \approx 1- \dfrac{1}{3\times 3!} + \dfrac{1}{5\times 5!}\\\\\\\int _0^1 \dfrac{\sin x }{x} dx \approx 1- \dfrac{1}{3\times 6} + \dfrac{1}{5\times 120}\\\\\\\int _0^1 \dfrac{\sin x }{x} dx \approx 1- \dfrac{1}{18} + \dfrac{1}{600}\\\\\\\int _0^1 \dfrac{\sin x }{x} dx \approx 0.9461[/tex]
More about the power series link is given below.
https://brainly.com/question/14318966
In class, there are 9 boys and 13 girls. If half of the class has a cold, how many girls must have a cold?
Answer: a or c one of those
Step-by-step explanation:
Your bank account is $32.00. You make the following withdrawals, in the following order: $15.00,$7.41,$35.79, and $ 0.53. After each withdrawal that leaves a negative balance, the bank adds a -$32.00 bank fee to your account. what is your new balance?
this is my third time posting this bc i kept getting the wrong answer please help me
Answer:
B
Step-by-step explanation:
So we have:
[tex]\frac{x^{\frac{2}{3}}}{y^{\frac{-3}{4}}}[/tex]
First, we recall that we can switch an exponent from the denominator to the numerator if we multiply the exponent by -1 and vice versa. Therefore:
[tex]=x^{\frac{2}{3}}}\cdot {y^{\frac{3}{4}}[/tex]
Now, use the following property:
[tex]a^{x/n}=\sqrt[n]{a^x}[/tex]
Therefore:
[tex]x^{\frac{2}{3}}=\sqrt[3]{x^2}[/tex]
And:
[tex]y^{\frac{3}{4}}=\sqrt[4]{y^3}[/tex]
And so together:
[tex]=x^{\frac{2}{3}}}\cdot {y^{\frac{3}{4}}\\=\sqrt[3]{x^2}\cdot\sqrt[4]{y^3}[/tex]
Our answer is B :)
Answer:
B
Step-by-step explanation:
the answer is the letter b
2) the quotient of 14 and 7
Answer:
The quotient of 7 and 14 is 2..
can some one please help me with this.
3 1⁄8 − 1 7⁄8 =
Answer:
1 2/8
Step-by-step explanation:
3 1/8 = 25/8
25/8 - 15/8 = 10/8 = 1 2/8
A couple wants to install hardwood into their bedroom. The wood is bought in 0.5×5 square foot pieces. They have 422 square feet of floor on which to install the hardwood. How many 0.5×5 sections must be purchased?
124 sections
25 sections
169 sections
84 sections
Answer:
169 sections
Step-by-step explanation:
A couple wants to install hardwood into their bedroom. The wood is bought in 0.5×5 square foot pieces
The area of the 0.5×5 square foot pieces
Area= 0.5*5.
Area= 2.5 square feet
They have 422 square feet of floor on which to install the hardwood.
Number of sections to be purchased
= 422/2.5
= 168.8 sections
Approximately= 169 sections
simplify the following expression
Answer:
See below
Step-by-step explanation:
√160c⁵d⁴
= √160 * √c⁵ * √d⁴
= √16 * √10 * √c² * √c² * √c * √d² * √d²
= 4 * √10 * c * c * √c * d * d
= 4c²d²√10c
Answer:
The answer is
[tex]4 {c}^{2} {d}^{2} \sqrt{10c}[/tex]Step-by-step explanation:
[tex] \sqrt{160 {c}^{5} {d}^{4} } [/tex]To solve the expression, expand the terms
That's
[tex] \sqrt{ {4}^{2} \times 10 {c}^{4} \times {cd}^{4} } [/tex]Using the rule
The square root of a product is equal to the product of the roots of each factor.
Expand
That's
[tex] \sqrt{ {4}^{2} } \times \sqrt{ {c}^{4} } \times \sqrt{ {d}^{4} } \times \sqrt{10c} [/tex]Reduce the surds
Thats
[tex] \sqrt{ {4}^{2} } = 4 \\ \sqrt{ {c}^{4} } = {c}^{2} \\ \sqrt{ {d}^{4} } = {d}^{2} [/tex]We have
[tex]4 \times {c}^{2} \times {d}^{2} \times \sqrt{10c} [/tex]We have the final answer as
[tex]4 {c}^{2} {d}^{2} \sqrt{10c} [/tex]Hope this helps you
1. The ratio of boys to girls in the seventh grade is 2:3. If there are 24 boys, how many girls are there?
Answer:
16
Step-by-step explanation:
2/3 * 24 = 16
3. Ann wants to paste 18 posters on her bedroom wall. She wants to put the same
number of posters in each row. How many rows could Ann make, 4.5, 9 or 10?
Answer:
9
Step-by-step explanation:
18÷2=9
So, Ann could have 9 rows of posters with 2 posters in each row.
August 22 3months later what day would it be
Answer:
november 22nd
Step-by-step explanation:
PRECALC HELP WILL GIVE BRAINLIEST
Answer:
(d, left, right) ⇒ (d, di, -di)
Step-by-step explanation:
In the complex plane, successive left turns make this your sequence of facing directions: 1, i, -1, -i, 1. Effectively, your facing direction is multiplied by i.
Successive right turns make this your sequence of facing directions: 1, -i, -1, i, 1. Effectively, your facing direction is multiplied by -i.
Your table can be filled as follows:
(initial d, left turn, right turn)
(-1, -i, i)
(1, i, -i)
(i, -1, 1)
(-i, 1, -1)
(d, di, -di)
Can someone come Plzzz help??
Answer:
The probability of HHH=1/8.
Sample space=(HHH,HHT,HTH,HTT,TTT,TTH,THT,THH).
Round to the nearest dollar $7,563.27
Answer:
$7,563
Step-by-step explanation:
We will round to the nearest whole number to round to the nearest dollar
$7,563.27
since we have 27 cents ( .27), that is less than 50 cents, we leave it alone
$7,563.00 or $7,563
Answer:
$7,563
Step-by-step explanation:
Rounding to the nearest dollar is just like rounding to the nearest whole number.
The number we are given is:
$7,563.27
To round to the nearest dollar, look to the tenths place. If it is less than or equal to 4, round down. If it is greater than or equal to 5, round up.
The tenths place has a 2. Therefore, we leave the number as is.
$7, 563
$7,563 rounded to the nearest dollar is $7,563.00
Can you please help me with this I’ll give a brain list
Answer: opposite
Step-by-step explanation:
Answer:
opposite
Step-by-step explanation:
the opposite of -4 is 4.
the absolute value of -4 is 4.
the reciprocal of -4 is -1/4.
Find the standard form of the equation of the ellipse with the given characteristics. Center: (1, 2); vertex: (−7, 2); minor axis of length 12
Answer:
(x-1)²/64 + (y-2)²/ 144= 1
Step-by-step explanation:
Given that
The standard form for an ellipse is
(x-h)/a² + ( y-k)/b²=1
So
h, k
is the centre of the ellipse, and
a is the distance from the centre to the vertices and c is the distance from the centre to the foci.
b is the minor axis.
So b² + c²= a²
In this example
a= -7-1= -8
What proportion of these candy bars have more than 300 calories per serving? (Round your answer to two decimal places.)
Answer: 0.12
Step-by-step explanation:
There are 65 candy bars. Out of that;
2 candy bars have 300 to 350 calories
1 candy bar has 350 to 400 calories
4 candy bars have 400 to 450 calories
1 candy bar has 450 to 500 calories
The total proportion out of 65 candy bars that have over 300 calories is;
= ( 2 + 1 + 4 + 1) / 65
= 8/65
= 0.12
Judah worked at the bakery for 14 hours last week. He spent $12 of his earnings on a cake for his father’s birthday. If he was left with $86 after buying the cake, what is Judah’s hourly wage?
Answer:
Judah's hourly wage is $7/hr.
Step-by-step explanation:
x = (86 + 12)/14
x = 98/14
x = 7
Answer:
$7 per hour
Step-by-step explanation:
$86+ 12( the money he spent on the birthday cake)=$98
$98 divided by 14=7
Evaluate f(x) = 6x - 2 for x = 3 Group of answer choices 7 16 10 61
Simplify the expression. 1/2 (-sin2x - cos 2x)
Answer:
1/2 (-sin2x - cos 2x)
Step-by-step explanation:
Distribute 1/2 to every term in the parentheses
Beverly has a backyard that is square. One of the sides is 10 feet long. What is the area of her back yard?
Answer: all of the sides are 10ft long
Step-by-step explanation:
A man has 12 different colored shirts and 20 different ties in his closet. How many shirts and tie combinations can he select to take on a trip if he only takes 3 shirts and 5 ties?
Steve drove for 4 1/2 hours at 68 mph, how far did Steve drive?
Distance = speed x time
Distance = 68 x 4 1/2
Distance = 306 miles
Answer: 306 miles
Step-by-step explanation:
Speed= distance/time
Distance= speed•time
Time= distance/speed
Solve 3[-x + (2 x + 1)] = x - 1.
Step-by-step explanation:
3(-x+2x+1)=x-1
3(x+1)=x-1
3x+3=x-1
3x-x=-1-3
2x=-4
x=-2
the cell that contains 28 joins female and cat. Explain the context of the joint frequency cell.
animals vs gender
Dog Cat Total
Male 32 8. 40
Female. 11. 28. 39
Total. 43. 36. 79
A. 28 of the cats in the distribution are female
B. In the distribution of cats, 8 are female
C. 28 of the dogs in the distribution are female
D. 28 animals in the distribution are female cats and dogs
The correct answer is A. 28 of the cats in the distribution are female
Explanation:
The table presented shows the number of female/male dogs and cats, as well as the total of animals in each category. Moreover, in this, the columns show the type of animal (dog or cat), while the rows show its gender (female/male). Also, these categories intersect to show the frequency. For example, number 32, which is the intersection of the categories Dog and Male shows there are 32 male dogs. In this context, if the number 28 joints the categories female and cat, this means 28 of the total animals are female cats and out of the total cats 28 are female. This makes option A the correct answer.
Answer: two-ways tables quiz
1. 38.0%
2. 54.4%
3. 28.5%
4. 21.3%
5. 71.5%
6. 21.8%
7. Twenty-eight of the cats in the distribution are female.
8. 74.4%
9. 49.4%
10. 62.0%
Step-by-step explanation:
given P(x)=x^2+x+1 find answer P(7)
We hat does (-9) mean
Answer:
(-9) still means -9 it doesn't really mean anything thou....but if u have another number besides it then it means to multiply like maybe 2(-9)then it will be -18...... but if it is just (-9) then it doesn't mean anything.....
Sum of the areas of two squares is 260 m². If the difference of their perimeters is 24 m then find the sides of the two squares.
Answer: x=14 and y=8
*Note: x and y are used as variables to solve the problem. Just know that the sides for one square is 14 and the other, 8.
Step-by-step explanation:
For this problem, we can use system of equations to solve. Let's use x for one side of a square and y for the other.
Equation 1:
x²+y²=260
We get this equation from the sum of the areas. The x² and y² are from the area. Since all sides of a square are equal lengths, we can directly square them.
Equation 2:
4x-4y=24
This equation comes from the difference of the perimeters. 4x and 4y are perimeters because perimeter is adding all sides of the square together. There are 4 sides to a square, therefore we get 4x and 4y.
We can use substitution method to solve.
4x-4y=24 [add both sides by 4y]
4x=24+4y [divide both sides by 4]
x=6+y
Now that we have x, we can plug it into any equation and solve.
(6+y)²+y²=260 [expand]
y²+12y+36+y²=260 [combine like terms]
2y²+12y+36=260 [subtract both sides by 36]
2y²+12y=224 [factor out 2]
2(y²+6y)=224 [divide both sides by 2]
y²+6y=112 [subtract both sides by 112]
y²+6y-112=0 [factor equation]
(y-8)(y+14)=0 [set each factor equal to 0 to solve]
y=8 and y=-14
We know that y=8 because (y+14)=0 gives you y=-14, but a length or area can NEVER be negative, only positive.
Now that we have y, we can plug it into any equation to find x.
4x-4(8)=24 [combine like terms]
4x-32=24 [add both sides by 32]
4x=56 [divide both sides by 4]
x=14
Now, we have x and y. x=14 and y=8.
The absolute value of 8 is
Answer:
8. Absolute values are always positive.
i enter the bedroom. there are 34 people. i kill 30 people. how many people are there in bedroom
Answer:
35
Step-by-step explanation:
Even if you killed 30 people, 34 people remained in the room (30 dead and 4 alive).
You must add a person which is YOU.
Answer:
there are 35 people in the bedroom.
Step-by-step explanation:
If the volume of a cube is increased by a factor of 10, by what factor does the surface area per unit volume change
Answer:
(1/10)∛100 ≈ 0.4642
Step-by-step explanation:
For a cube of volume V, the edge length is ...
s = ∛V
and the area is ...
A = 6s² = 6V^(2/3)
Then the ratio of area to volume is ...
r1 = A/V = 6V^(2/3)/V = 6V^(-1/3)
If the value of V is increased by a factor of 10, the ratio of area to volume is now ...
r2 = 6(10V)^(-1/3)
The factor by which the ratio changed is ...
r2/r1 = (6(10V)^(-1/3))/(6V^(-1/3)) = 10^(-1/3) = (1/10)∛100
The surface area per unit volume changes by a factor of (∛100)/10.
___
Example
For a cube of side length 2, the volume is 2³ = 8 and the surface area is 6·2² = 24. The ratio of surface area to volume is 24/8 = 3.
Multiplying the edge length by ∛10, we now have a volume of (2∛10)³ = 80, and a surface area of 6(2∛10)² = 24(10^(2/3)). The ratio of surface area to volume is ... 24(10^(2/3))/80 = 0.3∛100.
The ratio of area to volume changed by a factor of (0.3∛100)/3 = (∛100)/10, as above.