The Maclaurin series of sin(3x²) up to n = 3 is
[tex]=3x^2-\dfrac{9}{2}x^6+\frac{81}{40}x^{10}+\ldots[/tex]
The function is given in the question as
g(x) = sin(3x²)
Taylor (Maclaurin) series of sin(3x²) up to n = 3
A Maclaurin series is given by f(x),
[tex]f\left(x\right)=f\left(a\right)+\frac{f^'\left(a\right)}{1!}\left(x-a\right)+\frac{f^{''}\left(a\right)}{2!}\left(x-a\right)^2+\frac{f^{'''}\left(a\right)}{3!}\left(x-a\right)^3+\ldots[/tex]
[tex]f\left(x\right)=f\left(0\right)+\frac{f^'\left(0\right)}{1!}\left(x\right)+\frac{f^{''}\left(0\right)}{2!}\left(x\right)^2+\frac{f^{'''}\left(0\right)}{3!}\left(x\right)^3+\ldots[/tex]
We need to do to get the desired polynomial is to calculate the derivatives, evaluate them at the given point, and plug the results into the given formula.
f⁽⁰⁾(x) = f(x) =sin(3x²)
Evaluate the function at the point: f(0)=0
1st derivative: f(1)(x)=(sin(3x²))′ = 6xcos(3x²)
1st derivative at the given point: (f(0))′=1
2nd derivative: f(2)(x)=(f(1)(x))′=(6xcos(3x²))′=−36x2sin(3x2)+6cos(3x²)
Evaluate the 2nd derivative at the given point: (f(0))′′=6
3rd derivative: f(3)(x)=(f(2)(x))′=(6xcos(3x²))′=−36x2sin(3x²)+6cos(3x²)
Evaluate the 3rd derivative at the given point: (f(0))′′′=0
Now, use the calculated values to get a polynomial:
[tex]g(x)=0+\frac{0}{1!}x+\frac{6}{2!}x^2+\frac{0}{3!}x^3+\frac{0}{4!}x^4+\frac{0}{5!}x^5[/tex]
Thus, the Maclaurin series of sin(3x²) up to n = 3 is
[tex]=3x^2-\dfrac{9}{2}x^6+\frac{81}{40}x^{10}+\ldots[/tex]
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I dont understand this could you help me?
Answer:
Option 2 —› (56 - 42) / 7 = 2
Step-by-step explanation:
First you use PEMDAS to check.
P- parentheses
E- Exponents
M- Multiplication (can be switched with D)
D- Division (can be switched for M)
A- Addition
S- Subtraction
Now you need to solve each problem.
Option 1: INCORRECT
(56 - 42) / 7 = 5
(14) / 7 = 5
2 = 5
Option 2: CORRECT
(56 - 42) / 7 = 2
(14) / 7 = 2
2 / 2
I'll do the rest, so you can see how to solve.
Option 3: INCORRECT
56 - (42 / 7) = 2
56 - 6 = 2
50 = 2
Option 4: INCORRECT
(56 - 7) / 42 = 5
(49) / 42 = 5
1 1/6 = 5
I know the answer but I don't know how to solve
In a raffle, 1,500 tickets are sold for $3 each. One ticket will be randomly selected and the winner will receive a laptop computer valued at $1000. What is the expected value for a person that buys one ticket?
e(x)=-2.33
how do you find that answer ?
The solution to probability problem is the expected value for a person that buys one ticket is -$2.32
What is probability?Probability is a measure of the likelihood or chance that a specific event will occur, expressed as a number between 0 and 1, where 0 represents impossibility and 1 represents certainty.
According to the given information:
To find the expected value, you need to multiply each possible outcome by its probability and then add them together.
In this case, there are two possible outcomes: either the person wins the laptop computer (with a probability 1/1500), or they don't win anything (with a probability 1499/1500).
So, the expected value can be calculated as:
E(x) = (1/1500)($1000) + (1499/1500)(-$3)
E(x) = $0.67 - $2.99
E(x) = -$2.32
So the expected value for a person that buys one ticket is -$2.32.
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A surveyor makes the measures indicated in Fig. 19-71. For the figure, angle A = 34o and the Hypotenuse c = 159 ft. Note the angles are named with Capital Letters A, B, and C and the names or the sides opposite the angles are named with small letter
All parts of the triangle should be solved The parts of the triangle to include in the Problem Solution are: (1) degrees of all 3 angles A, B and C, (2) lengths of the two legs a, b , rounded to the nearest whole number, (3) length of the hypotenuse and (4) the area of the triangle with the proper units. That is 7 answers total.
The side lengths of the triangle are 89 ft, 132 ft and 159 ft
The angles of the triangle are 34 degrees, 56 degrees and 90 degreesThe area of the triangle is 5874 square unitsThe sides of the triangleThe given parameters are
Angle, A = 34 degrees
Hypotenuse = 159 ft
The length BC is calculated as
sin(A) = BC/Hypotenuse
So, we have
BC = Hypotenuse * sin(A)
This gives
BC = 159 * sin(34 degrees)
Evaluate
BC = 89 ft
The length AC is calculated as
cos(A) = AC/Hypotenuse
So, we have
AC = Hypotenuse * cos(A)
This gives
AC = 159 * cos(34 degrees)
Evaluate
AC = 132 ft
The angles for the triangleHere, we have
Angle, A = 34 degrees
Because the triangle is a right triangle, we have
Angle, C = 90 degrees
The sum of angles in a triangle is 180
So, we have
Angle B = 180 - 90 - 34
Angle B = 56
The area of the triangleThis is calculated as
Area = 0.5 * BC * AC
So, we have
Area = 0.5 * 89 * 132
Evaluate
Area = 5874
Hence, the area is 5874 square units
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If a publisher of nontechnical books takes great pains to ensure that its books are free of typographical errors the probability of any given page containing at least one such error is 0.005 and errors are independent of the page-to-page. What is the probability that one of its 400-page novels will contain exactly one page with errors? At most three pages with errors?
Part A: Probability that one of 400-page novels will have exactly one error-free page is 24.06%.
Part B.) No more than three pages contain errors: 40.06%.
Explain the term binomial distribution?The possibility that a value would take one among two independent values given a particular combination of factors or assumptions is summarized by the statistical distribution known as the binomial distribution.The given data in the question-
X has a binomial distribution that includes,400 pages make up the novel's page count.Error probability p = 0.005Probability of error-free page q = 01 - 0.005 = 0.995The following is the probability mass function (PMF) for X:
P(X = x) = ⁿCₓ . pˣ . qⁿ⁻ˣ
Part A.) One of 400-page novels will have exactly one error-free page.
P(x = 1) = ⁿCₓ . pˣ . qⁿ⁻ˣ
n = 400, x = 1
P(x = 1) = ¹⁰⁰C₁ . (0.005)¹ . (0.995)¹⁰⁰ ⁻ ¹
P(x = 1) = 0.2706
Thus, probability that one of 400-page novels will have exactly one error-free page is 24.06%.
Part B.) No more than three pages contain errors.
P(x ≤ 3) = P(x = 0) + P(x = 1) + P(x = 2) + P(x = 3)
P(x = 0) = ¹⁰⁰C₀ . (0.005)⁰ . (0.995)¹⁰⁰ ⁻ ⁰
P(x = 0) = 0.01346
P(x = 1) = ¹⁰⁰C₁ . (0.005)¹ . (0.995)¹⁰⁰ ⁻ ¹
P(x = 1) = 0.0270
P(x = 2) = ¹⁰⁰C₂ . (0.005)² . (0.995)¹⁰⁰ ⁻ ²
P(x = 2) = 0.00068
P(x = 3) = ¹⁰⁰C₃ . (0.005)³ . (0.995)¹⁰⁰ ⁻ ³
P(x = 3) = 0.0000027
Thus, P(x ≤ 3) = P(x = 0) + P(x = 1) + P(x = 2) + P(x = 3)
P(x ≤ 3) = 0.01346 + 0.00068 + 0.00068 + 0.0000027
P(x ≤ 3) = 0.4060021
Consequently, the likelihood of at maximum three pages having typographical errors is 40.06%.
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What is the solution for system of equations???
Answer:
(1, -2)
Step-by-step explanation:
The line is tangent to the parabola, so it intersects in only 1 point.
Answer: (1, -2)
Solve for X in graph the solution set label your number line below with at least three numbers
3(x+1)>12
Answer:
X+1>12/3
X+1>4
X>4-1
X>3
A cyclist rode 3.85 miles in 0.7 hours. How fast was she going in miles per hour?
A. 3.85 miles per hour
B. 0.18 miles per hour
C. 5.5 miles per hour
D. 1.4 miles per hour
A rectangular room is
5
meters longer than it is wide, and its perimeter is
34
meters. Find the dimension of the room.
Answer:
Step-by-step explanation:
P = 2(L + W)
P = 34
L = W + 5
34 = 2(W + 5 + W)
34 = 2(2W + 5)
34 = 4W + 10
34 - 10 = 4W
24 = 4W
24/4 = W
6 = W <=== 6 meters wide
L = W + 5
L = 6 + 5
L = 11 <=== 11 meters long
Point of intersections=
Which equation models the line on the graph?
Answer:
y = 2x - 4
Step-by-step explanation:
(3, 2) (1, -2)
m = y2-y1 / x2-x1
m = -2-2 / 1-3
m = -4/-2
m = 2/1
m = 2
y = 2x + b
2 = 2(3) + b
2 = 6 + b
b = -4
y = 2x - 4
Could you please give me brainliest for this? Thank you!
Can anyone help with this two question ? Please
let's go like the crab, go backwards, start at the last
if you don't have a Unit Circle, this is a good time to get one, there are many online.
Check the picture below.
[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ (\stackrel{x_1}{6}~,~\stackrel{y_1}{7})\qquad (\stackrel{x_2}{x}~,~\stackrel{y_2}{y}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ x +6}{2}~~~ ,~~~ \cfrac{ y +7}{2} \right) ~~ = ~~\stackrel{midpoint}{(-5~~,~~-5)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ x +6}{2}=-5\implies x+6=-10\implies \boxed{x=-16} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ y +7}{2}=-5\implies y+7=-10\implies \boxed{y=-17}[/tex]
6x + 45 is less than or equal to 240
Answer: neither
Step-by-step explanation:
To get rid of the fractions, we pick a useful number and multiply both sides of the equation by that number. The number is useful if multiplying eliminates all fractions.
Two UNO students want to start a business selling slushies at the Gene Leahey Mall during the summer. They will have an initial cost of $500 to buy equipment and an additional $1.25 cost for each slushie they sell. They plan to charge $3.50 for each slushie. Let C(x) represent the cost (in dollars) associated with starting and running the business and R(x) represent the revenue (in dollars) earned from sales. Let × represent the number of slushies sold
a. Write a linear function for cost.
C(x)
Write a linear function for revenue.
R(x)=
c. Find C(50). Show your work.
• Write C(50) as an (x, y) coordinate point. ——
• Write a sentence that explains the meaning of the point in the context of the problem.
D. Find R(50).
Represent R(50) as an (x, y) coordinate point. ——-
Write a sentence that explains the meaning of the point in the context of the problem?
e. If the students sell 50 slushies, do they make a profit? Use mathematical work to help explain your answer. Complete the sentence below.
If the students sell 50 slushies. do they make—— a profit? Because——
F. How many slushies do the students need to sell to break even? Use complete sentences to explain your problem solving strategy and your conclusion.
G. How many slushies do the students have to sell to make a profit of $1250? Use complete sentences to explain your problem solving strategy and your conclusion.
The linear function is C(x) = 500 + 1.25x and the revenue function is R(x) = 3.50x.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
From the data:
The linear function:
C(x) = 500 + 1.25x
For revenue:
R(x) = 3.50x
R(50) = 3.50(50) = $175
Using the C(x) and revenue function we can find the number of slushies and profit.
Thus, the linear function is C(x) = 500 + 1.25x and the revenue function is R(x) = 3.50x.
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Find the area of the shaded region. Round to the nearest tenth. All polygons are regular.
Check the picture below.
let's take a looksie at that, notice, if we split the circle into 6 even pieces, we end up with six 60° angles at the center, namely six equilateral triangles as you see there.
now, if we run a dashed line as you see from a corner to the other to make the flatter triangle which is shaded, we end up cutting the equilateral triangle into two equal halves, each with 30° and 30° angles, because the dashed line intercepts the green line at 90°.
well, the flatter triangle from corner to corner, is spanning over two equilateral triangles, if it's owning half of one, it must be also owning half of the other. What the dickens does that mean? well, it means the area of the flatter triangle that's shaded, is really the same area as a "whole" of one of those equilateral triangles.
so hmmm we have three of those flatter triangles shaded hmm, so let's simply get the area of three of those equilateral triangles and sum them up.
[tex]\textit{area of an equilateral triangle}\\\\ A=\cfrac{s^2\sqrt{3}}{4} ~~ \begin{cases} s=side\\[-0.5em] \hrulefill\\ s=12 \end{cases}\implies A=\cfrac{12^2\sqrt{3}}{4}\implies A=36\sqrt{3} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{\large area of the shaded region}}{36\sqrt{3}~~ + ~~36\sqrt{3}~~ + ~~36\sqrt{3}}\implies 108\sqrt{3}\qquad \approx\qquad \text{\LARGE 187.1}[/tex]
100 POINTS
The two-way frequency table contains data about students' preferred exercise.
What is the joint relative frequency of students who like running and swimming?
45%
37%
28%
14%
Answer:
28
Step-by-step explanation:
hope this helps if its wrong really sorry
22. Given f(x)=10x & g(x)=2x-4
Find the value of f(1)
Find the value of g(3)
Find the value of f(1)+g(3)
Find the value of f(10)-g(0)
Answer:
f(1)=10
g(3)=2
f(1)+g(3)=12
f(10)-g(0)=104
Step-by-step explanation:
f(x)=10x
g(x)=2x-4
f(1)=10×1=10
g(3)=2×3-4=2
f(1)+g(3)=10+2=12
f(10)-g(0)=(10×10)-(2×0-4)=100+4=104
Graph y = 2/3x
Where do i put the dots
Answer:
On (3,7) and (-2,7)
Step-by-step explanation:
The solution to a(x)-b(x)=0
Answer:
a = b
b = a
Step-by-step explanation:
I need help asap. please help me..............................................
The sequence of transformations that show figure A and figure B are congruent is: Translate figure A 4 units right and then reflect the image across the x-axis.
What is translation?Translation refers to a type of transformation that involve a straight line movement.
Movements as seen in translation includes
leftrightupdownThe left and right movements are on the horizontal direction controlled by the x coordinate.
The object moved 4 units right then reflected over the x axis to have the mirror image below the x axis
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10 Find the value of 2x+y for the simultaneous equations.
3x + 5y = 48
2x-y=19
y=3
x=11
hence answer 25
3x+5y=48
2x-y=19
eliminate x to find y
(3x+5y=48)2
(2x-y=19)3
(6x + 10y. = 96)
- minus direct
(6x - 3y. = 57)
=
13y = 39
Note: (10y -(-3y)=13y)
divide by 13 to remain with y
y =3
substitute to any equation to get x lets pick second one
2x-(3)=19
2x-3=19
2x=19+3
2x/2=22/2. (to remain with x value)
x=11
therefore 2x+ y results to 2(11) +3=25
Answer:
2x + y = 25
Step-by-step explanation:
Given equations:
[tex]\begin{cases} 3x + 5y = 48\\\;\;2x-y=19\end{cases}[/tex]
Rearrange the second equation to isolate y:
[tex]\implies 2x-y=19[/tex]
[tex]\implies 2x-19=y[/tex]
Substitute the found expression for y into the first equation and solve for x:
[tex]\implies 3x+5y=48[/tex]
[tex]\implies 3x+5(2x-19)=48[/tex]
[tex]\implies 3x+10x-95=48[/tex]
[tex]\implies 13x=143[/tex]
[tex]\implies x=11[/tex]
Substitute the found value of x into the equation for y and solve for y:
[tex]\implies y=2x-19[/tex]
[tex]\implies y=2(11)-19[/tex]
[tex]\implies y=22-19[/tex]
[tex]\implies y=3[/tex]
Therefore, the solution of the given system of equations is:
x = 11, y = 3To find the value of 2x + y, substitute the found values of x and y into the expression and solve:
[tex]\begin{aligned}\implies 2x+y&=2(11)+3\\&=22+3\\&=25\end{aligned}[/tex]
Therefore:
2x + y = 25If a polynomial f\mathopen{}\mathclose{\left(x\right)}f(x) has a remainder of 22 when divided by x-6x−6, what is f\mathopen{}\mathclose{\left(6\right)}f(6)?\
f\mathopen{}\mathclose{\left(6\right)}f(6) = (6-6)(something) + 22 = 0(something) + 22 = 22 which has a remainder of 22 when divided by x-6x-6. f\mathopen{}\mathclose{\left(6\right)}f(6) = \boxed{22}.
What is the remainder theorem?The remainder theorem states that when a polynomial is divided by a linear term, the remainder equals the value of the polynomial at the root of the linear term. This theorem may be used to determine the roots of a polynomial by dividing it by a linear term and solving for the remainder. For instance, when the polynomial x3+x2-5x+6 is divided by (x2), the result is identical to the polynomial's value at x=2. After finding the remainder, we may determine that the polynomial's root is 2, which we can do by solving for the remainder. This theorem may also be used to discover the roots of higher degree polynomials by combining linear terms.
How to solve?
f\mathopen{}\mathclose{\left(x\right)}f(x) can be written as (x-6)(something) + 22.
f\mathopen{}\mathclose{\left(6\right)}f(6) = (6-6)(something) + 22 = 0(something) + 22 = 22.
Therefore, f\mathopen{}\mathclose{\left(6\right)}f(6) = \boxed{22}.
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The variable y varies jointly with x and w when y = - 42, x = 2, and w = -3.
1.) Find the constant of variation.
k=
Answer:
k = 7
Step-by-step explanation:
given y varies jointly with x and w then the equation relating them is
y = kxw ← k is the constant of variation
to find k use the condition when y = - 42, x = 2 and w = - 3 , then
- 42 = k × 2 × - 3
- 42 = - 6k ( divide both sides by - 6 )
7 = k
constant of variation is k = 7
A 12,000-lb killer whale might eat as much as 14,000 lb of fish per month (assume a 30-day month). If the average weight of a certain type of fish is 2.8oz, estimate how many of these fish a killer whale would eat in a day.† (Round your answer to the nearest whole number.)
Answer:
2196 fish
Step-by-step explanation:
:)
Answer:
2196 fish
Step-by-step explanation:
your welcome
Would you use SSS or SAS to prove the triangles are congruent? If there is not enough information to prove the triangles are congruent, write not enough information. Explain your answer.
We can use both according to the given information.
• In 2 triangles if 2 sides of a triangle and 2 sides of another triangle are equal and if any one angle is equal to the angle in another triangle then we use SAS congruence rule
• In 2 triangles if 3 sides are equal to the 3 sides of another triangle then we use SSS congruence rule
• We can also use RHS (Right angle Hypotenuse Side). It is for 2 right angle triangle.
*Hope It Helps you*°Please Mark Me As Brainliest°Help please[tex]\sqrt{x-3} -\sqrt{x} =3[/tex]
Answer: No solution
Step-by-step explanation:
[tex]\sqrt{x-3}=\sqrt{x} +3\\[/tex]
square both sides
x-3=x+9
x=x+12
0=12
0 does not equal 12, and therefor, there is no solution.
Identify the slope and y-intercept of the line below.
Slope=?
y-intercept=?
Answer:
Slope- y=1/4x-6
Y intercept= (0,-6)
Hope this helps!
Find g(x), where g(x) is the translation 5 units down of f(x)=x2.
Write your answer in the form a(x–h)2+k, where a, h, and k are integers.
If we want to translate (aka move) [tex]f(x) = x^2[/tex] down 5 units, we need to subtract 5 from the [tex]x^2[/tex].
[tex]g(x) = x^2-5[/tex]
The [tex]k[/tex] in the [tex]a(x-h)^2 +k[/tex] form will always be the vertical translation component. If you translate up, [tex]k[/tex] is positive. If you translate down, [tex]k[/tex] is negative.
help meeeeeeeeeeeeeeee pleaseeeeeeehelp meeeeeeeeeeeeeeee pleaseeeeeeehelp meeeeeeeeeeeeeeee pleaseeeeeeehelp meeeeeeeeeeeeeeee pleaseeeeeee
Answer:
Step-by-step explanation:
im not in 100th grade yet
Farrah is painting vases to sell in a local craft show. She paints 8 vases in 2 hours. Which is a reasonable estimate of the amount of time it will take her to paint 50 vases?
Responses
A between 13 and 14
B between 14 and 15
C between 12 and 13
D between 11 and 12
Answer:
C.)
Step-by-step explanation:
1.) Since she does 8 vases in 2 hours, she would do 4 vases in 1 hour.
2.) By using this, we divide 50/4 to figure out the amount of hours. This is equal to 25/2, which is equal to 12.5.
3.) Now, check the options. C.) fits this situation the best. Therefore, C.) is the answer.
Help fast please!!!!!!!Simplify.
(-√7) (-√7)
O A. √7
B. -7
OC.
C. 7
о
O
D. 49
E. -49
K
Answer:
7
Step-by-step explanation:
seven is the value e you would get