The third derivative of f(x) at x=0 is −150.
To find the third derivative of f(x) at x=0, we can utilize the Maclaurin series representation of f(x).
The Maclaurin series expansion of f(x) is given by:
[tex]f(x)=1-9 x+16 x^2-25 x^3+\ldots[/tex]
To find the third derivative, we first need to determine the general expression for the n-th term of the Maclaurin series. The general term of the series is given by:
[tex]f^{(n)}(0) \frac{x^n}{n !}[/tex]
where [tex]f^{(n)}(0)[/tex] represents the n-th derivative of f(x) evaluated at x=0.
Now, let's identify the pattern in the given series:
[tex]f(x)=1-9 x+16 x^2-25 x^3+\ldots[/tex]
The coefficients of the terms seem to be perfect squares of consecutive odd numbers. So, the n-th term of the series can be expressed as [tex](-1)^n \cdot(2 n+1)^2[/tex].
Now, let's find the third derivative of f(x) at x=0:
[tex]\begin{aligned}& f(x)=1-9 x+16 x^2-25 x^3+\ldots \\& f^{\prime}(x)=-9+32 x-75 x^2+\ldots \\& f^{\prime \prime}(x)=32-150 x+\ldots \\& f^{\prime \prime \prime}(x)=-150+\ldots\end{aligned}[/tex]
Now, evaluating f′′′(x) at x=0, we get:
[tex]f^{\prime \prime \prime}(0)=-150[/tex]
So, the third derivative of f(x) at x=0 is −150.
Complete Question:
Find the third derivative of f at x = 0 if the Maclaurin series for:
[tex]f(x) = 1 - 9x + 16x^2 - 25x^3 +.....[/tex]
A fair number cube with sides labeled from 1 to 6 is rolled 20 times. the results of the simulation are shown in a dot plot. which dot plot models an unfair data-generating process?
The dot plot will be 1:4, 2:4, 3:0, 4:4, 5:4,6:4 and there is a face with 3 has not rolled option second is correct.
What is dot plot?A dot plot, also referred to as a dot chart or stripe graph, is a sort of simple histogram-like figure used in statistics for little data sets with values falling into a number of discrete bins.
Since the width of each "bar" of dots is equal to the number of items in a certain class, a dot plot is similarly to a bar diagram.
We have:
A fair number cube with sides labeled from 1 to 6 is rolled 20 times.
Total number on, a fair number of cubes = 6
So the dot plot can be shown as:
1:4, 2:4, 3:0, 4:4, 5:4,6:4
There is a face with 3 has not rolled.
Thus, the dot plot will be 1:4, 2:4, 3:0, 4:4, 5:4,6:4 and there is a face with 3 has not rolled option second is correct.
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Given f(x)=x2+14x+40 .
Enter the quadratic function in vertex form in the box.
What is the exact volume of a cylinder whose radius is 21 centimeters and whose height is 30 centimeters?
answer in terms of pie
Simplify -62 ÷ 12 - 2(-7).
To simplify -62 ÷ 12 - 2(-7), evaluate the expression inside the parentheses first, then perform the division and subtraction.
Explanation:To simplify the expression -62 ÷ 12 - 2(-7), we need to follow the order of operations, which is PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) in this case. First, we need to evaluate the expression inside the parentheses: 2(-7) = -14. Then, we perform the division: -62 ÷ 12 = -5. Finally, "we subtract: -5 - (-14) = -5 + 14 = 9".
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Give an exact answer in simplified form. 5y+3 > -7y + 13 5y+3>−7y+13 (see pic
Th answer to the inequality will be evaluated as follows:
5y+3>-7y+3
putting like terms together we obtain:
5y+7y>3-3
2y>0
dividing both sides by 2 we get:
(2y)/2>0/2
thus
y>0
The number N is the produce of the first 1000 positive integers and can be written as 1000!.We say "1000 factorial."This is, N=1000!=1000x999x998x997x...x3x2x1.N is divisible by 5, 25, 125, 625,...Each of these factors is a power of 5.That is 5=5^1, 25=5^2, 125=5^3,625=5^4, and so on. Determine the largest power of 5 that divides N.
(08.05 HC) The work of a student to solve a set of equations is shown: Equation A: y = 15 − 2z Equation B: 3y = 3 − 4z Step 1: −3(y) = −3(15 − 2z) [Equation A is multiplied by −3.] 3y = 3 − 4z [Equation B] Step 2: −3y = 15 − 2z [Equation A in Step 1 is simplified.] 3y = 3 − 4z [Equation B] Step 3: 0 = 18 − 6z [Equations in Step 2 are added.] Step 4: 6z = 18 Step 5: z = 3 In which step did the student first make an error?
Answer:
STEP 2
Step-by-step explanation:Simplifying
-3(y) = -3(15 -2z)
should yield
-3y = -45 +6z
Amanda owns a clothing store that sells graphic t-shirts. n is the number of shirts she sells each month. the revenue function of her store is r = 25n. the cost function of her store is c = 10n + 900. using your calculator, what is the break-even point of amanda's store?
Answer:
n = 60 shirts
Step-by-step explanation:
The break-even point is the point where revenue is equal to cost. This means we take the equation for revenue, r = 25n, and set it equal to the equation for cost, c = 10n + 900:
25n = 10n + 900
Subtract 10n from each side:
25n - 10n = 10n + 900 - 10n
15n = 900
Divide both sides by 15:
15n/15 = 900/15
n = 60
2/3 - 4x + 7/2 = -9x + 5/6
Pete is purchasing an mp3 player for 199.90 he gives the sales clerk 2 fifty dollar bills, 4 twenty dollar bills and 4 five dollar bills how much should he receive back
A line of best fit predicts that when x equals 35, y will equal 34.785, but actually equals 37. What is the residual in this case?
What is the distance between point (3, 2) and line y = 1/4x-9
. Stephen deposited $1800 into a savings account for which interest is compounded weekly at a rate of 3.2%. How much interest will he earn after 10 years?
58.81
678.59
2478.59
im just putting this up to see if my answer was write. i did the math and unless i messed up writing i got the second answer
Of the following options, what could be a possible first step in solving the equation −7x − 5 = x + 3?
Adding 7x to both sides of the equation
Subtracting 5 from both sides of the equation
Adding x to both sides of the equation
Combining like terms, −7x + x = − 6x
add 7x to both of the sides
Greg wants to move out of his dormitory and into an apartment near his college. His parents agreed, on the condition that the rent is no more than 25% of the cost of dorm living. To get an idea of rent amounts for one-bedroom apartments, Greg looks at listings in a local newspaper and on an Internet site.
Which answer best describes the sample and population?
A. Sample: listings in a local newspaper and on an Internet site
Population: all available apartments near the college
B. Sample: all available apartments near the college
Population: all available dormitories near the college
C. Sample: all available dormitories near the college
Population: all available apartments near the college
D. Sample: all available apartments near the college
Population: listings in a local newspaper and on an Internet site
WILL GIVE BRAINLIEST!!!! PLZ HELPPP!!!Which equation is the BEST fit for the data in the graph?
A) y = (1/4)x
B) y = (-1/4)x
C) y = (1/4)x-1
D) y = (1/4)x - 1
Find the x-intercepts for the parabola defined by the equation below. y=2x^2-6x+4
Carlos swam the perimeter of a rectangular pool seven times. If the length of the pool is 21 ft and the width of the pool is 9 ft, how many feet did Carlos swim?
The total length did Carlos swim is 420 feet.
To find the perimeter.
What is rectangle?A rectangle is a type of quadrilateral that has its parallel sides equal to each other and all the four vertices are equal to 90 degrees.
Given that:
Let the perimeter of rectangular swimming pool be x metres.
Then, its length =21 feet.
The width of the pool = 9 feet
The Perimeter of a rectangle =2(Length+Breadth)
According to the given condition, we have
Perimeter of a rectangle =2(Length+Breadth)
Perimeter of a rectangle=2(21+9)
Perimeter of a rectangle=2*30
Perimeter of a rectangle=60 feet
But, carlos swam the perimeter of a rectangular pool seven times.
Old perimeter=7*60=420 feet
Thus ,the total length did Carlos swim is 420 feet.
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Which expression is equivalent to mc003-1.jpg?
Answer:
Option A is correct
The expression which is equivalent to [tex](f\cdot g)(5)[/tex] is [tex] f(5) \cdot g(5)[/tex]
Step-by-step explanation:
Using the formula:
[tex](f \cdot g)(x) = f(x) \cdot g(x)[/tex] .....[1]
Given the expression:
[tex](f\cdot g)(5)[/tex]
Substitute the value of x = 5 in [1]
we get;
[tex](f \cdot g)(5) = f(5) \cdot g(5)[/tex]
Therefore, the expression which is equivalent to [tex](f\cdot g)(5)[/tex] is [tex] f(5) \cdot g(5)[/tex]
What is the measure of BAC
50
80
100
130
Two large numbers of the Fibonacci sequence are F61 = 2,504,730,781,961 and F62 = 4,052,739,537,881. If these two numbers are added together, what number results?
A. F123
B. F60
C. F63
D. F64 - 1
Easy math problem, please help.
O is the center of the circle. Assume that lines appear to be tangent are tangent. What is the value of x?
A. 34
B. 36.5
C. 73
D. 107
Answer:
Option C. 73
Step-by-step explanation:
In the given figure Δ OPQ is the right angle triangle because radius is always perpendicular to the tangent drawn on the circle from an external point.
Here OQ is radius and PO is tangent.
So ∠OQP = 90°
Now sum of all angles of a triangle is 180°
Therefore, ∠OPQ + ∠OQP + ∠POQ = 180°
17° + 90° + x° = 180°
107 + x = 180
x = 180 - 107
x = 73°
Option C. 73
Which of the following terms correctly describe the figure given below? Check all that apply.
I think its Polyhedron, pyramid, solid.
Answer:
Hence, the correct options are Polyhedron, Pyramid and Solid
Step-by-step explanation:
According to the options, we have,
1. Polyhedron is a solid figure in three dimensions having polygons as its faces along with sharp vertices and straight edges.
So, we can see that the given figure have polygonal faces with sharp vertices and straight edges.
Thus, it is a polyhedron.
2. Polygon is a closed two dimensional figure bounded by straight lines.
But, the given figure is not a 2-D figure and so is not a polygon.
3. Prism is a polyhedron with polygons as its faces along with a second base which is a translated copy of the first base.
Since, the given figure is a polyhedron but it does not have a second base which is a translated copy of the first base.
So, the given figure is not a prism.
4. Pyramid is 3-D figure having triangular outer surfaces converging to single point with polygonal base.
As, we can see that the given figure have polygonal base and triangular sides converging to a point.
So, the given figure is a pyramid.
5. Cube is a 3-D figure with all the six faces as squares.
But, the given figure does not have square faces and so is not a cube.
6. Solid is a figure having three dimensions.
Since, the given figure does have three dimensions.
So, it is a solid.
Hence, the correct options are Polyhedron, Pyramid and Solid.If you can buy 1⁄4 pizza for 5 dollars, how much can you purchase for 8 dollars? Write your answer as a fraction.
Write an equation to match each graph:
Write an equation to match each graph.
Solution:
The first graph is V shaped graph centered at origin, (0,0) and the graph is not shifted or translated. So, the equation of first graph is,
y=|x|
The second graph is V shaped graph centered at (1,0) and y=|x| is horizontally shifted right by 1 unit. So, the equation of second graph is,
y=|x-1|
The third graph is also V shaped but, it is inverted V graph centered at (0,1) . As, the graph is inverted V So, the graph must have y=-|x|. But, as the center is (0,1). So, the graph is shifted up by 1 unit. So, the equation of the third graph is,
y=-|x|+1
The fourth graph is shifted V graph, whose center is (1,-1). So, y=|x| is shifted right by 1 unit and down by 1 unit. So, the equation of fourth graph is,
y=|x-1|-1
The center of fifth graph is (-1,0), So, y=|x| graph is shifted left by 1 unit. So, the equation of fifth graph is
y=|x+1|
URGENT PLEASE HELP
Suppose 20% of all widgets produced at a factory are defective.
A simulation is used to model widgets randomly selected and then recorded as defective or working.
Which simulation best models the scenario?
Place 50 equally sized pieces of paper in a hat. Of the 50, 5 read “defective” and the rest read “working”.
Place 25 equally sized pieces of paper in a hat. Of the 25, 5 read “defective” and the rest read “working”.
Place 20 equally sized pieces of paper in a hat. Of the 20, 5 read “defective” and the rest read “working”.
Place 100 equally sized pieces of paper in a hat. Of the 100, 5 read “defective” and the rest read “working”.
The length of a rectangle is 7 cm less than twice its width. if the area of the rectangle is 39 cm2, find the dimensions of the rectangle.
for the function d(x)=7x^3 - 6x^2 what is the vaule of d(4)
How to find the shaded region of a circle with a rectangle inside?
Christine runs 7 miles in 60 minutes. at the same rate, how many miles would she run in 24 minutes?
Christine would run approximately 2.8 miles in 24 minutes at the same rate she runs 7 miles in 60 minutes.
Explanation:To find out how many miles Christine would run in 24 minutes, we can set up a proportion. We know that Christine runs 7 miles in 60 minutes, so we can write the proportion as:
7 miles / 60 minutes = x miles / 24 minutes
Now, we can cross-multiply and solve for x:
7 * 24 = 60 * x
168 = 60x
x = 168 / 60
x ≈ 2.8 miles
So, her speed would be 7/60 = 0.1167 miles per minute. Now, to find out the distance she would cover in 24 minutes at this speed, we multiply her speed per minute by 24 minutes. So, 0.1167 * 24 = approximately 2.8 miles. Therefore, at the same rate, Christine would run about 2.8 miles in 24 minutes.
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