The power series expansion of f(x) = 4x^2 - 39x + 98 around 5 is f(x) ≈ 3 + (x-5) + 4(x-5)^2.
To expand f(x)=4x^2-39x+98 as a power series around 5, we need to use the formula for a power series:
f(x) = ∑(n=0 to infinity) [f^(n)(a)/n!] * (x-a)^n
where f^(n)(a) represents the nth derivative of f(x) evaluated at x=a. In this case, a=5.
To find the derivatives of f(x), we can use the power rule and the constant multiple rule:
f'(x) = 8x - 39
f''(x) = 8
f'''(x) = 0
f''''(x) = 0
...
Notice that the derivatives beyond the second derivative are all zero. This is because f(x) is a quadratic function, so all higher-order derivatives are zero.
Now we can plug these derivatives into the formula for the power series:
f(x) = f(5) + f'(5)*(x-5) + (f''(5)/2!)*(x-5)^2 + ...
f(5) = 4(5)^2 - 39(5) + 98 = -23
f'(5) = 8(5) - 39 = 1
f''(5) = 8
So the power series expansion of f(x) around x=5 is:
f(x) = -23 + (x-5) + 4/2!*(x-5)^2 + 0*(x-5)^3 + 0*(x-5)^4 + ...
Simplifying this expression, we get:
f(x) = -23 + (x-5) + 2(x-5)^2 + ...
And that's the power series expansion of f(x) around x=5!
Hi! To expand the function f(x) = 4x^2 - 39x + 98 as a power series around 5, we will use the Taylor series expansion formula:
f(x) = f(a) + f'(a)(x-a) + (f''(a)/2!)(x-a)^2 + ...
where a = 5. First, let's find the derivatives of f(x):
f(x) = 4x^2 - 39x + 98
f'(x) = 8x - 39
f''(x) = 8
Now, we'll evaluate the derivatives at a = 5:
f(5) = 4(5)^2 - 39(5) + 98 = 100 - 195 + 98 = 3
f'(5) = 8(5) - 39 = 40 - 39 = 1
f''(5) = 8
Finally, we'll plug these values into the Taylor series expansion formula:
f(x) ≈ 3 + 1(x-5) + (8/2!)(x-5)^2
f(x) ≈ 3 + (x-5) + 4(x-5)^2
So, the power series expansion of f(x) = 4x^2 - 39x + 98 around 5 is f(x) ≈ 3 + (x-5) + 4(x-5)^2.
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Can you answer this for 20 points? With which countries was France at war in 1792 and 1793?
Answer:
They pitted France against Great Britain, the Holy Roman Empire, Prussia, Russia, and several other monarchies. They are divided in two periods: the War of the First Coalition (1792–97) and the War of the Second Coalition (1798–1802)
Step-by-step explanation:
Angel repairs used furniture. He expects to use 48 oz of wood filler this month. There are 16 oz in 1 lb. How many pounds of wood filler does Angel expect to use this month?
Answer: 3
Step-by-step explanation:
48 divided by 16 is 3
The number of pounds expected to use this month is 3 pounds.
What is unit conversion?It is the conversion of one unit to another unit with its standard conversion.
Example:
1 hour = 60 minutes
1 minute = 60 seconds
1 km = 1000 m
We have,
16 oz = 1 lb
Multiply 3 on both sides.
48 oz = 3 lb
Thus,
3 pounds of wood is in 48 oz.
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A rectangle has a length of (x + 6) units and a width of (x - 5) units. What is the area of the rectangle in terms of x?
Answer:
Area = x2 +x - 30
Step-by-step explanation:
area = length x width
(x+6) (x-5) = x2 +6x -5x -30 = x2 + x -30
In 2010, the population of a city was 180,000. From 2010 to 2015, the population grew by 7%. From 2015 to 2020, it fell by 4%. How much did the population grow from 2010 to 2015, to the nearest 100 people?
Answer:
I. Exponential Growth. (1 ) t y C r. = +. Final. Amount. Initial. Amount. Rate of ... value increases by 7% each year. ... Step 1 Write the exponential growth function for this ... nearest hundredth. ... The population after 7 years will be approximately 38,783 people. ... Cesium-137 left from a 100 milligram sample after 180 year
Step-by-step explanation:
i think its right if not have a great day
Answer:
9800
Step-by-step explanation:
Which linear inequality best represents the graph shown?
Answer:
B
Step-by-step explanation:
For questions 7 and 8 find the unknown angle.
Answer:
58 degrees for Question 7, and 71 degrees for Question 8
Step-by-step explanation:
For question 7:
180 - 99 = 81
81 + 41 = 122
180 - 122 = 58
For Question 8:
142 / 2 = 71
Answer: 7) 58 degrees 8) 71 degrees
Step-by-step explanation:
7) 41 + x = 99 degrees (the two interior opposite angle is equal to the exterior angle)
subtract 41 on both sides
x = (99 - 41) degrees
x = 58 degrees
8) x + x = 142 degrees
2x = 142
divide 2 on both sides
x = 71 degrees
Math Teacher is giving extra credit to who ever can come up with the best theme for his kids birthday party!!!
Has to be a movie!
You can choose
A. Hunger Games
B. Men in Black
C. Classic Horror Movies
D. Jurassic Park
OR!!
Awnser With your own suggestion!!!!!!!
Answer:
C
Step-by-step explanation:
CLASSIC HORROR MOVIES
Please answer this!!!
Will be Brainlist!!!
Answer:
show the question
sorry
Step-by-step explanation:
plz follow me
Answer:
1) а 2)b
вот правильный ответ
Pedro tiene 335 en monedas de 5 y de 10, si en total tiene 52 monedas ¿cuantas monedas tiene de cada una?
ayuda por favor
Answer:
37 monedas de $5 y 15 monedas de $10
Step-by-step explanation:
37 x 5 = 185
15 x 10 = 150
185 + 150 = $335
A CIRCLE HAS A CIRCUMFENCE 43.96 YD FIND THE RADUIS OF THE CIRCLE
Answer:
≈ 7
Step-by-step explanation:
Polar bears eat 8.4 pounds of fish a day. Penguins eat about 0.80 of that amount. How many pounds if fish do penguins eat?
Rearrange p=r+3 to make r the subject
Answer:
r = p-3 this is correct answer of this question
The equation p=r+3 can be rearranged as r=p-3
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given equation is p=r+3
p equal to r plus r
Plus is the operator of addition and p and r are variables
Subtracting 3 from both sides, we get:
p - 3 = r + 3 - 3
Simplifying the right-hand side:
p - 3 = r
Therefore, r = p - 3.
Hence, the equation p=r+3 can be rearranged as r=p-3
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- A unicycle tire has a radius of 13 inches. About how far will the unicycle travel in 20 rotations?
F.1633 inches
G.10,613 inches
H.82 inches
J.520 inches
Answer:
1061.32 you made a typo on G
Step-by-step explanation:
To find the distance travelled by the tire we need the circumference of it
The formula for circumference is 2πr we know pi is roughly 3.14 and the radius is 13
we plug the numbers in and get
2* 3.14* 13
6.28*13
81.64
81.64 is the circumference, now we simply just multiply 81.64 by 13 to get 1061.32
Im guessing number G was supposed to be 1061.32 instead of 10,613
316 students went on a field trip. Six buses were filled and 10 students traveled in cars. How many students
were in each bus?
Answer:
51
Step-by-step explanation:
316-10= 306
306 divided by 6 = 51
I NEED HELP NOW ITS DUE TODAY AND I HAVE MORE AHHHHHHHHH
Lin needs to save up $20 for a new game. How much money does she have if she has saved 25% of her goal?
Answer:
She has $5
Step-by-step explanation:
Find the equation of the line that passes through both points (6,-5) (0,3)
Answer:
y = -4/3x + 3
Step-by-step explanation:
please help me with this
Answer:
D. [tex]\sqrt{250}[/tex]
Step-by-step explanation:
First, use prime factorization of 250 to get [tex]\sqrt{2*5^3}[/tex]
Then apply the exponent rule, [tex]a^{b+c} =a^{b}*a^{c}[/tex]
=[tex]\sqrt{2*5^2*5} }[/tex]
Apply radical rule: [tex]\sqrt{ab}= \sqrt{a} \sqrt{b}, a\geq 0, b\geq 0[/tex]
=[tex]\sqrt{5^{2}} \sqrt{2*5}[/tex]
Apply radical rule: [tex]\sqrt{a^{2}} =a, a\geq 0[/tex]
=5[tex]\sqrt{2*5}[/tex]
=5[tex]\sqrt{10}[/tex]
Answer:
D. I did the math on my calculator
pls help me with this I have to go to bed soon( I need the volume of the sphere)
Volume= 4/3πr^3
r = 18m
Volume = 4/3*3.14*18^3
Volume = 4/3*3.14*5832
Volume= 24416.639999 m^3
PLEASE HELP!! WILL MAKE BRAINLIEST!! What is..... 3.064 x 1,000
The coordinates of the vertices of △UVW are U(−2,−1), V(2,−1), and W(2,−8). Find the side lengths to the nearest hundredth and the angle measures to the nearest degree.
Answer:
UV = 4; VW = 7, UW ≈ 8.06
m∠V = 90°, m∠U ≈ 60°, m∠W ≈ 30°
Step-by-step explanation:
Using the distance formula, find the length of UW⎯⎯⎯⎯⎯⎯⎯.
UW=(2−(−2))2+(−8−(−1))2‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√
Simplify.
UW=(4)2+(−7)2‾‾‾‾‾‾‾‾‾‾‾‾√
Square.
UW=16+49‾‾‾‾‾‾‾√
Simplify.
UW=65‾‾‾√
Use a calculator to approximate.
UW≈8.06
Therefore, UW≈8.06.
Using the distance formula, find the length of UV⎯⎯⎯⎯⎯⎯.
UV=(2−(−2))2+(−1−(−1))2‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√
Simplify.
UV=(4)2+(0)2‾‾‾‾‾‾‾‾‾‾√
Square.
UV=16+0‾‾‾‾‾‾√
Simplify.
UV=16‾‾‾√
Simplify.
UV=4
Therefore, UV=4.
Using the distance formula, find the length of VW⎯⎯⎯⎯⎯⎯.
VW=(2−2)2+(−8−(−1))2‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√
Simplify.
VW=(0)2+(−7)2‾‾‾‾‾‾‾‾‾‾‾‾√
Square.
VW=0+49‾‾‾‾‾‾√
Simplify.
VW=49‾‾‾√
Simplify.
VW=7
Therefore, VW=7.
The figure shows the same triangle U V W on a Cartesian plane as in the beginning of the task. The length of segment U V is 4 units. The length of segment V W is 7 units. The length of segment U W is 8.06 units.
Notice that UW2=UV2+VW2. So, by the Converse of the Pythagorean Theorem, △UVW is a right triangle.
Since VW⎯⎯⎯⎯⎯⎯ and UV⎯⎯⎯⎯⎯⎯ are perpendicular, m∠V=90°.
Therefore, m∠V=90°.
By the definition of tangent, tan∠U=VWUV.
Take the inverse tangent of both sides.
m∠U=tan−1(VWUV)
Substitute 7 for VW and 4 for UV.
m∠U=tan−1(74)
Use a calculator to calculate the inverse tangent.
The figure shows a calculator screen on which the inverse tangent of seven fourths is calculated. The result of the calculation is 60 point 2 5 5 1 1 8 7.
m∠U≈60°
Therefore, m∠U≈60°.
The figure shows the same triangle U V W on a Cartesian plane as in the beginning of the task. Angle V is a right angle. Angle U measures 60 degrees.
The acute angles of a right triangle are complementary by the corollary of the Triangle Sum Theorem.
So, m∠U+m∠W=90°.
Substitute 60° for m∠U.
60°+m∠W≈90°
Subtract 60° from both sides.
m∠W≈90°−60°
Simplify.
m∠W≈30°
Therefore, m∠W≈30°.
Answer the following question in *full sentences*
What does the equation 100+0.05p=0.25p represent?
The value of "p" will be "0.002".
Equation:According to the question,
[tex]100+0.05p=0.25p[/tex]By subtracting "0.25p" from both sides, we get
→ [tex]100+0.05p-0.25p=0.25p-0.25p[/tex]
[tex]100-0.2p=0[/tex]
[tex]100=0.2p[/tex]
[tex]p = \frac{0.2}{100}[/tex]
[tex]= 0.002[/tex]
Thus the above approach is right.
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can someone help me out?
"match each equation with its three solutions"
Answer:
Step-by-step explanation:
A. (1)
B. (4)
C. (2)
D. (5)
E. (3)
pease say if i got it right
Answer:
It is not correct. It should be A.
Step-by-step explanation:
u can use desmos to check ur answer
Look at the arithmetic sequence below and select the correct recursive and explicit formula for the sequence.
-1, 3, 7, 11...
Recursive Formula: Response area
Explicit Formula:
Answer:
+4 each time
Step-by-step explanation:
A clothing store sells clothing for 2 times the wholesale plus $10. The store sells a pair of pants to customers for $48. How much did the store pay wholesalefor the pants?
Answer:
19$
Step-by-step explanation:
Let w represent the wholesale cost of the pants, or the price paid by the store
2w + 10 = 48 Subtract 10 from both sides.
2w = 38 Divide both sides by 2.
w = 19
plz answer.
6-x=13.
Answer:
x=-19
Step-by-step explanation:
Answer:
6-x=13
6-13=x
x=6-13
x=-7
Give the least common denominator: 3/4, 7/8 _____
Step-by-step explanation:
step 1. LCD of 3/4 and 7/8 is 8.
The entire digits of pie times the square root of 1
Answer:
3.1415926
Step-by-step explanation:
3.1415926 * 1 = 3.1415926
Answer:
g4 bk.58i
Step-by-step explanation:
The y-intercept of the the inverse of the function f(x) = 1/4 x-9/4 is
Answer:
Since f(x) is a linear equation the graph of f(x) is a line with a slope of –3/4 and a yintercept of (0, 2). In looking at the graph, you can see that ...
Find the slope of a graph
I'll GIVE BRAINLESS
Answer: 5/4
Step-by-step explanation: