The power series representation for the function f(x) = x^3(x - 6)^2 is as follows: f(x) = x^5 - 12x^4 + 36x^3 - 216x^2 + 216x.
To obtain the power series representation, we expand the function using the binomial theorem and collect like terms.
First, we expand (x - 6)^2 using the binomial theorem: (x - 6)^2 = x^2 - 12x + 36.
Next, we multiply the result by x^3 to get the power series representation of the function: f(x) = x^3(x - 6)^2 = x^5 - 12x^4 + 36x^3.
We can further simplify the expression by expanding x^5 = x^3 * x^2 and collecting like terms: f(x) = x^5 - 12x^4 + 36x^3 - 216x^2 + 216x.
This power series representation expresses the function f(x) as an infinite sum of terms involving powers of x, starting from the fifth power. Each term represents a coefficient multiplied by x raised to a certain power.
It's important to note that the power series representation is valid within a certain interval of convergence, which depends on the properties of the function and its derivatives.
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A dairy facility has a bulk milk tank that is shaped like a right circular cylinder. The
tank has a height of 12 feet and a diameter of 216 inches.
If the milk tank was cut to be modeled by a truncated cylinder to of its height,
find the volume, in cubic feet, of the milk tank to the nearest hundredth.
Answer:
800
Step-by-step explanation:
HELP ME PLZ URGENT DUE TODAY
A town has a population of 5000 and grows at 3.5% every year. What will be the population after 15 years, to the nearest whole number?
Answer:
8377
Step-by-step explanation:
Growth rate is exponential, so it is determined by the formula (1+growth rate)^n where n is years
1.035^15 = 1.675...
multiply by 5000, you get 8376.744....
Which one is it??????
Step-by-step explanation:
Down 10n
Is answer
hope it helps you to
On which number line do the points represent negative seven and one over two and +1? (4 points)
Answer:
A number line is used in the mathematical positioning of real numbers that include the numbers from positive infinity to negative infinity. This includes rational, irrational, fractions, and whole numbers. In this case, we are given with an expression that we have to reduce to lowest terms: negative seven and one over two and +1. The first one is equal to -7.5 while the other one is equal to +1. Positive numbers lie on the right side of zero (center of the line) while negative numbers lie on the left on the other hand. -7.5 lies between -8 and -7 while +1 lies exactly between 0 and 2. Both of which are positive numbers.
Answer:A i did the test i got A correct
Step-by-step explanation:
brainliest to whoever can answer questions correctly
Answer:
Have you tried 5 x pi?
Good luck! Hope that helps!
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
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°.
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
7 x 1/6
Please help if you can
Answer:
7/6
Step-by-step explanation:
U just need to multiply 7 x 1/6 = 7/6 = 1.16
the length of a room is 2 m longer than its breadth .if the area of its floor is 63 sq.m.calculate the length and the breadth of the room
Answer:
Given :-the length of a room is 2 m longer than its breadth .if the area of its floor is 63 sq.m.calculate the length and the breadth of the room
To Find :-Length and breadth
Answer :-Let the length and breadth be l + 2 and l
Now,
[tex] \large \sf \: Area = l + 2 \times l [/tex]
[tex] \large \sf \: 63 = l + 2 \times \: l[/tex]
[tex] \large \sf \: 63 = 2l + {l}^{2} [/tex]
[tex] \large \sf \: {l}^{2} + 2l - 63 = 0[/tex]
[tex] \large \sf \: {l}^{2} (9l - 7l) - 63 = 0[/tex]
[tex] \large \sf \: l(l + 9) - 7(l + 9)[/tex]
Either
[tex] \large \sf \: l = - 9[/tex]
or,
[tex] \large \sf \: l = 7[/tex]
Length can't be negative,
So,
L = 9
B = 7
Please mark as brainliest :)
All intergers are rational numbers? True or false
not all are integers because they are a bit different
Need help in rush...someone pls help me! And pls show work
Answer:
7.2 or 7.20 my work is explained below!
first divide $3.00 by 5. our answer would be .6 (check: .6x5=3)
so now we know .6 is the cost of 1 ticket. so next, we would multiply .6 by 12 to get our answer. our answer would be 7.2 or 7.20.
I hope this helped, have a good day / night! :)
Answer:
[tex]\frac{5}{3}=1.66666666667 \\1.66666666667 * 6 = 10\\10 * 2 = 20[/tex]
Step-by-step explanation:
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
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
The congruence theorem that can be used to
prove ABAE = ACAD is
SSS.
O ASA.
SAS.
HL.
what is the answer?
Answer:
The answer is HL which is option D.
Step-by-step explanation:
Congruent shapes have equal corresponding sides and angles.
The congruence theorem that can be used to prove is HL
[tex]\triangle BAE \cong \triangle CAD[/tex] means that, the triangles are congruent.
From the figure, we have the following congruent sides
AB and AC --- SideAE and AD --- SideBE and CE --- Side (Hypotenuse Leg)The above highlights mean that the theorem can be used to prove that the triangles are congruent is HL.
This is so, because the hypotenuse of both triangles are equal.
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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:
PLEASE HELP!! WILL MAKE BRAINLIEST!! What is..... 3.064 x 1,000
Can someone solve this equation for me?
[tex]f(x)=(1-0.08)^{(\frac{1}{52})^{12t}[/tex]
Answer:
$\frac{4\cdot\left(5^2\right)^5\left(-20\right)^3\left(-8\ right)^{-6}}{5^{-3}\cdot\:25^3\ ... 3(−8) −65 −3· 25 3(( −5) −2) −4 =−251024 ( Decimal : −0.0244140625) .
plz answer.
6-x=13.
Answer:
x=-19
Step-by-step explanation:
Answer:
6-x=13
6-13=x
x=6-13
x=-7
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
Give the least common denominator: 3/4, 7/8 _____
Step-by-step explanation:
step 1. LCD of 3/4 and 7/8 is 8.
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:
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)
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 solve please , ill give Brainly to whoever is first.
Answer:
1314 in²
Step-by-step explanation:
Let l be the length, w be the width and h be the height.
[tex]SA=2(lw+lh+wh)[/tex]
Plug in the given values
[tex]SA=2(17*5+17*26+5*26)\\SA=2(85+442+130)\\SA=2(657)\\SA=1314[/tex]
Therefore, the surface area of the shape is 1314 in².
I hope this helps!
Can someone please help with this math question??
Answer:
Hm im not sure but hold on, i think i found it. 1 and 76
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
(need help fast)
Which of the following is an open statement?
A)
An angle that measures 95° is an obtuse angle.
B)
An angle that measures 95° is an acute angle.
C)
An angle that measures 40° is an acute angle.
D)
∠XYZ is an acute angle.
Answer:
D) is the right answer.
Hope it helps!
Thanks!
Answer:
I believe the correct answer is C) An angle that measures 40° is an acute angle. I'm not 100% sure if this is the correct answer.
Complete the table to find the rule for the translation, the coordinates of triangle A′B′C′, and the coordinates of the translated image, triangle A″B″C″.
the coordinates For the purple triangle A= -4,5 B= -2,1 C=-5,2
Step-by-step explanation:
Which linear inequality best represents the graph shown?
Answer:
B
Step-by-step explanation: