Find a power series representation for the function. (Give your power series representation centered at x = 0.)
f(x) = x2 x 4 + 81
f(x) = [infinity] n = 0.
Answers
Answer:
attached below
Step-by-step explanation:
The Function; F(x) = x^2 / (x^4 + 81 )
power series representation
F(x) = x^2 / ( 81 + x^4 )
= ( x^2/81 ) / 1 - ( -x^4/81 )
attached below is the remaining part of solution
Related Questions
Joaquin drew the triangle below.
On a coordinate plane, triangle K L J has points (3, 6), (4, 0) and (negative 5, 0).
Which statement must be true about a figure that is congruent to Joaquin’s triangle?
It has two angles on the x-axis.
It has a side that is 9 units long.
It has a side that lies on the x-axis.
It has an obtuse angle.
Answers
Answer:
It has a side that is 9 units long.
Step-by-step explanation:
Answer:
B) It has a side that is 9 units long.
Step-by-step explanation:
Since it does not have two angles on the X-axis, a side that lies on the X-axis, or an obtuse angle the reasonable answer would be B as it is true, and all of the others are false.
Tyler and Elena are on the cross country team. Tyler’s distances and times for a training run are shown on the graph. Elenas distances and times for a training run are given by the equation y=8.5x, calculate Tyler’s pace per minute
Answers
Answer:
8.2 miles per minute
Step-by-step explanation:
Given
See attachment for graph
Required
The rate of Tyler's graph
This means that we calculate the slope (m) of the graph using:
[tex]m = \frac{y_1 - y_2}{x_1 - x_2}[/tex]
So, we have:
[tex](x_1 ,y_1) = (0,0)[/tex]
[tex](x_1 ,y_1) = (1,8.2)[/tex]
So, we have:
[tex]m = \frac{y_1 - y_2}{x_1 - x_2}[/tex]
[tex]m = \frac{0 - 8.2}{0 - 1}[/tex]
[tex]m = \frac{-8.2}{- 1}[/tex]
[tex]m = 8.2}[/tex]
If f (x)=3x-2 and g(x) =6-4 find f(x) + g(x)
Answers
Answer:
3x
Step-by-step explanation:
NO LINKS OR ANSWERING WHAT YOU DON'T KNOW!!!!!
7. Suppose y varies inversely with x, and y = 39 when x = 1/3. What is the value of y when x = 26.
a. 3
b. 2
c. 1/2
d. 13
8. Suppose y varies inversely with x, and y = 25 when x = -1/5. What inverse variation equation relates x and y?
a. y = 5/x
b. y = -5/x
c. y = 5x
d. y= -5x
Answers
Answer:
Problem 7) C
Problem 8) B
Step-by-step explanation:
Recall that inverse variation has the form:
[tex]\displaystyle y=\frac{k}{x}[/tex]
Where k is the constant of variation.
Problem 7)
We are given that y = 39 when x = 1/3. Thus:
[tex]\displaystyle 39=\frac{k}{{}^{1}\!/ \!{}_{3}}[/tex]
Solve for k:
[tex]\displaystyle k=\frac{1}{3}(39)=13[/tex]
Hence, our equation is:
[tex]\displaystyle y=\frac{13}{x}[/tex]
Then when x = 26, y equals:
[tex]\displaystyle y=\frac{13}{(26)}=\frac{1}{2}[/tex]
Problem 8)
We are given that y = 25 when x = -1/5. Thus:
[tex]\displaystyle 25=\frac{k}{-{}^{1}\!/ \!{}_{5}}[/tex]
Solve for k:
[tex]\displaystyle k=-\frac{1}{5}(25)=-5[/tex]
Hence, our equation is:
[tex]\displaystyle y=-\frac{5}{x}[/tex]
What is the range of g?
y
--
.
9
7.
6+
5+
4+
3+
2+
1+
.
3
{4}}
-7 -6 -5 -4 -3 -2
+++
2 3 4 5 6 7
-2
-3
-4+
-5
-6+
7
7
Answers
Answer:
y 9 5 473648
Step-by-step explanation:
What is the solution set for |z+4|> 15
Answers
Answer:
I think that answer would be B.
Step-by-step explanation:
DO THIS AND ILL MARK! PLEASE
Answers
Answer:
Sin = 7/25
Cos = 24/25
Tan = 7/24
Step-by-step explanation:
The ratio for sin is opposite/hypotenuse, cos is adjacent/ hypotenuse, and tan is opposite/ adjacent.
A boy leaves station X on a bearing of 035' to station Y. which is 21km away. He then travels to another station Z on a bearing of 125 degrees . If Z is directly East of X, what is the distance from X to his present position?
Answers
9514 1404 393
Answer:
36.6 km
Step-by-step explanation:
We assume the initial bearing of the boy is 35°. Then he will make a 90° turn to a heading of 125°. A diagram shows the distance of interest is the hypotenuse of a right triangle in which 35° is the angle opposite the side of length 21 km.
The relevant trig relation is ...
Sin = Opposite/Hypotenuse
sin(35°) = (21 km)/XZ
XZ = (21 km)/sin(35°) ≈ 36.61 km
The distance from X to Z is about 36.61 km.
_____
The attached diagram has the angles measured in the usual way for a Cartesian plane: CCW from the +x axis. This will correspond to bearing measures if we relabel the axes so that +x is North, and +y is East.
Please help NO LINKS
Answers
[tex]\bar{x} = 0[/tex]
[tex]\bar{y} =\dfrac{136}{125}[/tex]
Step-by-step explanation:
Let's define our functions [tex]f(x)\:\text{and}\:g(x)[/tex] as follows:
[tex]f(x) = x^2 + 1[/tex]
[tex]g(x) = 6x^2[/tex]
The two functions intersect when [tex]f(x)=g(x)[/tex] and that occurs at [tex]x = \pm\frac{1}{5}[/tex] so they're going to be the limits of integration. To solve for the coordinates of the centroid [tex]\bar{x}\:\text{and}\:\bar{y}[/tex], we need to solve for the area A first:
[tex]\displaystyle A = \int_a^b [f(x) - g(x)]dx[/tex]
[tex]\displaystyle \:\:\:\:\:\:\:=\int_{-\frac{1}{5}}^{+\frac{1}{5}}[(x^2 + 1) - 6x^2]dx[/tex]
[tex]\displaystyle \:\:\:\:\:\:\:=\int_{-\frac{1}{5}}^{+\frac{1}{5}}(1 - 5x^2)dx[/tex]
[tex]\displaystyle \:\:\:\:\:\:\:=\left(x - \frac{5}{3}x^3 \right)_{-\frac{1}{5}}^{+\frac{1}{5}}[/tex]
[tex]\:\:\:\:\:\:\:= \dfrac{28}{75}[/tex]
The x-coordinate of the centroid [tex]\bar{x}[/tex] is given by
[tex]\displaystyle \bar{x} = \dfrac{1}{A}\int_a^b x[f(x) - g(x)]dx[/tex]
[tex]\displaystyle \:\:\:\:\:\:\:= \frac{75}{28}\int_{-\frac{1}{5}}^{+\frac{1}{5}} (x - 5x^3)dx[/tex]
[tex]\:\:\:\:\:\:\:=\dfrac{75}{28}\left(\dfrac{1}{2}x^2 -\dfrac{5}{4}x^4 \right)_{-\frac{1}{5}}^{+\frac{1}{5}}[/tex]
[tex]\:\:\:\:\:\:\:= 0[/tex]
The y-coordinate of the centroid [tex]\bar{y}[/tex] is given by
[tex]\displaystyle \bar{y} = \frac{1}{A}\int_a^b \frac{1}{2}[f^2(x) - g^2(x)]dx[/tex]
[tex]\displaystyle \:\:\:\:\:\:\:=\frac{75}{28}\int_{-\frac{1}{5}}^{+\frac{1}{5}} \frac{1}{2}(-35x^4 + 2x^2 + 1)dx[/tex]
[tex]\:\:\:\:\:\:\:=\frac{75}{56} \left[-7x^5 + \frac{2}{3}x^3 + x \right]_{-\frac{1}{5}}^{+\frac{1}{5}}[/tex]
[tex]\:\:\:\:\:\:\:=\dfrac{136}{125}[/tex]
She uses a scale of 1 centimeter to 6 inches
the scale drawing of the front face is
Answers
Answer:
change inches into centimeter and then divide it
hope this help
What is the following product? Assume x>0 and y>0 v5x^8y^2•v10^3•v12y
Answers
Answer:
[tex]10x^{5}y \sqrt{6xy}[/tex]
Step-by-step explanation:
Match each equation with its graph.
Answers
2.2
3.3
Good luck:)
A circle has a circumference of 2cm. Which statement about the circumference and area is true?
A comparison of the area and circumference is not possible since the area cannot be determinec
The numerical values of the circumference and area of the circle are equal.
The numerical value of the circumference is greater than the numerical value of the area.
The numerical value of the circumference is less than the numerical value of the area.
ОО
Answers
Answer:
The numerical values of the circumference and area of the circle are equal.
Create your own proportion problems?
Answers
Answer:
See Explanation
Step-by-step explanation:
Required
Proportion problems
An example is:
y is directly proportional to x such that: y=4 when x = 2;
Derive the equation
For direct proportions, we have:
[tex]y\ \alpha\ x[/tex]
This gives:
[tex]y = kx[/tex]
Make k the subject
[tex]k = y/x[/tex]
So:
[tex]k = 4/2 =2[/tex]
So, the equation is:
[tex]y = kx[/tex]
[tex]y = 2x[/tex]
Assume the above question is for inverse proportion
The variation will be:
[tex]y\ \alpha\ \frac{1}{x}[/tex]
This gives:
[tex]y\ = \frac{k}{x}[/tex]
Make k the subject
[tex]k =x*y[/tex]
[tex]k =2* 4 = 8[/tex]
So, the equation is:
[tex]y\ = \frac{k}{x}[/tex]
[tex]y = \frac{8}{x}[/tex]
Which ordered pair makes both inequalities true?
y> - 2x + 3
ysx-2
- + -3 2-1
X
Answers
Answer:
Step-by-step explanation:
On the graph of two inequalities, solution of two inequalities is defined by the common shaded area.
That means all the points which lie in this area will satisfy both the inequalities.
From the graph attached,
Points given in the options (0, 0), (0, -1) and (1, 1) are not lying in the solution area.
Since, ordered pair given in 4th option is not clear in the picture, Option (4) may be the answer.
f(x)=3x+2 what is f(5)
Answers
Answer:
17
Step-by-step explanation:
Substitute.
f(x)=3(5)+2
=15+2
=17
I hope this helps!
Step-by-step explanation:
if the equation if f(x) = 3x + 2, then f(5) would be equal to 3*5 + 2 = 17.
Simplify the radical expression below square root of 5/64
A square root 5/8
B 5/64
C square root 5/64
D 5/8
Answers
Answer:
a
Step-by-step explanation:
square root distribute to numerator and denominator so both get square rooted [tex]\sqrt{5}[/tex]/8
Children arrive at a house to do Halloween trick-or- treating according to a Poisson process at the unlucky rate of 13/hour. What is the probability that the time between the 15th and 16th arrivals will be more than 4 minutes ? (Hint: Think exponential.)
a) e e-2 = 0.1353
b) e-13/15 = 0.4204
c) e-1 = 0.3679
d) 1-2-1 = 0.6321
Answers
Answer:
0.4204 probability, option b.
Step-by-step explanation:
Exponential distribution:
The exponential probability distribution, with mean m, is described by the following equation:
[tex]f(x) = \mu e^{-\mu x}[/tex]
In which [tex]\mu = \frac{1}{m}[/tex] is the decay parameter.
The probability that x is lower or equal to a is given by:
[tex]P(X \leq x) = \int\limits^a_0 {f(x)} \, dx[/tex]
Which has the following solution:
[tex]P(X \leq x) = 1 - e^{-\mu x}[/tex]
The probability of finding a value higher than x is:
[tex]P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}[/tex]
Children arrive at a house to do Halloween trick-or- treating according to a Poisson process at the unlucky rate of 13/hour
13 arrivals during an hour, which means that the mean time between arrivals, in minutes is of [tex]\mu = \frac{13}{60} = 0.2167[/tex]
What is the probability that the time between the 15th and 16th arrivals will be more than 4 minutes ?
This is P(X > 4). So
[tex]P(X > 4) = e^{-0.2167*4} = 0.4204[/tex]
So the correct answer is given by option b.
40 points! Need help finding.
Answers
The cordent plan of the answer is 2
Answer:
The scale factor will just be 2
Step-by-step explanation:
The length of PQ is twice as larger than the length of AB.
so from 12 to 6 or 6 to 12, we multiply 6 by 2 which equals to 12
Please help me figure out if this truth table is equivalent or not. People who show their work and give a proper answer shall receive brainliest
Answers
Answer:
The statements are logically equivalent.
The 6th column is:
F T F F
The 7th column is:
F T F F
Step-by-step explanation:
The 6th column is just the opposite of the 5th column
The 7th column is T only if both the 1st and 4th are T
The volume, V, of a sphere in terms of its radius, r, is given by , V(r)=4/3(pie)r^3. Express r as a function of V, and find the radius of a sphere with volume of 150 cubic feet. Round your answer for the radius to two decimal places.
r(V)=
A sphere with volume 150 cubic feet has radius
_________ feet.
Answers
Step-by-step explanation:
If
[tex]V=\dfrac{4\pi}{3}r^3[/tex]
then we can solve for r as
[tex]r = \sqrt[3]{\dfrac{3V}{4\pi}}[/tex]
If the volume of the sphere is 150 ft^3, then the radius is
[tex]r = \sqrt[3]{\dfrac{3(150\:\text{ft}^3)}{4\pi}} = 3.30\:\text{ft}[/tex]
The radius of the given sphere with a volume of 150 cubic feet is 2.29 feet, correct to two decimal places.
Given that
the volume of a sphere = 150 cubic feet.
the radius of the sphere=????
what is a Sphere?a round solid figure, or its surface, with every point on its surface equidistant from its center.
as we know,
the volume of a sphere
[tex]V=\frac{4}{3} *\pi *r^3[/tex]
[tex]r = \sqrt[3]{\frac{3V}{4\pi } }[/tex][tex]r = \sqrt[3]{\frac{3*150}{4\pi } }[/tex][tex]=2.29 feet[/tex]
therefore, the radius of the given sphere is 2.29feet
to get more about sphere refer to the link,
https://brainly.com/question/22807400
The asymptote of the function f(x) = 3x + 1 – 2 is . Its y-intercept is
Answers
Answer:
-1
Step-by-step explanation:
1-2=-1
y=mx+b
b= y intercept
Answer:
-1
Step-by-step explanation:
There is a bag with only red marbles and blue marbles.
The probability of randomly choosing a red marble is
7/10th
There are 42 red marbles in the bag and each is equally likely to be chosen.
Work out how many marbles in total there must be.
Answers
Answer:
60 marbles in total
Step-by-step explanation:
Find how many marbles there are in total by dividing 42 by 0.7:
42/0.7
= 60
So, there are 60 marbles in total
Suppose the random variables X, Y, and Z have the following joint probability distribution. x y z f ( x , y , z ) 1 1 1 0.05 1 1 2 0.10 1 2 1 0.15 1 2 2 0.20 2 1 1 0.20 2 1 2 0.15 2 2 1 0.10 2 2 2 0.05 Determine the conditional probability distribution of X given that Y
Answers
Answer:
Determine the conditional probability distribution of X given that Y = 1 and Z = 2. Round your answers to two decimal places (e.g. 98.76).
answer:
Given that Y = 1 : 2/5
Given that Z = 2 : 3/5
Step-by-step explanation:
The conditional probability distribution of X F x | yz^( x )
Given that Y = 1
F x | yz . ( x | yz ) = 2/5
Given that z = 2
= 3/5
attached below is the detailed solution
Tonya wants to estimate what proportion of the students in her dormitory like the dorm food. She interviews a simple random sample of 50 students living in the dormitory. She finds that 14 think the dorm food is good. Find a 90% confidence interval for the true proportion of students that think the dorm food is good.
a. 0.176 to 0.384
b. 28%
c. 0.28 +/- 0.03
d. 0.156 to 0.404
Answers
Answer:
Step-by-step explanation:
The solution of the problem has been solved on paper and attached in the attachment section. Kindly refer to that and feel free to ask any doubt.
If the angles (4x + 4)° and (6x – 4)° are the supplementary angles, find the value of x.
Answers
Answer:
18
Step-by-step explanation:
Supplementary angles means sum of angles is 180.
4x + 4 + 6x - 4 = 180
4x + 6x + 4 - 4 = 180
10x = 180
x = 180 / 10
x = 18
Answer:
x=18 degree
Step-by-step explanation:
If they are supplementary angles, then their sum = 180 degree
4x+4 + 6x-4 =180
4x+6x + 4-4 = 180
10x = 180
x=180/10
x=18
The diagram shows that `/_A cong /_D` and `bar(AB) cong bar(DE)`. Which other statement do you need to prove triangle congruency through the SAS criterion?
A. /_C cong /_F
B. bar(BC) cong bar (EF)
C. /_B cong /_E
D. bar(AC) cong bar(DF)
Answers
Answer:
Option D
Step-by-step explanation:
In the given triangles ΔABC and ΔDEF,
∠A ≅ ∠D
AB ≅ DE
By SAS property of congruence of two triangles,
Two sides and the included angle of one triangles should be congruent to corresponding two sides and the included angle of the other triangle.
Therefore, AC ≅ FD will be the desired property to prove the given triangles congruent.
Option D will be the correct option.
Answer:
Step-by-step explanation:
Find the area of the figure
Please help :)
Answers
9514 1404 393
Answer:
66.5 cm²
Step-by-step explanation:
A horizontal line at the "knee" on the right will divide the figure into a 4 cm by 2 cm rectangle, and a trapezoid with bases 4 cm and 9 cm, and height 11-2 = 9 cm. Then the total area of the figure is ...
A = LW + 1/2(b1 +b2)h
A = (4 cm)(2 cm) + (1/2)(4 cm +9 cm)(9 cm) = 8 cm² +58.5 cm²
A = 66.5 cm² . . . . area of the figure
In chapter 9, we discussed Confidence Interval methodology to draw conclusions about the difference in the brain size of the children with and without autism. Discuss a different methodology to conclude if there is any significant difference in the average brain size of the children with and without autism.
Answers
Answer:
Two sample t test
Step-by-step explanation:
The two sample t test can be used in the scenario described above, where two independent samples are obtained, we take a certain sample of children with autism and then another sample of children without autism. The number of children chosen for each sample should be random and could be of equal or unequal sizes. The mean and standard deviation of each of sample A and B are deternined and used to perform the analysis to determine if the mean of each sample are equal or not. This test is also called the WELCH T TEST
Find the area of the figure below, formed from a triangle and a parallelogram.
144 square millimeters
120 square millimeters
72 square millimeters
96 square millimeters
Answers
total area =A1+A2+A3
A1=1/2b*h
A1=1/2*8mm*6mm
A1=24mmsquare
A2=1/2b*h
A2=1/2*8mm*6mm
A2=24mmsquare
A3=b*h
A3=8mm*6mm
A3=48mmsquare
Atotal=24mmsquare+24mmsquare+48mmsquare
Atotal=96mmsquare
