The radius of convergence of the maclaurin series is 1 unit.
It is given that maclaurin series [tex]\rm \frac{2x}{(1+x^2)}[/tex]
It is required to find the radius of the convergence of the maclaurin series.
What is maclaurin series?It is defined as the expansion of a function that provide the approximation of the given function at any point of function.
We have:
[tex]\rm \frac{2x}{(1+x^2)}[/tex]
To find the radius of convergence of the maclaurin series, we must find the roots of denominator hence:
[tex]\rm 1+x^2= 0\\\\\rm x^2 = -1\\\\[/tex]
From the complex number: the roots are imaginary:
[tex]\rm x_1 = i\\x_2 = -i[/tex]
i is the iota
and the distance from the origin (0,0) is 1.
Thus, the radius of convergence of the maclaurin series is 1 unit.
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on Sunday Mary pay $6 each on two tickets to a movie theater movies for $9.58 each Mary paid with 3 $20 bills how much changed
PLEASE HELP 50 point will give brainlyest
Evaluate 81000−−−−√3 .
1/125
6/500
8/500
2/10
Help me solve this please!
A shell fits into a golden rectangle with a length of 8 in. What is the shell's width? write your answer is simplified radical form and rounded to the nearest tenth of an inch.
Select one:
a. About 4.9 inches
b. About 4.1 inches
c. About 5.3 inches
The correct answer is option(a) about 4.9 inches.
To find the width of a golden rectangle with a given length, we will use the golden ratio formula that is
l / w = (1 + √5) / 2
Where, l = length of rectangle & w = width of rectangle
By applying the above formula we get the golden ratio, which is ≈ 1.618.
The formula for a golden rectangle is length(l) = 1.618 × width.
Given that length is 8 inches, we set up the equation:
8 = 1.618 × width
Solving for width:
width = 8 / 1.618 = 4.948...
The simplified radical form of 4.948... is ≈ 4.9 inches.
Thus, the correct answer is about 4.9 inches or option (a).
The angle of elevation to the top of a building in chicago is found to be 11◦ from the ground at a distance of 1000 feet from the base of the building. find the height of the building.
12x2 = 18x
i need someone to explain this
suppose you drop a tennis ball from a height of 15 feet. After the ball hits the floor, it rebounds to 85% of its previous height. how high will the ball rebound after its third bounce? round to the nearest tenth
What is the point-slope equation of the line with a slope 4/3 that goes through the point (-4,6)?
[tex]\bf (\stackrel{x_1}{-4}~,~\stackrel{y_1}{6})~\hspace{10em}slope = m\implies \cfrac{4}{3}\\\\\\\begin{array}{|c|ll}\cline{1-1}\textit{point-slope form}\\\cline{1-1}\\y-y_1=m(x-x_1)\\\\\cline{1-1}\end{array}\implies y-6=\cfrac{4}{3}[x-(-4)]\implies y-6=\cfrac{4}{3}(x+4)[/tex]
Answer:
The point-slope form of the equation is y - 6 = 4/3(x + 4), which is answer B.
Step-by-step explanation:
In order to find the point-slope form of any equation, start with the base form of the equation.
y - y1 = m(x - x1)
Now input the slope given as m, and the point in for x1 and y1.
y - y1 = m(x - x1)
y - 6 = 4/3(x - -4)
y - 6 = 4/3(x + 4)
When he was 40 Keefer began investing $150 per month in various securities for his retirement savings. His investments averaged a 4.5% annual rate of return until he retired at age 70. What was the value of Keefer's retirement savings when he retired? Assume monthly compounding of interest.
The difference of a number and 8 is the same as 34 less the number. find the number.
giving brainliest please help, and give steps if possible. Im trying to learn this.
Answer:
[tex]f(x)g(x) = - 30x^{3} + 31 {x}^{2} + 6x[/tex]
Step-by-step explanation:
[tex](fg)(x) \\ (fx) = 6 - 5x \\ g(x) = {6x}^{2} + x \\ substitute \: and \: calculate: \\ f(x)g(x) = - 30x^{3} + 31 {x}^{2} + 6x[/tex]
What is the linear function that best fits the data set?
The local linear approximation of a function f will always be greater than or equal to the function's value if, for all x in an interval containing the point of tangency
peter put $8,000 into a savings account that pays 6% interest, compounded continuously. what will he have after 5 years?
Alan is giving a basic math test in his class. One of the questions in the test is about finding two factors of the number 221. Which are the two factors of the given number? The two factors of the number 221 are ___ and ____.
Kenny is making creamy rice pudding his recipe requires 4 cups of milk he has a quart of milk in his fridge dose he have enough milk explain
A local movie theater charges $12 for an adult ticket and $10 for a child's ticket. a group of eight people spent a total of $86 on tickets to a movie. how many adults and how many children were in the group? write a system of linear equations based on the description. use x to represent the number of adults and y to represent the number of children.
Express answer in exact form.
A segment of a circle has a 120 arc and a chord of 8in. Find the area of the segment.
My brother owes me $10. I already have $10. My dads friend gave me and him $20 to split in half. He gave me the $20 and took my $10. Does he still owe me. Explain plz
A car is traveling at a speed of 50 miles per hour. Each wheel of the car makes 770 revolutions per minute. To the nearest tenth of an inch, what is the diameter of each car wheel? (Note: 1 mile = 5,280 feet)
Answer: 21.8 inches
Given:
A car is traveling at a speed of 50 miles per hour. Each wheel of the car makes 770 revolutions per minute.
To get the diameter of each car wheel
Get first the length of revolution (circumference of the wheel) in inches.
Speed=50 miles/hr
=50miles/60 minutes
= 0.833333 miles/minute
=.833/5280=4400ft= 52,800 inches/minute
Since there are 770 revolutions per minute, per revolution (circumference of the wheel) =
=52,800/770
=68.57 inches
Formula of diameter given the circumference is:
D=C/π
D=68.57/3.14
D= 21.8 inches
Answer:
21.8
Step-by-step explanation:
just took test
write an equation of an ellipse in standard form with the center at the origin and a height of 3 units and width of 1 unit
The equation of an ellipse with the specified attributes, using the center as the origin, is x2/0.25 + y2/2.25 = 1.
Explanation:The question asks for the equation of an ellipse with the center at the origin and a height of 3 units and width of 1 unit. In an ellipse, the center is the midpoint of both the major and minor axes. The major axis can be the horizontal (width) or vertical (height) axis, and the minor axis is the other one.
Given that the height of the ellipse is 3 units, this determines the major axis and its length of 2a=3, which means a=1.5. The width of the ellipse is 1 unit, this determines the minor axis and its length of 2b=1, which means b=0.5.
Using these values, the equation of such an ellipse, centered at the origin, in standard form is x2/0.25 + y2/2.25 = 1
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The equation of an ellipse in standard form with the center at the origin, a height of 3 units and width of 1 unit is [tex]\(4x^2 + (y^2/2.25) = 1\).[/tex]
Explanation:The equation of an ellipse in standard form with the center at the origin can be given by [tex]\(rac{{x^2}}{{a^2}} + rac{{y^2}}{{b^2}} = 1\)[/tex], where a is the semi-major axis and b is the semi-minor axis. Based on the information given in yourquestion, the height of the ellipse is 3 units which means the semi-major axis b is 1.5 units (since it's half the height). Similarly, the width of the ellipse is 1 unit which means the semi-minor axis a is 0.5 units (since its half the width). Substituting these values into the standard form of the ellipse we get: [tex]\(4x^2 + (y^2/2.25) = 1\)[/tex]
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how do I solve (x-5)(x-1)=0
Help Geometry!!
AC is tangent to circle O at A. If , m<BY= 24 , what is m<YAC?
a) 48
b) 156
c) 78
d) 132
Solve the quadratic equation. 8x2 + 16x + 8 = 0 A) 1 B) -1 C) 1 and 8 D) 1 and -1
How do you use properties of exponents and logarithms to rewrite functions in equivalent forms and solve equations?
Final answer:
To use properties of exponents and logarithms effectively, one must apply specific rules such as the logarithm of a product being the sum of the logarithms and the logarithm of a number raised to an exponent being the product of the exponent and the logarithm. Log transformations help linearize and solve equations involving exponents.
Explanation:
To rewrite functions in equivalent forms and solve equations using the properties of exponents and logarithms, one must understand several key rules and relationships. For example, the common logarithm (log) indicates the power to which 10 must be raised to equal a given number.
Two essential properties we use are:
The logarithm of a product of two numbers is the sum of the logarithms of the two numbers (log xy = log x + log y).The logarithm of a number raised to an exponent is the product of the exponent and the logarithm of the number (log x^n = n log x).Exponential and logarithmic functions are inverses. This relationship allows us to simplify complex expressions and solve exponential equations by taking the logarithm of both sides. For instance, the natural logarithm (ln or loge) and the base e exponential are inverse functions, so ln (e^x) = x and e^(ln x) = x.
A log transformation can linearize functions that involve an exponent by taking the log of both sides of the equation. This technique is valuable in solving equations where the variable is an exponent.
Simplify the square root of 864.
I cant remember this, please tell me how you got the answer.
HELP!!!!!!NEED TO PASS!!!!WILL GIVE THE BRAIN!!!!!!!!!!!
"the placement test for a college has scores that are normally distributed with a mean of 600 and a standard deviation of 60.if the college accepts only the top 1% of examinees, what is the cutoff score on the test for admission?"
someone help me please
A catapult is malfunctioning and not throwing objects in the intended manner. The builders have modeled the path of the objects thrown by using the following parametric equations. rewrite the parametric equations by eliminating the parameter.
x(t)=2t-1
y(t)= square root of t; t> or equal to 0
Answer:
The equation is [tex]y ^ 2 = \frac{x + 1}{2}[/tex]
Step-by-step explanation:
The parameter that we have is t. We want to eliminate this parameter in both equations, therefore in the first equation we solve for t and in the second equation we solve for the variable t.
We have:
[tex]x = 2t-1\\\\x + 1 = 2t\\\\t = \frac{x + 1}{2}[/tex]
Now we solve the other equation for t.
[tex]y= \sqrt{t}[/tex]
[tex]y ^ 2 = t[/tex] because [tex]t> 0[/tex]
As [tex]t = y ^ 2[/tex] and also [tex]t = \frac{x + 1}{2}[/tex]
Then:
[tex]y ^ 2 = \frac{x + 1}{2}[/tex]
The correct answer is:
D. [tex]x=2y^{2} -1, y\geq 0[/tex]