On observing the provided question, we can say that the the provided equation f(x) = is the basic cubic function.f(x) = 8100
What is function?An statement, rule, or law in mathematics that specifies the connection between an independent variable and a dependent variable (the dependent variable). A relationship between a group of inputs and one output each is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. Y=X2 is an illustration of this. You only receive one output for y if you enter anything for x. The fact that x is the input value leads us to argue that y is a function of x.
basic cubic function is = f(x) = x^2
x = 90
f(x) = 8100
To know more about functions visit:
brainly.com/question/28193995
#SPJ1
On solving the provided question, we can say that It is possible to construct a parking lot since the angle J's measurement is 180 - (50 + 90) = 40. More than 38 degrees, 40 degrees.
what are angles?An angle is a form in Euclidean geometry made composed of two rays, called the angle's sides, that meet at a point in the middle known as the angle's vertex. In the plane where the rays are placed, two rays can produce an angle. An angle is also produced when two planes intersect. They're known as dihedral angles. In plane geometry, an angle is the form that two rays or lines with a common termination might take. The Latin word "angulus," which means "horn," is where the English word "angle" comes from. The two rays, also known as the sides of the angle, have a common termination known as the vertex.
It is possible to construct a parking lot since the angle J's measurement is 180 - (50 + 90) = 40. More than 38 degrees, 40 degrees.
To know more about angles visit:
https://brainly.com/question/14569348
#SPJ1
HELP ME OLEASE IM BEGGINF
The graph below shows the number of blocks away from home Bentley is 21 minutes after he left his house, until he got back home.
What is distance-timed graph?The distance-timed graph is the type of graph that is used to represent the relationship that exists between the distance covered by a moving object and the time take to reach its destination.
The distance covered from house to store= 4 blocks
The time used = 2 minutes
The distance covered from store to the bank = 10 blocks
The time used = 7 minutes
The time used to return home from the bank = 12 minutes
Therefore, Bentley is 21 minutes after he left his house, until he got back home. That is 2+7+12 = 21 minutes.
Learn more about graph here:
https://brainly.com/question/25184007
#SPJ1
18.
A button is circular, as shown. The
button has a diameter of 6.4
centimeters What is the area of the
button in square centimeters?
The area of the circle with diameter 6.4 is 32.15 square centimeters.
What is area of the circle?A circle closed plane geometric shape. In technical terms, a circle is a locus of a point moving around a fixed point at a fixed distance away from the point.
Area of a circle is the region occupied by the circle in a two-dimensional plane. It can be determined easily using a formula:
[tex]A = \pi r^2[/tex]
Given that the diameter of the circle is 6.4 centimeters.
The radius of the circle is thus half of the diameter that is 3.2 centimeters.
The area of the circle is given by the formula:
[tex]A = \pi r^2[/tex]
Substitute the value of r = 3.2 in the formula:
[tex]A = (3.14) (3.2)^2\\\\A = 32.15[/tex]
The area of the circle is 32.15 square centimeters.
Learn more about area here:
https://brainly.com/question/27683633
#SPJ1
In a right triangle, given legs of lengths 5 and 12, find the length of the hypotenuse.
The length of the hypotenuse is 13 units
How to find the length of the hypotenuse.From the question, we have the following parameters that can be used in our computation:
Legs = 5 and 12 units
The length of the hypotenuse of the right triangle can then be calculated using
Hypotenuse² = Leg 1² + Leg 2²
Substitute the known values in the above equation, so, we have the following representation
Hypotenuse² = 5² + 12²
So, we have
Hypotenuse² = 169
Take the square roots
Hypotenuse = 13
Hence, the hypotenuse is 13 units
Read more about right triangle at
https://brainly.com/question/1248322
#SPJ1
You roll a number cube and record an odd number 12 times in a row. As the number of times you roll an odd number increases, what happens to the theoretical probability that you roll an even number? (Please show step by step explanation)
When the number of times you roll an odd number increases, the theoretical probability that you roll an even number would decrease.
How is the probability of rolling an even number affected ?As the number of times you roll an odd number increases, the theoretical probability that you roll an even number decreases. This is because the probability of rolling an even number is inversely proportional to the number of times you roll an odd number.
If you are rolling a fair die, the probability of rolling an even number is 3/6 or 1/2, and the probability of rolling an odd number is also 3/6 or 1/2.
As the number of times you roll an odd number increases, the number of rolls that are left for an even number decreases, thus the probability of rolling an even number decreases as well.
For example, if you roll the die 10 times and 6 of them are odd numbers, the probability of rolling an even number in the remaining 4 rolls is 4/4 or 1 (100%) because you are guaranteed to roll an even number.
Find out more on theoretical probability at https://brainly.com/question/8652467
#SPJ1
How to solve and the equation
Answer:19
Step-by-step explanation:
I think this is right
DUE SOON! PLEASE HELP! QUESTION DOWN BELOW!
Answer:
a)not quadratic
b)quadratic
c)quadratic
d)not quadratic
a) x=-3
b) maximum is (-3,4)
c)[tex](-3-\sqrt{2},0)[/tex] and[tex](-3+\sqrt{2},0)[/tex]
d)(0,-14)
e) Domain: (-∞,∞), {xIx∈ℝ}
Range: (-∞,4), {yIy≤4}
Step-by-step explanation:
Hope this helps!
For the following two numbers, find two factors of the first number such that their product is the first number and their sum is the second number.
40,13
The two factors such that their product is the first number and their sum is the second number are 8 and 5.
What is a factor?A factor is defined as the number that divides another number, leaving no remainder.
In other words, if multiplying two numbers gives us a product, then the number we multiply is a factor of the product and divided by the product.
The factors of 40 and 13 such that their product is the first number and their sum is the second number = 8 and 5.
That is, 8×5 = 40
8+5 = 13
Learn more about factors here:
https://brainly.com/question/26504247
#SPJ1
Transversal Geometry
find the value of x
Answer:
x = 67°
Step-by-step explanation:
When two parallel lines are cut by a transversal, the pair of angles formed on the interior of the parallel lines but on the opposite sides of the transversal are called alternate interior angles and they are congruent.
x = 67°
what will be the value stored in the variable x after the execution of the following code snippet? int a
The result of running the code is that x will be 20.
Therefore, your software is saying:
Place x at 30. (I'm assuming that you don't care about the case here because you wrote an X in capital letters that don't exist anywhere else;)
Place y at 20.
If y is not equal to x-10, ask. "If yes, put x to the value of x-5; if no, set x to the value of y," is the next step.
Your question receives the response "no," and x is then set to the value of y since the values of x and y you selected to result in y being equal to x-10. The result of running the code is that x will be 20.
Know more about code
https://brainly.com/question/26134656
#SPJ4
Full question
After execution of the following code, what will be the value of x? X = 30; y = 20; if (y ! = (x - 10)) x = x - 5; else x = y;
please help, need asap. do 30, and 31....30 points!!!!!!!!!!!!!!!!!
The indicated measures:
m∠ABC = 138° and m∠BCD = 52°.
What is an angle addition postulate?According to the Angle Addition Postulate, an angle's measure is equal to the sum of the measures of any two adjacent angles. The Angle Addition Postulate can be used to determine the measurement of a missing angle or to determine the angle produced by two or more other angles.
Given:
The angle measures:
m∠DAE = 16° and m∠EDC = 64°.
The diagonals of the kite intersect at 90°.
(1).
In ΔAED,
the sum of all the angles of the triangle is 180°.
m∠DAE + m∠ADE + m∠AED = 180°
m∠ADE = 180 - 90 - 16
m∠ADE = 74°
According to the angle addition postulate,
m∠ADE + m∠EDC = m∠ADE
m∠ADE = (74 + 64)°
m∠ADE = 138°
From the property of kites,
m∠ADE = 138° = m∠ABC.
(2). m∠EBC = m∠EDC,
m∠EBC = 64°
In ΔBCD,
the sum of all the angles of the triangle is 180°.
m∠DBC + m∠BCD + m∠CDB = 180°
m∠BCD = 180 - 64 - 64
m∠BCD = 52°
Therefore, 138° = m∠ABC and m∠BCD = 52°.
To learn more about the angle addition postulate;
brainly.com/question/14957499
#SPJ1
How much more does the cat eat than the parrot? The Parrot eats 3/8 pounds of food, and the cat eats 7/8 pounds of food. Write and solve an equation to represent the problem?
The equation and solution of the problem are 3/8-7/8 and 1/2.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.
Given;
The food parrot eats = 3/8pounds
The food cat eats = 7/8pounds
Now, food eaten more by cat =7/8-3/8
=(7-3)/8
=4/8
=1/2
Therefore, the answer to equation will be 1/2.
Learn more about equations here;
https://brainly.com/question/25180086
#SPJ1
The nth term of a sequence is 60 - 8n.
Find the largest number in this sequence.
Answer:
The largest term is 52.---------------------------------
Given sequence:
t(n) = 60 - 8nThis is decreasing sequence since the common difference is negative, d = - 8.
Therefore the first term is the largest one:
t(1) = 60 - 8*1 = 60 - 8 = 52What am I doing wrong in this problem? List the data in the following stem-and-leaf plot. The leaf represents the tenths digit. 14 15 1447 16 56 17 8 18 366 Separate the numbers in the list by a comma. The list is: 151, 154, 154, 157, 165, 166, 178, 183, 186, 186
It will stand for the 15.1, not The 151.
So therefore here you got almost correct the answer,
but you misunderstood about the leaves because the leaves will stand for the decimal.
The 10th means that after the decimal,
So the foundation must be the 15.1.
15.4, 15.7, 16.5 16.6 17.8 18.3 18.6 and 18.6.
A stem and leaf diagram is a way of displaying a collection of numbers. The ‘stem’ consists of the first part of every number, usually the first digit(s) and the ‘leaf’ consists of the latter part of every number, usually the last digit. We need to know how to draw them and how to use them.
Draw a stem-and-leaf diagram to represent Scott’s data.
Step 1: Figure out what our key will be. The stem will be the first two digits, whilst the leaf will be the last digit. Our key is any number that is in the list, represented in terms of a stem and leaf.
Step 2: Use our key to draw our stem part of the diagram, which will have to include: 15,16,17,18,
Step 3: Rewrite the data in numerical order.
151, 154, 154, 157, 165, 166, 178, 183, 186, 186
Step 4: Fill in the ‘leaf’ values (the last digit of every value) alongside the correct ‘stem’ value, to complete the stem and leaf diagram.
14 15 1447 16 56 17 8 18 366
14
15 1447
16 56
17 8
18 366
151 , 154 , 154 , 157
165 , 166
178
183 , 186 ,186
it will stand for the 15.1, not The 151. So therefore here you got almost correct the answer, but you misunderstood about the leaves because the leaves will stand for the decimal. The 10th means that after the decimal, So the foundation must be the 15.1, 15.4, 15.7, 16.5 16.6 17.8 18.3 18.6 and 18.6.
To know more about stem and leaf diagram visit brainly.com/question/17886846
#SPJ4
A coordinate plane. The x- and y-axes each scale by one. A graph of a line intersects the points one, negative three, and three, zero. What is the slope of the line?
The slope of a given line is m=1.5.
What is slope of a line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The formula to find the slope of a line is slope = (y₂-y₁)/(x₂-x₁).
The coordinate points of a line are (1, -3) and (3, 0).
Substitute, (x₁, y₁) and (x₂, y₂) in m=(y₂-y₁)/(x₂-x₁), we get
m= (0+3)/(3-1)
= 3/2
= 1.5
Therefore, the slope of a given line is m=1.5.
To learn more about the slope of a line visit:
https://brainly.com/question/14511992.
#SPJ1
Evaluate the function over the domain {-2, -1, 0, 1, 2}. As the values of the domain
4. 10^x
increase, do the values of the range increase or decrease?
The range of the function is {0.01, 0.1, 1, 10, 100}. With an increase in the value of the domain, the range of the function is increasing.
What is a function?
A function from a set X to a set Y allocates exactly one element of Y to each element of X. The set X is known as the function's domain, while the set Y is known as the function's codomain.
Given function is
f(x) = 10^x.
Given domain is {-2, -1, 0, 1, 2}.
Now putting x = -2, -1, 0, 1, 2 in the function f(x) = 10^x.
When x = -2:
f(-2) = 10^(-2)
f(-2) = 0.01.
When x = -1:
f(-1) = 10^(-1)
f(-1) = 0.1.
When x = 0:
f(0) = 10^(0)
f(0) = 1.
When x = 1:
f(1) = 10^(1)
f(1) = 10
When x = 2:
f(2) = 10^(2)
f(2) = 100
The range of the function is {0.01, 0.1, 10, 100}
The values of the range increase with the increase of domain.
To learn more about range, click on the below link:
https://brainly.com/question/29019847
#SPJ1
A basketball player's chance of scoring a free throw is estimated to be 25. The player tries 20 shots and the number of baskets is recorded. This event is a binomial experiment because
A. there are only two outcomes; the number of trials is not fixed; the probability is the same for each trial; the trails are independent of each other.
B. there are only two outcomes; the number of trials are fixed; the probability is not the same for each trial; the trails are independent of each other.
C. there are only two outcomes; the number of trials are fixed; the probability is the same for each trial; the trails are independent of each other.
D. there is only one outcome; the number of trials are fixed; the probability is not the same for each trial; the trails are independent of each other.
This event is a binomial experiment because C. there are only two outcomes; the number of trials is fixed; the probability is the same for each trial; the trials are independent of each other.
What is a binomial experiment?A binomial experiment is a random experiment with a fixed number of repeated trials with independent outcomes, successes or failures, yes or no, and heads or tails.
In a binomial experiment, the probability of "success" p is the same for each outcome as the chance of "failure" q is the same for each outcome.
The number of free throw shots in this experiment is 20 and they are either missed or scored.
Thus, the fixed number of trials with only two outcomes satisfied as a binomial experiment.
Learn more about binomial experiments at https://brainly.com/question/9325204
#SPJ1
Consider the scale drawing of Balanced Rock in Arches National Park. What is the actual height of the structure? Round your answer to the nearest whole foot.
Based on the image provided, the actual height of the structure would be 1/975.36.
What is a scale?This refers to a picture or model that is made based on the proportion of an original structure. Most models are smaller than their original.
What is the scale factor in the image?According to the image, 1 centimeter represents 32 feet of the actual structure, which means there is a 1:32 scale factor, let's calculate then the number of centimeters in total to know the height:
1 foot = 30.48 cm
32 feet = x
x= 30.48 x 32/ 1 = 975.36 cm
Based on this the height can be expressed as 1/975.36.
Learn more about scale in https://brainly.com/question/1287267
#SPJ1
In this polygon, all angles are right
angles.
What is the area of this polygon?
Enter your answer in the box.
____ ft²
In this polygon, all angles are right angles. The area of this polygon = 334 ft²
What is the polygonal area formula?To calculate the area of a regular polygon, just apply the formula below: Half of a perimeter multiplied by apothem equals area. What it means is as follows: The perimeter is the sum of the lengths of all the sides. A segment known as an apothem joins the midpoint of any perpendicular side to the midpoint of a polygon.
The equation for the area of a regular polygon with n sides is [l2n]/[4tan(180/n)]. where n is the number of sides and l is the length of the sides of the polygon.
To calculate the area of a regular polygon, use the formula Area = (number of sides length of one side apothem)/2.
Given data :
Area of polygon
= Area AGEF + Area BCDG
= 21 x 7 + 17 x 11
= 147 + 187 = 334 ft²
Learn more about Area of polygon refer to :
brainly.com/question/20110859
#SPJ1
Answer:334 ft
Step-by-step explanation: i did the test
Can you please solve this problem.
Answer: 10y
Step-by-step explanation:
4(y-2)+6y+8
4(y-2)=4y-8
4y-8+6y-8
*8's cancel out*
6y+4y=10y
okay i retook it sorry it was bad before
Answer: The first orange is the best deal at $0.8 per orange. The second cand is the best deal at $0.45 per candy.
Step-by-step explanation:
First orange: 5 for $4 equals $4/5 per orange, which equals $0.8 per orange.
Second orange: 10 for $9 roughly equals $1.111 per orange
Third orange: $0.82 each
The first orange is the best deal at $0.8 per orange
First candy: 3 for $1.5 equals $1.5/3 per candy, which equals $0.5 per candy.
Second candy: 4 for $1.8 equals $0.45 per candy
Third candy, 10 for $4.6 equals $0.46 per candy
PLEASE HELP ASAP:
A bag has 1 speckled pen, 3 black pens,
and 7 yellow pens. You randomly pull a pen
from the bag, put it back, and then pull out
another one.
What is the probability of not getting a yellow and then not getting a yellow? Write
your answer as a fraction.
Answer:
[tex]\textrm{P(no yellow on two picks )} = \dfrac{16}{121}[/tex]
Step-by-step explanation:
The total number of pens is 1 + 3 + 7 = 11 out of which 7 are yellow.
(We don't really care what color the other pens are since we are interested only in the yellow pens)
[tex]\textrm{P(yellow on first pick )} = \dfrac{\textrm{Number of yellow pens}}{\textrm{Total number of pens}} = \dfrac{7}{11}[/tex]
The probability of not getting a yellow on first pick is the complement of this probability and is 1 less than the probability of picking an yellow
[tex]\textrm{P(not yellow on first pick )} = 1- \dfrac{7}{11} = \dfrac{4}{11}[/tex]
Since we are putting back the pen after the first pick, the total number of pens as well as pens of each color remain the same.
Therefore the probability of not getting a yellow on second pick is the same as the first pick and is [tex]\dfrac{4}{11}[/tex]
The combined probability of not getting an yellow on both picks is the product of these probabilities
[tex]\textrm{P(no yellow on two picks )} = \dfrac{4}{11}\cdot \dfrac{4}{11} = \dfrac{16}{121}[/tex]
A couple is starting a family and decides to have four children. Assume that the probability of having a boy or having a girl are equal. Find the probability model for the number of girls the couple has
Consequently, the probability of producing precisely one girl or exactly one male 0.25 + 0.25 = 0.5P(x = 1) = 4C1 * 0.5^1 * 0.5^3; 0.9375 ; 0.5
What is probability?Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty.
Due to this:
p = 0.5
Modeling the probability of how many females the couple has:
[tex]P(x =x) is equal to nCx * px * (1 - p) (n - x)\\P(x = 0) = 4C0 * 0.5^0 * 0.5^4 = 0.0625\\\=P(x = 1) = 4C1 * 0.5^1 * 0.5^3 = 0.25\\P(x = 2) = 4C2 * 0.5^2 * 0.5^2 = 0.375\\P(x = 3) = 4C3 * 0.5^3 * 0.5^1 = 0.25\\P(x = 4) = 4C4 * 0.5^4 * 0.5^0 = 0.0625[/tex]
likelihood of having at least one female
N = 4 trials in total.
P(x 1) is equal to p(x = 1) plus p(x = 2) plus p(x = 3) plus p(x = 4)
Employing the relation
P(x =x) is equal to nCx * px * (1 - p) (n - x)
use a calculator
P(x ≥ 1) = 0.9375
Chances of getting just one female or exactly one boy
3 females OR 3 boys OR 1 boy
P(x = 1)
P(x =x) is equal to nCx * px * (1 - p) (n - x)
P(x = 1) = 4 * 0.5 * 0.125
P(x = 1) = 0.25
The likelihood of getting one girl and three males or vice versa is 0.25
Consequently, the likelihood of producing precisely one girl or exactly one male
0.25 + 0.25 = 0.5P(x = 1) = 4C1 * 0.5^1 * 0.5^3 is 0.9375 ; 0.5
To know more about probability here
https://brainly.com/question/11234923
#SPJ1
if the expression 4x + 2(x - 4) is equivalent to x +2 then what is the value of x?
Answer:
x=2
Step-by-step explanation:
4x + 2(x - 4) is equivalent to x +2
first, distribute. 4x+2x-8
next, combine like terms. 6x-8
6x-8 = x+2
we need to group all the variable terms on one side, and all the constant terms on the other side of the equation. (6x-8)+(8-x)=(x+2)+(8-x)
get rid of the parenthesis. 6x-8+8-x=x+2+8-x
combine like terms. 6x-x-8+8=x-x+2+8
solve. 5x=10
divide both by 5. 5x/5=10/5
x=2
work out: 8^1/3/5^-2
The solution to the indices is 50.
What is an Indices?Index (indices) is the power or exponent which is raised to a number or a variable. The plural of index is indices. Indices contain constants and variables. The constant is a value which cannot be changed and a variable quantity can be assigned any number or its value can be changed.
Indices are a convenient tool in mathematics to correctly denote the process of taking a power or a root of a number. Taking a power is simply a case of repeated multiplication of a number with itself while taking a root is just equivalent to taking a fractional power of that same number.
8^1/3 / 5^-2
Applying the necessary laws of indices;
= 8^1/3 / 5^-2
= ∛8 / (1/5^2)
= 2 / (1/25)
= 2 x (25/1)
= 50
Learn more about indices here: https://brainly.com/question/170984
#SPJ1
Selkirk Company obtained a $15,000 note receivable from a customer on January 1, 2021. The note, along with interest at 9%, is due on July 1, 2021. On February 28, 2021, Selkirk discounted the note at Unionville Bank. The bank’s discount rate is 12%.
Required:
Prepare the journal entries required on February 28, 2021, to accrue interest and to record the discounting for Selkirk. Assume that the discounting is accounted for as a sale.
A journal entry is a format used in accounting to record transactions. The amount we owe someone else that we must get in the future is known as notes receivable.
What is Notes receivable?Notes receivable are claims for which official documents of credit, like promissory notes, are issued as proof of debt. In most cases, the credit instrument has a minimum term of 30 days and imposes an interest payment obligation on the debtor.
Given the following information:
Note receivable $15,000
Rate of interest 9%
Discount rate 12%
Period 2 months
Preparing journal entry to record accrued interest
To prepare the journal entry, we must first calculate the interest. We can compute interest by multiplying the notes receivable, the interest rate, and the period, i.e.
Interest = Notes receivable × Rate of interest × Period
Interest = 15000 × 0.09 × 2/12
Interest = 225
Now we can prepare the journal entry
Date Particulars Debit ($) Credit($)
February 28, 2016 Interest receivable 250
Interest 250
To record accrued interest
Preparing the journal entry to record discounting
To begin preparing the Journal entry, we must first calculate the necessary data.
We can calculate the cash as the difference between Maturity Value and Discount. That is,
Cash = Maturity Value – Discount
The value of Maturity is unknown. We can compute it as the sum of the receivable notes and interest. That is,
Maturity Value = Notes receivable + Interest
Interest =Notes receivable × Rate of interest × Period
= $15,000 × 0.1 × 6/12
= $1,500 × 0.5
= $750
Maturity Value = Notes receivable + Interest
= $15,000 + $750
= $15,750
Discount =Maturity Value × Discount rate × Period
= $15,750 × 0.12 × 4/12
= $1,890 × 0.33
= $630
Finally, we can calculate cash
Cash = Maturity Value – Discount
= $15,750 − $630
= $15,120
Loss on sale = Cash – Notes receivable - Interest
= $15,120 − $15,000 − $250
= $130
Finally, we can prepare our journal entry.
Date Particulars Debit ($) Credit($)
February 28,2016 Cash 15,120
Loss on sale 130
Notes receivable 15,000
Interest 250
(To record discounting)
Thus, Cash & Loss are debited, & Notes Receivable & Interest are credited.
Learn more about Notes Receivable
https://brainly.com/question/13741240
#SPJ1
please help due soon!!!!
The sum of all a triangle's sides' lengths is the formula for calculating a triangle's perimeter.
What is a formula of perimeter of triangle?The whole length of a shape's boundary is referred to in geometry as the perimeter of the shape. By multiplying the lengths of all the sides and edges that surround an object, the perimeter may be calculated. It is measured in measures of length that are linear, such as centimeters, meters, inches, or feet.
The sum of all a triangle's sides' lengths is the formula for calculating a triangle's perimeter.
Add the sides' lengths to find a triangle's perimeter. As an illustration, the perimeter of a triangle with sides a, b, and c is given by P = a + b + c.
To learn more about perimeter refer to:
https://brainly.com/question/19819849
#SPJ1
find a power series representation for f(x) = arccot(x).
The power series representation for f(x) = arccot(x) is
[tex]\pi /2- \lim_{n \to \infty} (-1)^n\frac{x^2^n^+^1}{2n+1}[/tex]
The power series ∑aₙxⁿ is an infinite series and looks like a function of x. An easy way to illustrate the idea of a power series representing a function is to use the geometric series as an example.
The power series is a very important kind of infinite series where the terms contain the powers of a variable. A power series is a series of the general form:
∑aₙ(x-x₀)ⁿ=a₀+a₁(x-x₀)+a₂(x-x₀)²+a₃(x-x₀)³+.........
called a power series centered at x₀
where x is a variable,
x₀ is a real constant, and the
aₙ's are real constants called the coefficients of the series.
The given power series representation is f(x) = arccot(x).
we observe that f '(x)=-1/(1+x²) and find the required series by integrating the power series for -1(1+x²)
arccot(x)=∫-1/(1+x²)dx
⇒∫-(1-x²+x⁴-x⁶+....)dx
⇒C-x+1/3x³-x⁵/5+1/7x⁷-......
To find C we put x=0 and obtain C=arccot(0)=π/2
Therefore,
C=π/2-x+1/3x³-x⁵/5+1/7x⁷-.......
f(x)=π/2- ∑(-1)ⁿₓ x^2n+1/2n+1
To know more about power series representation:
https://brainly.com/question/28158010
#SPJ4
There are 5 gallons of lemonade in the container. How much is remaining in the container after Coach Miller pours g gallons for the players?
The remaining lemonade in the container after Coach Miller pours g gallons for the players is, (5 - g) gallons.
What is mean by Subtraction?Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.
We have to given that;
There are 5 gallons of lemonade in the container.
Now, Initially lemonade available in Container = 5 gallons
Here, Coach Miller pours g gallons for the players.
Hence, Lemonade remaining in Container = (5 - g) gallons
Learn more about the subtraction visit:
https://brainly.com/question/17301989
#SPJ1
It costs $4 per ride at an amusement park, plus a $10 fee to get in. Write an equation to represent the total cost (y) for any number of rides (x).
4. United Bank offers a 15-year mortgage at an APR of 4.2%. Capitol Bank offers
a 25-year mortgage at an APR of 4.5%. Marcy wants to borrow $120,000.
a. What would the monthly payment be from United Bank?
b. What would the total interest be from United Bank? Round to the nearest
ten dollars.
c. What would the monthly payment be from Capitol Bank?
d. What would the total interest be from Capitol-Bank? Round to the nearest
ten dollars.
e. Which bank has the lower total interest, and by how much?
f. What is the difference in the monthly payments?
uw.nadin
g. How many years of payments do you avoid if you decide to take out the
shorter mortgage?
Monthly payment for United bank = $1207.70, monthly payment for capitol bank =$1834.62. Total interest from United bank = $75600 and from capitol bank = $135000.
What is total interest?
Total interest is determined by the addition of all the interest payments.
what would be the monthly payment and total interest from each bank?
United bank offers mortgage at an APR of 4.2%
APR means annual percentage rate.
mortgage is offered for the period of 15 years.
initial principal amount of Marcy = $120000
we need to determine the monthly payment from United bank.
at first, we will determine the rate of interest per month.
monthly interest rate = (4.2) / (100 × 12) = 0.0035
1 year = 12 months
15 years = 15×12 = 180 months
monthly payment is calculated by the formula = [rate + (rate) / {(1+rate)∧month}⁻¹] ×principal
monthly payment = [ 0.0035 + (0.0035) / {(1+0.0035)∧180}⁻¹] ×120000
= $1207.70
from united bank monthly payment = $1207.70
Now we calculate the monthly payment from Capitol bank.
APR for capitol bank = 4.5%
number of years for which mortgage is issued = 25 years
number of months = 12×25 = 300.
monthly interest rate = (4.5) / (100×12) = 0.00375
monthly payment for capitol bank = [0.00375 + (0.00375) / {(1+0.00375)∧300}⁻¹] × 120000
= 1834.62
monthly payment from Capitol bank = $1834.62
total interest from Capitol bank = principal money × yearly interest rate × time period.
Total interest = 120000 × 4.5/100× 25
= $135000 for the Capitol bank
Total interest from United bank = principal amount × yearly interest × time period
= 120000× 4.2/100 × 15
total interest from united bank = $75600
United bank has lower total interest.
difference in monthly payment = 1834.62 - 1207.70
= 626.92 dollars
To learn more about annual percentage rate visit:
https://brainly.com/question/13358341
#SPJ1