Answers
Answer:
x/(1-x)
Step-by-step explanation:
We start by induction. The first 2 terms are x/(1-x^2) and x^2/(1-x^4), respectively. When we add them together using special factorizations, we get: (x^3+x^2+x)/(1-x^4). We quickly realize that the numerator is a geometric series. Applying the following formula, we can simplify our expression to (x^4-x)/(1-x^4)(x-1). Now, we introduce our 3rd term, and add that to our sum. That gets us: (x^7+x^6+...+x)/(1-x^8). This is another Geometric series, and we apply the exact same formula, for this new fraction: (x^8-x)/(1-x^8)(x-1). We realize this is a pattern, and we can utilize this pattern for the sum of the first n terms.
We look at the exponents. For the first 3 terms, the Degree is 8, for the first 2 terms, the Degree is 4. We take note that this looks like x^2^n.
Using that our general formula IS: (attached to this text) (x^2^n-x)/(1-x^2^n)(x-1). Now, when 0<x<1 and n approaches infinity, what do we get?
all terms x^2^n are so small, it's basically redundant, and can be crossed off. This leaves us with -x/(x-1), which can be simplified to x/(1-x).
Related Questions
PLEASE HELP ANSWERING THIS QUESTION QUICKLY! THIS QUESTION IS SO CONFUSED!
Based on the graph above, estimate to one decimal place the average rate of change from x=1 to x=3 (Blank).
Explain!
Thanks!
Answers
The average rate of change from x=1 to x=3 is -1
How to find the average rate of change from x=1 to x=3?On the given graph, we have the following function values
f(1) = 6
f(3) = 4
The average rate of change from x=1 to x=3 is then calculated as
Rate = [f(3) - f(1)]/[3 - 1]
This gives
Rate = [4 - 6]/[3 - 1]
Evaluate
Rate = -1
Hence, the average rate of change from x=1 to x=3 is -1
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Positive multiples of 4
Answers
Answer:
4, 8, 12, 16, 20, 24, 28, 32, 36, and 40 are some multiples of 4 that are positive.
help help help.........
Answers
Answer:
The answer is A
Domain means look at the x-axis. So you’re looking at it from left to right and finding the smallest number to the highest number on the x-axis. In this case, the smallest number the graph falls on is -2 and it stops at 4.
Remember: a filled in circle means “greater than or equal to”
. If C lies between A and B on AB, then AC + CB = AB. What can you logically conclude about AB?
Answers
Answer: AB is twice the size of AC and twice the size of CB
Step-by-step explanation: "Lies between" means that it's in the middle. C is in the middle of A and B. A to C would be the same distance of C to B because C seperates the segments into 2 equal halves. AB is the whole segment including C, you could do AC + AC if you substituted it for the lengths and you would still get AB
[tex]f(x)=x^{2} +2x-24[/tex]
Answers
(X+6)(x-4)
Hope this helps
Is 7 a solution of 5x - 3 = 12 ? Justify your answer
Answers
Answer:
Step-by-step explanation:
NO x=3
Use the segment addition postulate to solve for the length of BC, if AC = 16, BC = x + 11, and AB = 3x-7.
Answers
In the lab, Miguel has two solutions that contain alcohol and is mixing them with each other. He uses twice as much Solution A as Solution B. Solution A is 12% alcohol and Solution B is 16% alcohol. How many milliliters of Solution B does he use, if the resulting mixture has 120 milliliters of pure alcohol? Number of milliliters of Solution B: X Ś
Answers
Miguel uses 300 mL Solution B and 600 mL Solution A.
What is termed as the percentages?A percentage is a relative value that symbolizes the hundredth part of any quantity.One percent (symbolized 1%) is one hundredth part; thereby, 100 percent symbolizes the entire amount as well as 200 percent clarifies twice the given amount.Let x represent the amount of Solution B used.
2x = the quantity of Solution A used.
Solution A is alcohol = 12%.
Solution B is alcohol = 16%.
Given that 12% = 0.12 and 16% = 0.16, we can calculate the following equation:
2x(0.12) + x(0.16) = 120 (Recall that pure alcohol has a concentration of 100% = 1.00.)
0.24x + 0.16x = 120
0.40x = 120
x = 300 mL
Thus, Miguel makes use of 300 mL of Solution B and 2(300) = 600 mL of Solution A.
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Solve, 3|x−4|−6≤9.
Graph the solution on the number line.
Answers
Answer:
Step-by-step explanation:
Tracey paid $145 for an item that was originally priced at $360. What percent of the original price did Tracey pay?
Round your percentage answer to two decimal places.
Do NOT include a
%
symbol with your answer.
Answers
Answer:
Tracy paid 40.28 percent of the total price.
Wayne recorded the eye colors of the people who have already signed up for a lecture on genetics.
green 2
blue 30
brown 38
What is the experimental probability that the next person to sign up will have blue eyes?
Write your answer as a fraction or whole number.
P(blue)=
Answers
The experimental probability of next person to have Blue eyes is 3/7.
Probability :Probability is the branch of mathematics that studies the possible outcomes of given events together with the outcomes' relative likelihoods and distributions.
It is based on the possible chances of something to happen.
Probability (P) = Number of a Favourable outcome {n (E)} / Total number of outcomes {n (S)}
Simply, P = n (E) / n (S)
Given, Eye colors of the people
Green = 2
Blue = 30
Brown = 38
To find the probability of next person to have blue eyes, first we will add the given eye colors
Total number of Eye Colors = 2 + 30 + 38 = 70
Number of Blue Eyes = 30
Then, Probability to have blue eyes P(blue) = Number of Blue Eyes / Total number of Eye Colors
= 30/70
= 3/7
So, there is 3/7 chances to next person to have blue eyes.
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Answer:
3/7
Step-by-step explanation:
Question
Shonda jogs 5 miles per hour.
Graph the relationship between the number of hours Shonda jogs and the total number of miles jogged.
Answers
here hope this helps u
The total weight of 15 boxes is 45 pounds. How muchwould 40 boxes weigh
Answers
15/45 = 40 x 3 = 120 pounds
Answer:
40 boxes would weigh 120 pounds. nice
15/45 = 40 x 3 = 120 pounds
Step-by-step explanation:
:)
WILL GIVE BRAINIST.
1. The soccer team is making pizzas for a fundraiser. They put1/4 of a pound of cheese on each pizza. If they have 12 one-pound packages of cheese, how many pizzas can they make? pizzas ?
2. Dan purchased 3 ½ yards of mulch for his garden. Mulch costs $25 a yard. How much did Dan pay for his mulch? $
3. Mr. Hamilton owns 2 ¾ acres of land. He plans to buy 1 and 1/3 more acres. How many acres will he own? Write your answer as an improper fraction. acres
Answers
2. $25 per yard and there’s 3.5 yards, 25 x 3.5 = $87.50 spent on mulch
3. 2.75 as an improper fraction is 11/4 and 1.66 is 4/3, to get the same denominator you multiply one by 3 and the other by 4 and get 33/12 and 16/12, (33/12)+(16/12)=49/12 acres
wall has an
area
tim
9 123m2
of faint will couet 14 m²
Hattie needs to work out how
of paints will need to
many
use
A
A
المعلن
tin's
buy.
estimation to work out how many ting
needs.
Answers
Find the average rate of change of f (x)=x-2√x on the interval [1, 9].
Answers
The average rate of change of f(x) = x - 2√x on the interval [1, 9] is 1/2.
What is average rate of change?It is a measure of how much the function changed per unit, on average, over that interval.
We have,
f(x) = x - 2√x
On the interval [1,9].
[1, 9] = [a, b]
The average rate of change:
= f(b) - f(a) / b - a
= f(9) - f(1) / 9 - 1
= [(9 - 2√9) - (1 - 2√1)] / 8
= [ (9 - 6) - (1 - 2) ] / 8
= (3 + 1) / 8
= 4 / 8
= 1/2
Thus the average rate of change of f(x) = x - 2√x on the interval [1, 9] is 1/2.
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how do you solve this problem
chan is filling a box with 1 inch cubes. he filled the bottom layer with 5x1 inch cubes long, and 4x1 inch cubes wide. The box is 6 inches tall.
Answers
Answer:
120 cubes will fill the box
Step-by-step explanation:
You want to know the number of 1-inch cubes it takes to fill a box that is 5 cubes long, 4 cubes wide, and 6 inches tall.
LayerTo cover the bottom of the box, Chan needs to make an array of cubes that has 4 rows with 5 cubes in each row. That layer will have ...
4 × 5 = 20 . . . . cubes per layer
VolumeEach layer occupies 1 inch of height, and the box is 6 inches high. The volume of the box will be filled with six of these layers. That will take this many cubes:
(6 layers) × (20 cubes/layer) = 6 × 20 cubes = 120 cubes
Chan will need 120 cubes to fill the box.
2x + 5 < -3 or 6x - 5 > 7
Answers
Answer: 2x-5/3=7
Tiger shows you, step by step, how to Isolate x (Or y or z) in a formula
PLEASE HELPPPP
In a particular year, a total of 60,831 students studied in two of the most popular host countries when traveling abroad. If 5981 more students studied in the most popular host country than in the
second most popular host country, find how many students studied abroad in each country.
There were …..
students who studied abroad in the most popular host country.
Answers
Answer:
66812
Step-by-step explanation:
60831+5981=66812
A group of 15 students were assigned a novel to read during class. The data below represents the number of pages each student read.8, 8, 10, 11, 12, 12, 13, 14, 16, 16, 18, 18, 18, 20, 24Which of the following box plots correctly summarizes the data?
Answers
The box plots that correctly summarize the data is the option B from the image
This is further explained below.
What are box plots?Generally, a straightforward method of depicting statistical information on a plot, in which a rectangle is used to represent the second and third quartiles of the data, and in which the median value is typically shown by a vertical line drawn within the rectangle.
On each side of the rectangle, there are two horizontal lines that represent the lower quartile and the higher quartile.
A boxplot is a graphical representation of the distribution of data that is based on a summary of five numbers and follows a defined format.
In conclusion, The box plot in the illustration with choice B accurately summarizes the data.
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CQ
Image attached
A group of 15 students were assigned a novel to read during class. The data below represents the number of pages each student read.
8, 8, 10, 11, 12, 12, 13, 14, 16, 16, 18, 18, 18, 20, 24
Which of the following box plots correctly summarizes the data?
A
B.
C.
D
the difference between nine times a number and one more than five times the number
Answers
The required expression for the given statement is 4x + 1.
What is an expression?An expression is a number, or a variable, or a combination of numbers and variables and operation symbols.
The given statement is,
the difference between nine times a number and one more than five times the number
Let x be the number.
Thus, we have
nine times a number = 9x
one more than five times the number = 1 - 5x
Thus, the numerical expression we get is
9x + (1 - 5x)
Expanding we get
9x + 1 - 5x
Solving we get
4x + 1
this is the required expression
Thus, the required expression for the given statement is 4x + 1.
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wats the answer help mee
Answers
Need an explanation?
Answer:
6
Step-by-step explanation:
The diameter is half of the given radius, therefore, split the radius in half.
[tex]\frac{12\:in^2}{2} = 6\:in^2[/tex]
help me if you can please
Answers
Answer:
f(0) = 5, f(7) = 1328, f(-5) = -460
Step-by-step explanation:
[tex]f(x) = 4x^3 - 7x + 5[/tex]
We should substitute the values in the brackets into the equation to find the function's value at that x point.
[tex]f(0) = 4(0)^3 - 7(0) + 5\\\to f(0) = 5[/tex]
[tex]f(7) = 4(7)^3 - 7 \times 7 + 5\\\to f(7) = 4 \times 343 - 49 + 5\\\to f(7) = 1328[/tex]
[tex]f(-5) = 4(-5)^3 - 7(-5) + 5\\\to f(-5) = 4 \times -125 + 35 + 5\\\to f(-5) = -460[/tex]
A parcel of land measures 4 x 105 acres. If the parcel is divided into
five equally sized parts, how many acres is each part?
Answers
Answer: the answer would be 0.8 x 21 acres of land
Step-by-step explanation:hope it helps, brainliest? i could really use it
4-5 what are the answers!! please give correct answers ill give brainlist!!!!
Answers
Answer:
4a.) 0.0005 = 5 x 10 to the exponent -4
4b.) 0.0025 = 2.5 x 10 to the exponent -3
5a.) 2 x 10 to the exponent -2 = 0.02
5b.) 16 x 10 to the exponent -4 = 0.0016
Tip:
The number being multiplied has to be less than or equal to 10. Count the places the decimal point moves from the end of the number to the number in the original equation.
Example: 0.05 = 5 x 10 to the exponent -2
0.05 has 2 spaces for the decimal point to move up to 5 going right. We use a negative decimal because 0.05 is less than 5. Here is an example where the exponent is positive:
5000 = 5 x 10 to the exponent 3
5000 has 3 spaces for the decimal point to move down to 5 going left.
What is the slope of the line represented by the equation y = x - 3?
O-3
--3--
45
O3
Answers
Answer:
Slope is 1
Step-by-step explanation:
From the general linear equation:
[tex]{ \rm{y = mx + c}}[/tex]
m is the slope
Comparing with the equation given:
[tex]{ \rm{y = { \green{1}}x - 3}}[/tex]
Hey, could somebody help me out with this?
-----------------------------------------------------------------
Upload the worksheet with your constructions below.
Answers
A girl owns 1 pairs of pants, 3 shirts, 4 ties, and 3 jackets. How many different outfits can the girl wear to school if each outfit must consist of one of each item?
Answers
Answer: She can wear 3 outfits to school because
Step-by-step explanation: She is able to wear the pants multiple times so she can have 1 pants 1 shirt 1 tie and 1 jacket for three days
Solve the linear equation 7x+4^2=12x-8
Answers
Answer:
x = 24/5
Step-by-step explanation:
6.2 HELPPPPPPPP!!!!!!!!!!!!!!!!!!!!
Graph the image of the figure using the transformation given.
Captionless Image
LAST 3 PICS ARE THE OPTIONS
Answers
Answer: It's the third answer choice.
Step-by-step explanation:
It is the only one that LOOKS like it's reflected over the y-axis (i check the math as well)