If a negative charge is spread uniformly over the surface of the balloon, it will contract.
A spherical balloon that is initially uncharged will expand if the positive charge is spread uniformly over its surface. This is because the positive charge creates an electrostatic force that pushes the surface of the balloon away from the center, causing it to expand.
On the other hand, if a negative charge is spread uniformly over the surface of the balloon, it will contract. This is because the negative charge creates an electrostatic force that pulls the surface of the balloon towards the center, causing it to contract.
In both cases, the magnitude of the force depends on the amount of charge added to the surface and the distance between the charged particles. However, the direction of the force is determined by the sign of the charge, with a positive charge causing the balloon to expand and a negative charge causing the balloon to contract.
Therefore, If a negative charge is spread uniformly over the surface of the balloon, it will contract.
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If Zis the centroid of ∆RST, RZ= 42, ST= 74, TW = 51, and ZY= 23, find each measure.
The parallel segments are MN & LK, MP & JK and NP & JL
The side lengths are listed below and the perimeter is 84 units
How to name the parallel segmentsBy definition, parallel segments are segments that extend indefinetely and do not meet
Using the above as a guide, we have the following:
Segments MN and LK are parallelSegments MP and JK are parallelSegments NP and JL are parallelThe lengths of the segments
The midsegments are given as
MP = 17, LK = 24 and PN = 13
This means that
JK = 2 * MP
JK = 2 * 17
JK = 34
Also, we have
MN = 1/2 * LK
MN = 1/2 * 24
MN = 12
Lastly, we have
JL = 2 * PN
JL = 2 * 13
JL = 26
For the perimeter, we have
Perimeter = JK + LK + JL
Perimeter = 34 + 24 + 26
Perimeter = 84
Hence, the perimeter is 84 units
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Math on the Spot The distance between Professor Burger's house and Chris' house is 12 miles. Lila's house is on the way from Professor Burger's house to Chris' house. The distance between Lila's house and Chris' house is 5 miles. Write and solve an equation to find the distance x between Professor Burger's house and Lila's house.
The equation to find the distance between Professor Burger's house and Lila's house is x + 5 = 12 and the solution of the equation is 7 miles.
Distance between Professor Burger's house and Chris' house = 12 miles
Lila's house falls between Professor's house and Chris' house.
Distance between Lila's house and Chris' house = 5 miles
Let's assume x to be the distance between Professor Burger's house and Lila's house.
Thus the equation to solve this problem will be
x + 5 = 12
The next step will be,
x = 12 - 5
x = 7
Therefore, the distance between Professor Burger's house and Lila's house is 7 miles.
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What are the essential pieces and parts of finding probability?In order to earn full credit for this question using the following terms: outcome(s), sample space, event(s).
The probability of an event can be calculated by dividing the number of favorable outcomes by the number of possible outcomes in the sample space.
Outcome(s): An outcome is a possible result of a random experiment. For example, in a coin flip, an outcome could be either heads or tails.
Sample Space: The sample space is the set of all possible outcomes of a random experiment. In the coin flip example, the sample space would be {heads, tails}.
Event(s): An event is a subset of the sample space that includes one or more outcomes. For example, if the event is getting heads in the coin flip, the event would be {heads}. The probability of an event is the number of outcomes in the event divided by the total number of outcomes in the sample space.
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to the company's managers. suppose winco's performance scores really are normally distributed. this year, managers with scores less than 157 received c grades and those with scores of at least 355 received a grades. a. (2 points) what are the z-scores associated with the 9th and 91st percentiles from the standard normal distribution?
The performance score associated with the c grade is 157, and the performance score associated with the a grade is 355.
What is Z-score?The z-score is a numerical measurement used in statistics to indicate how many standard deviations a particular value is from the mean of a dataset. It is calculated by subtracting the mean from the data point and dividing the result by the standard deviation. The resulting number is the z-score. The z-score is a useful tool for identifying outliers in a dataset, as values with z-scores that are too high or too low can be easily identified. Z-scores can also be used for comparing data points from different datasets, as z-scores are independent of the mean and standard deviation of the dataset. Z-scores can also be used for comparing data points from different datasets, as z-scores are independent of the mean and standard deviation of the dataset. This makes them ideal for normalizing data from different sources or for comparing data from different time periods or from different locations.
The z-score associated with the 9th percentile from the standard normal distribution is -1.28, and the z-score associated with the 91st percentile is 1.28.
b. (2 points) what are the performance scores associated with the c grade and the a grade?
The performance score associated with the c grade is 157, and the performance score associated with the a grade is 355.
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please help me!!! i need to pass this assignment! Find P(4) and P(2).
Answer:
1/4
Step-by-step explanation:
The probability of the spinner landing on any one number = 1/8 since there are 8 possible outcomes and we are looking for the probability of one outcome out of those
So P(2) = P(4) = 1/8
P(4) and P(2) is the sum of these two probabilities = 1/8 + 1/8 = 2/8 = 1/4
write down the bearing in both compass bearing and three figure bearing
The compass bearing measure is N60°E and the three figure bearing measure is 060°
Reading the measurement of a bearingFrom the question, we ae to write the measurement of the bearing in both compass bearing and three figure bearing
Compass bearing
The line is between the North and E poles. The line measures 60°. Therefore, N60°E.
Hence, the compass bearing measure is N60°E
Three figure bearing
Reading from the North pole in the clockwise direction, the bearing of the line is 60°.
Hence, the three figure measure is 060°
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given 2 3 2 3 ½sij¼ 4 5 and ½ai¼ 1 102 012 4 2 5; 303 3 evaluate (a) sii, (b) sijsij, (c) sjisji, (d) sjkskj, (e) amam, (f) smnaman, and (g) snmaman.
The evaluation of (a) sii, (b) sijsij, (c) sjisji, (d) sjkskj, (e) amam, (f) smnaman, and (g) snmaman was done by using the corresponding formulas and the given values. The results were 3, 6, 6, 6, 2, 6, and 24 respectively.
To evaluate (a) sii, we will use the formula sii = ai + bi. In this case, ai = 1 and bi = 2, so sii = 1 + 2 = 3.
To evaluate (b) sijsij, we will use the formula sijsij = ai × bi. In this case, ai = 2 and bi = 3, so sijsij = 2 × 3 = 6.
To evaluate (c) sjisji, we will use the formula sjisji = aj × bj. In this case, aj = 2 and bj = 3, so sjisji = 2 × 3 = 6.
To evaluate (d) sjkskj, we will use the formula sjkskj = ak × bk. In this case, ak = 3 and bk = 2, so sjkskj = 3 × 2 = 6.
To evaluate (e) amam, we will use the formula amam = ai × aj. In this case, ai = 1 and aj = 2, so amam = 1 × 2 = 2.
To evaluate (f) smnaman, we will use the formula smnaman = ai × aj × ak. In this case, ai = 1, aj = 2, and ak = 3, so smnaman = 1 × 2 × 3 = 6.
To evaluate (g) smnaman, we will use the formula smnaman = ai × aj × ak × bm. In this case, ai = 1, aj = 2, ak = 3, and bm = 4, so smnaman = 1 × 2 × 3 × 4 = 24.
The evaluation of (a) sii, (b) sijsij, (c) sjisji, (d) sjkskj, (e) amam, (f) smnaman, and (g) snmaman was done by using the corresponding formulas and the given values. The results were 3, 6, 6, 6, 2, 6, and 24 respectively.
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g this model is a special case of the weibull distribution; it could be described as one of the other continuous random variables we discussed in class. what other distribution can be used to describe it, specifically (include name of distribution and any parameter values)? what is the expression for the probability density function?
Weibull distribution is a continuous distribution related to the shape of parameter where k∈(0 , ∞) with g distribution : g(t) = 1- exp ( -t^k) , t ∈[0, ∞).
Other distribution is probability density function defined as
g(t) = kt^( k -1) exp ( -t^k) , t ∈ (0, ∞).
Weibull distribution is a continuous random variable distribution.It is based on the parameter of shape where k∈(0 , ∞).Defined as g distribution : g(t) = 1- exp ( -t^k) , t ∈[0, ∞).Name of other distribution related to Weibull distribution is probability density function.Expression used to defined probability density function is g(t) = kt^( k -1) exp ( -t^k) , t ∈ (0, ∞).Therefore, Weibull distribution is defined on basis of shape parameter k,
g(t) = 1- exp ( -t^k) , t ∈[0, ∞) and other distribution includes probability density function is g(t) = kt^( k -1) exp ( -t^k) , t ∈ (0, ∞).
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After 16 years in an account with a 6.2% annual interest rate compounded continuously, an investment is worth a total of $58,226.31. What is the value of the principal investment? Round the answer to the nearest penny.
The value of the principal investment is $21,597.30. The solution has been obtained by using the concept of compound interest.
What is compound interest?
When interest is calculated, both the principal and the interest that has accumulated over the previous period are used. Compound interest accounts for the principal when calculating the interest for the subsequent month, as opposed to simple interest, which does not. In algebra, the letter C.I. is frequently used to denote compound interest.
We are given that after 16 years in an account with a 6.2% annual interest rate compounded continuously, an investment is worth a total of $58,226.31.
This means that
P(t) = $58,226.31
t = 16 years
r = 6.2%
We know that formula for continuous compounding interest is
[tex]P(t) = P_{0} e^{rt}[/tex]
So, using this, we get
⇒58,226.31 = Pe^(0.062*16)
⇒58,226.31 = Pe^(0.992)
⇒58,226.31 = P*2.696
⇒P = $21,597.30
Hence, the value of the principal investment is $21,597.30.
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What is the area of the kite?
A kite with both diagonals is shown. The diagonals intersect each other so that the shorter diagonal is split into parts that are 2 feet and 2 feet and the longer diagonal is split into parts that are 10 feet and 20 feet.
please show work
the area of the given kite will be 60 feet².
What is area of Kite?
A polygon with four vertices and four sides enclosing four angles is called a quadrilateral. A unique quadrilateral known as the kite has successive sides that are all congruent, but the opposite sides are not. A rhombus is a kite that has four congruent sides. A kite's diagonals are perpendicular. The area of a kite is calculated as half of the diagonal product, which is the same as the area of a rhombus. The formula: can be used to express the area of a kite.
Area of Kite = 1/2*D1 * D2
D1 = long diagonal of kite
D2 = short diagonal of kite
The diagonals intersect each other so that the shorter diagonal is split into parts that are 2 feet and 2 feet and the longer diagonal is split into parts that are 10 feet and 20 feet.
So Area = 1/2 * 4 * 30 = 60 feet²
Hence the area of the given kite will be 60 feet².
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How to solve 3x+4y=10, 2x+5y=9 in using graphical method.
Answer:(-2,4) (6,-2)
Step-by-step explanation: 1.We solve the equation with x = -2 and get y = 4 , (-2,4) which is a coordinate
2. we solve the equation with x=6 and gets y= -2 (6,-2) is a coordinate
Mark these two coordinates to get a line in the graph!
(a) How many vectors (x1, x2, x3, . . . , xn) are there for which each xi is either 0 or 1 andx1 + x2 + · · · + xn = k.(b) Do the same problem as before but under the condition thatx1 + x2 + · · · + xn ≥ k.
(a) Each xi in the vector (x1, x2, ..., xn) can be either 0 or 1.
Therefore, there are 2 possibilities for each xi.
The number of vectors that can be formed by combining these values is equal to the number of combinations of 2 possibilities, taken n times.
The number of vectors (x1, x2 . . ., xn) such that each xi is either 0 or 1 and n where k is a non-negative integer less than or equal to n is 2^n.
the same problem as before but under the condition thatx1 + x2 + · · · + xn ≥ k,
This is equivalent to 2^n. For example, if n = 2, then there are 2 possibilities for x1 (either 0 or 1) and 2 possibilities for x2 (either 0 or 1). The total number of vectors that can be formed is 2 * 2 = 2^2 = 4. In general, the number of vectors that can be formed is equal to 2^n.
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The complete question is :-
determine the number of vectors (x1, x2 . . ., xn) such that each xi is either 0 or 1 and n where k is a non-negative integer less than or equal to n.
Sofia has $4.35 in quarters and nickels in her pocket. She has 3 more nickels than quarters. Write an equation that can be used to determine the number of quarters, x , Sofia has.
Answer:
Let's say x is the number of quarters. Then the number of nickels is x + 3.
The total value of the quarters is 0.25x, and the total value of the nickels is 0.05(x + 3).
The total value of both types of coins is 4.35:
0.25x + 0.05(x + 3) = 4.35
0.25x + 0.05x + 0.15 = 4.35
0.3x + 0.15 = 4.35
0.3x = 4.2
x = 14
So Sofia has 14 quarters and 17 nickels.
Answer:
.25q + .05(q - 3) = 4.35
Step-by-step explanation:
Let q = the number of quarters
Let n = the number of nickels
.25q + .05n = 4.35
n = q- 3
Substitute q - 3 for n
.25q + .05(q - 3) = 4.35
20 newspapers in 4 piles = 15 newspapers in
piles
The number of piles when the newspaper is 15 will be 3.
What are ratio and proportion?A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.
20 newspapers in 4 piles.
We know that the ratio of the newspaper to pile is constant. Then 15 newspapers in piles will be given as,
15 / x = 20 / 4
15 / x = 5
x = 15 / 5
x = 3
The number of piles when the newspaper is 15 will be 3.
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Use the Binomial Theorem to expand (a+b)^15. You can use your calculator to determine the coefficient. Show the step.
a box contains 10 identical markers (except in colors): 5 black, 3 blue and 2 red. three different markers are selected. find the probability of selecting at least one red marker.
The probability of selecting at least one red marker probability = [tex]\frac{1}{5}[/tex]
A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.
Given that,
In the box contains ,
Black markers are = 5
Blue markers are = 3
Red markers are = 2
The given scenario will not affect the required probability as the selection of the second one is a case of future.
We need to find the probability of the first marker is red.
The probability is,
Probability = [tex]\frac{red marker}{total markers}[/tex]
Total markers = 5 + 3 +2
= 10
Probability = [tex]\frac{2}{10}[/tex]
Probability = [tex]\frac{1}{5}[/tex]
The probability of selecting at least one red marker probability = [tex]\frac{1}{5}[/tex]
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the temperature outside was 88 degrees fahrenheit. what would be the temperature is it is increased by %25
Answer:
110.0%
Step-by-step explanation:
25% of 88 is 22. 88+22=110 Fahrenheit
to get this you divide 88 by 100 which is 0.88, then multiply by 25 which gets you 22.
Expand this equation to write an identity: (a-b)^3
The equation using the identity rule is a^3 - 3a^2b + 3ab^2 - b^3
How to expand the equation using the identity ruleThe equation (a-b)^3 can be expanded using the binomial theorem, where the variables are the two numbers (a and b),
From the question, we have the following parameters that can be used in our computation:
(a-b)^3
When expanded, we have
a^3 - 3a^2b + 3ab^2 - b^3
Hence, the expansion is a^3 - 3a^2b + 3ab^2 - b^3
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32,16,8
find the 9th term
1/8 is the 9th term in sequence .
What does sequence look like in math?
A sequence is a collection of numbers in a particular order. To go forward in the defined pattern, three dots are shown. A phrase is used to refer to each number in the series.
One is the first word, three is the second, five is the third, and so on, in the series 1, 3, 5, 7, 9,... There are groups of numbers called number sequences that adhere to a pattern or norm. Arithmetic sequences are those in which the rule is to add or remove a number each time. A geometric sequence is one where the rule is to multiply or divide by a specific amount each time. A word is used to describe each number in a sequence.
a₉ = 1/8
the general term through the pattern aₙ = 32(1/2)ⁿ⁻¹
Substitute and calculate aₙ = 1/8
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Assume that you graph lines f and g on the same coordinate plane and they intersect at point (4, 5). Which of the following statements is NOT true.
Assuming you graph lines f and g on the same coordinate plane and they intersect at point (4, 5), a statement which is not true include the following: D. Other points that are on line f are also solutions of the system.
What is a point of intersection?In Mathematics, a point of intersection can be defined as the location on a graph where two (2) lines intersect or cross each other, which is primarily represented as an ordered pair containing the point that corresponds to the x-coordinate (x-axis) and y-coordinate (y-axis) on a cartesian coordinate.
Based on the graph of the lines representing the system of equations, we can reasonably and logically deduce that the correct solution set lies in Quadrant I and it is denoted by the point of intersection of both the x-axis and y-axis, which is given by the ordered pair (4, 5).
In conclusion, the ordered pair (4, 5) is a solution to the system of equations and it is located on both lines f and g.
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solve for y please: 3/y-4 = 4/5
Answer:
7.75
Step-by-step explanation:
Multiply y-4 both sides
(y-4) 3/y-4 =4/5(y-4)
3=4/5(y-4)
3/(4/5)=y-4
(3/(4/5))+4
Put in calculator
y=31/4
y=7.75
Answer:
y = 7.75
Step-by-step explanation:
3 = 4/5 x y-4
3x5 = 4 x y-4
15 = 4y-16
15+16 = 4y
31/4 = y
y = 7.75
Find the circumference and the area of a circle with a radius of 9mm.
Write your answers in terms of pi, and be sure to include the correct units in your answers.
suppose we roll a red and a green die. let a = ""the red die shows a 2 or a 5"" and b = ""the sum of the two dice is at least 7."" are a and b independent?
we roll a red and a green die. let a = ""the red die shows a 2 or a 5"" and b = ""the sum of the two dice is at least 7."" are a and b independent.
Probability plays a vital role in all fields like the economy, medicine, etc. It intends to forecast the events that will be happening in the future. So its values never come in negative. It has two main rules.
Rule of multiplication
Rule of addition.
The green and red dice are rolling,
the sample space = {(1,1)(1,2)......(1,6) (2,1).....(2,6)(3,1)....(3,6).......(6,6)}
let A be the event of the red shown a 2or a or 5
let B be the event of the sum of the two dice is at most 7.
The probability of the red die shown as a 2 or a 5
total outcome =36
favorable case =24
the probablity=24/36=4/6=2/3
let B be the event of the sum of the two dice is at most 7.
p(B)=21/36=0.5833
p(AnB)=13/36=0.3611
P(A)P(B)=0.3888
Hence a and b are independent.
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Find CE.. please help asap
The length of side CE is 5/6 units
How to determine the length CEFrom the question, we have the following parameters that can be used in our computation:
The triangle
On the triangle, we have the following ratio
x - 2 : 2 = x + 1 : 8
Express as fraction
(x - 2)/x = (x + 1)/8
So, we have
8x - 16 = 2x + 1
Evaluate the like terms
6x = 17
So, we have
x = 17/6
The value of CE is
CE = x - 2
CE = 17/6 - 2
So, we have
CE = 5/6
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a jar of crunchy peanut butter contains 1.41 kg of peanut butter. if you use 8.0 % of the peanut butter for a sandwich, how many ounces of peanut butter did you take out of the container? express your answer to two significant figures.
A kilogram is a unit of mass in the metric system and is often used to measure the weight of food items. One kilogram is equivalent to 35.27 ounces. To determine how many ounces of peanut butter you used for your sandwich, you need to convert the mass in kilograms to ounces.
In this case, the jar contains 1.41 kg of peanut butter. To find the amount of peanut butter you used, you multiply the total amount by the percentage of the peanut butter you used. In this case, 8.0% of 1.41 kg is 0.11 kg of peanut butter.
Finally, you convert the 0.11 kg of peanut butter to ounces using the conversion factor of 35.27 ounces per kilogram. So 0.11 kg * 35.27 oz/kg = 3.88 ounces of peanut butter.
This answer is expressed to two significant figures because the original mass of the peanut butter is given to two significant figures (1.41 kg) and the percentage of peanut butter used is also given to two significant figures (8.0%).
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a van is travelling due east at a speed of 28 miles per hour. if the van started off 154 miles directly north of the city of smithville, how fast is the distance between the van and smithville changing when the van has travelled 38 miles? (do not include units in your answer, and round to the nearest hundredth.)
The distance between the van and Smithville is changing at a rate of 40.83 miles per hour.
To calculate how fast the distance between the van and Smithville is changing, we can use the following steps:
Calculate the total distance between the van and Smithville by subtracting the distance the van has travelled (38 miles) from the total distance the van is from Smithville (154 miles): 154 - 38 = 116 miles.Calculate the rate of change by dividing the total distance (116 miles) by the amount of time it has taken the van to travel that distance (38 miles/28 miles per hour = 1.36 hours): 116/1.36 = 85.29 miles per hour.Round the rate of change to the nearest hundredth: 85.29 rounded is 85.30, which is 40.83 miles per hour.Learn more about mathematics:
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The tape diagram shows that Rita answered 14 questions correctly on a post-test. Rita learned a lot in this unit, so that was 350\%350%350, percent as many questions as she answered correctly in the pre-test.
A tape diagram with one tape split into 7 equal parts. All 7 parts are shaded. A curved brace above the whole tape is labeled 14. A curved brace below the whole tape is labeled 350 percent.
A tape diagram with one tape split into 7 equal parts. All 7 parts are shaded. A curved brace above the whole tape is labeled 14. A curved brace below the whole tape is labeled 350 percent.
Complete the table to show different percentages of the questions Rita answered correctly on the pre-test.
Number of questions correct Percentage
350\%350%350, percent of the correct pre-test questions
50\%50%50, percent of the correct pre-test questions
100\%100%100, percent of the correct pre-test questions
350% of the correct pre-test questions - 7
50% of the correct pre-test questions - 1
100% of the correct pre-test questions - 2
What is Tape Diagram?A diagram that resembles a piece of tape that is used to show how numbers relate to one another. Also known as length model, fraction strip, bar model, and strip diagrams.
Given:
There are 7 units to represents 14 Questions and 350%.
So, 14/7 = 2 and 350/ 7= 50%
one unit represent 2 questions and 50%.
and, 2 units represents 4 questions and 100%.
then, 350% of the correct pre-test questions - 7
50% of the correct pre-test questions - 1
100% of the correct pre-test questions - 2
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A stock valued at 100$ decreases by 2% each year
Answer:
2%
Step-by-step explanation:
how to write an expression for csc[arccos(x -1)]
An algebraic expression which is equivalent to the expression
csc[arccos(x -1)] is equal to 1 / √2x - x² .
Let us consider the expression arccos(x - 1 ) = y .
arccos(x - 1 ) = y
⇒ cos y = (x - 1 ) ___( 1 )
Now the required algebraic expression is equivalent to :
csc[arccos(x -1)]
= csc y
= ( 1 / sin y )
= 1 / √ 1 - cos²y __(2)
Substitute the value of cosy from (1 ) in the expression ( 2 ) we get,
= 1 / √ 1 - ( x - 1 )²
= 1 / √ 1 - ( x² -2x + 1 )
= 1 / √ 1 - x² + 2x - 1
= 1 / √ 2x - x²
Therefore, the expression csc[arccos(x -1)] is equivalent to an algebraic expression is 1 / √ 2x - x².
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the volume of a container is found to be 38.5 in3. what is the volume in units of cm3?
The volume of a container is found to be 38.5 in³. Its volume in units of cm³ will be 630.902 cm³.
Unit conversion is a process with multiple steps involving multiplication or division by a numerical factor, particularly a conversion factor. The procedure may also demand the selection of the correct number of substantial digits and rounding. Different units of conversion are used to calculate different parameters.
We convert the units of any quantity to understand better. For example, the length of a table is measured in inches; on the other hand, the length of a garden is measured in yards to make it simple to comprehend. We cannot calculate the length of a finger in miles.
To create a formula to convert 38.49 in³ to cm³, we start with the fact that 1 inch is 2.54 centimetres, which means that you multiply inches by 2.54 to get centimetres. We can therefore make the following equation:
inches × 2.54 = centimeters
(inches × 2.54)³ = centimeters³
inches³ × 16.387064 = centimeters³
in³ × 16.387064 = cm³
Now that we have the in³ to cm³ formula, we can calculate and convert 38.5 in³ to cm³. Here is 38.5 in³ converted to cm³, along with the math and the formula:
= in³ × 16.387064
= 38.5 × 16.387064
= 630.902 cm³
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