The interval on which f(x) is increasing is (-∞, -1) and (3, ∞).
To find the interval on which the function f(x) = x³ - x² - 9x + 3 is increasing, we need to determine where the derivative of the function is positive.
First, let's find the derivative of f(x):
f'(x) = 3x² - 6x - 9
3x² - 6x - 9 = 0
3(x - 3)(x + 1) = 0
x - 3 = 0 or x + 1 = 0
x = 3 or x = -1
These are the critical points of the function.
Let's test a value from each interval:
For x < -1, let's use x = -2:
f'(-2) = 3(-2)² - 6(-2) - 9 = 12 + 12 - 9 = 15 > 0
For -1 < x < 3, let's use x = 0:
f'(0) = 3(0)² - 6(0) - 9 = -9 < 0
For x > 3, let's use x = 4:
f'(4) = 3(4)² - 6(4) - 9 = 12 - 24 - 9 = -21 < 0
From these test values, we can see that f(x) is increasing on the interval (-∞, -1) and (3, ∞).
Therefore, the interval on which f(x) is increasing is (-∞, -1) and (3, ∞).
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2[tex]x^{2} =-8[/tex]
[tex]2x^2=-8\\x^2=-4[/tex]
No real solutions.
Complex solutions:
[tex]x=\sqrt{-4} \vee x=-\sqrt{-4}\\x=2i \vee x=-2i[/tex]
A rectangles width is 1/2 of its length. Its area is 338 square centimeters. What are its dimensions?
The width of the rectangle is 13 cm and the dimension is 26 cm x 13 cm
Given data ,
Let the length be L and width be W
Now , the width is 1/2 of the length, so we can write:
W = (1/2)L
The area of a rectangle is given by the formula:
Area = Length x Width
Given that the area is 338 square centimeters, we can write:
338 = L × W
Substituting W with (1/2)L, we have:
338 = L × (1/2)L
To solve this equation, we can multiply both sides by 2 to eliminate the fraction:
676 = L²
Taking the square root of both sides, we find:
L = √676
L = 26
So the length of the rectangle is 26 centimeters.
Substituting this value back into the equation for the width, we have:
W = (1/2)L
W = (1/2)(26)
W = 13
Hence , the dimensions of the rectangle are length = 26 centimeters and width = 13 centimeters
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AB =
Round your answer to the nearest hundredth.
Answer:
hello
the answer is:
Sin B = CA/AB ----> Sin 65° = 5/AB ----> 0.906 = 5/AB
----> AB = 5.51
In a survey of 2267 adults in a recent year, 1220 say they have made a New Year's resolution. Construct 90% and 95% confidence intervals for the population proportion.
The 90% confidence interval for the population proportion of adults who made a New Year's resolution is approximately 0.523 to 0.554, while the 95% confidence interval is approximately 0.517 to 0.559.
To construct 90% and 95% confidence intervals for the population proportion based on the survey results of 1220 adults who made a New Year's resolution out of a total of 2267 adults, we can use the formula for confidence intervals for a proportion.
Calculate the sample proportion:
The sample proportion is the number of individuals who made a New Year's resolution divided by the total sample size.
Sample proportion [tex]\hat{p}[/tex] = 1220 / 2267 = 0.5386
Determine the standard error:
The standard error measures the variability of the sample proportion and is calculated using the formula:
Standard error[tex](SE) = \sqrt{((\hat{p } \times (1 - \hat{p})) / n) }[/tex]
where n is the sample size.
Calculate the margin of error:
The margin of error represents the range within which the true population proportion is likely to fall.
It depends on the desired level of confidence and is calculated by multiplying the standard error by the appropriate critical value from the standard normal distribution.
For a 90% confidence interval, the critical value is 1.645.
For a 95% confidence interval, the critical value is 1.96.
Margin of error = Critical value [tex]\times[/tex] Standard error
Construct the confidence intervals:
The confidence interval is calculated by adding and subtracting the margin of error from the sample proportion.
For the 90% confidence interval: [tex]\hat{p}[/tex] ± Margin of error
For the 95% confidence interval: [tex]\hat{p}[/tex] ± Margin of error
Using these steps and the provided information, we can construct the confidence intervals for the population proportion.
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With a full tank of gas, you can drive 455 miles and your car can go 24 miles per gallon. Write an equation to model this situation (use m for miles you can drive and g for gallons used from the tank).
Given the functions listed,
a) Determine the rule for (f - g)(x)
b) Evaluate (f – g)(-2)
f(x)=2x^2-3x+4 & g(x) = 8x +7
The rule for (f - g)(x) is (f - g)(x) = 2x² - 11x - 3 and the value of (f - g)(-2) is 27
Determining the rule for (f - g)(x)From the question, we have the following parameters that can be used in our computation:
f(x) = 2x² - 3x + 4
g(x) = 8x + 7
The rule for (f - g)(x) is calculated as
(f - g)(x) = f(x) - g(x)
Substitute the known values in the above equation, so, we have the following representation
(f - g)(x) = 2x² - 3x + 4 - 8x - 7
So, we have
(f - g)(x) = 2x² - 11x - 3
Evaluating the function (f - g)(-2)Here, we have
x = -2
Substitute the known values in the (f - g)(x) = 2x² - 11x - 3, so, we have the following representation
(f - g)(-2) = 2(-2)² - 11(-2) - 3
Evaluate
(f - g)(-2) = 27
Hence, the value of (f - g)(-2) is 27
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50 Points! Multiple choice algebra question. Photo attached. Thank you!
The period of the trigonometric function in this problem is given as follows:
A) 540º.
How to define a trigonometric function?The standard definition of the sine function is given as follows:
y = Asin(B(x - C)) + D.
For the tangent function, we have that it is similar to the sine function, that we use tan() instead of sin().
For which the parameters are given as follows:
A: amplitude.B: the period is 2π/B.C: phase shift.D: vertical shift.The coefficient B for the equation is given as follows:
B = 2/3.
Hence the period of the function is given as follows:
2π/(2/3) = 3π = 540º.
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50 Points! Multiple choice algebra question. Photo attached. Thank you!
The phase shift of the trigonometric function is given as follows:
D) 90º to the left.
How to define a trigonometric function?The standard definition of the sine function is given as follows:
y = Asin(B(x - C)) + D.
For the cosine function, we have the same definition, we only use cos() instead of sin().
For which the parameters are given as follows:
A: amplitude.B: the period is 2π/B.C: phase shift.D: vertical shift.For this problem, we have that the phase shift is of C = 90. As we are adding inside of the domain of the function, the phase shift is to the left.
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Find the slope and the y intercept of the line -6x + 3y =-3
The slope and y-intercept include the following:
Slope = 2.
y-intercept = -1.
What is the slope-intercept form?In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;
y = mx + b
Where:
m represent the slope or rate of change.x and y are the points.b represent the y-intercept or initial value.Based on the information provided above, we have the linear equation:
-6x + 3y =-3
By making y the subject of formula, we have:
3y = 6x - 3
y = 2x - 1
By comparison, the slope and the y-intercept include the following:
Slope, m = 2.
y-intercept, b = -1.
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Julia has 12 different flowers in her garden. She has 5 roses what fraction of the flowers are roses?
Answer:
5/12
Step-by-step explanation:
Since Julia has 12 different flowers and we know she has 5 roses
we can turn it into a fraction which will be 5/12.'
URGENT PLEASE HELP 15 POINTS!!!!
A consumer affairs investigator records the repair cost for 22 randomly selected TVs. A sample mean of $83.23 and standard deviation of $22.67 are subsequently computed. Determine the 95% confidence interval for the mean repair cost for the TVs. Assume the population is approximately normal.
Step 1 of 2 : Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.
Using a t-distribution with 21 degrees of freedom (since n-1 = 22-1 = 21), and a 95% confidence level, we can find the critical value from a t-table or calculator.
The critical value is ±2.080.
Rounded to three decimal places, the critical value is 2.080.
Calculator
A computer generates 90 integers from 1 to 8 at random. The results are recorded in this table.
Outcome
Number of times outcome occurred
9%
What is the experimental probability of the computer generating a 3 or a 5?
O 20%
O 18%
1
O 40%
26
2 3
8
10
4
12
ស
5
8
6
6
7
9
8
11
The experimental probability of the computer generating a 3 or a 5 is given as follows:
20%.
How to calculate a probability?The parameters that are needed to calculate a probability are given as follows:
Number of desired outcomes in the context of a problem/experiment.Number of total outcomes in the context of a problem/experiment.Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.
The total number of outcomes in the table is given as follows:
90.
The desired number of outcomes is given as follows:
10 + 8 = 18.
Hence the experimental probability is given as follows:
p = 18/90 = 0.2 = 20%.
Missing InformationThe problem is given by the image presented at the end of the answer.
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select the correct answer. when does the price of an item increase?
Answer: when the value of the dollar decreases, also when demand is high.
Step-by-step explanation: economics
Paul designed a patio for his backyard. The patio will cost
$3 per square foot to construct. His design and the scale
he will use to build the patio are both shown below.
How much will Paul spend constructing the patio?
Scale
1 cm = 3 ft.
5 cm
4 cm
8 cm
dollars
6.4 cm
Paul will spend $1,382.4 constructing the patio.
Looking at the design, we can see that the length of the patio is represented by 8 cm, and the width is represented by 6.4 cm. To convert these measurements to feet, we multiply them by the scale factor:
Length = 8 cm * 3 ft/cm = 24 ft
Width = 6.4 cm * 3 ft/cm = 19.2 ft
The area of the patio is calculated by multiplying the length and width:
Area = Length * Width = 24 ft * 19.2 ft = 460.8 ft²
The cost to construct the patio is $3 per square foot. Therefore, Paul will spend:
Cost = Area * Cost per square foot = 460.8 ft² * $3/ft² = $1,382.4
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Determine whether the expression 3m^3np^6 is a monomial.
The expression 3m³np⁶ is a monomial
A monomial is an algebraic expression that consists of only one term.
In this case, the expression 3m³np⁶ has a single term as it is the product of constants (3), variables (m, n), and their exponents (3, 1, and 6).
Therefore, it meets the criteria of a monomial.
Hence, the expression 3m³np⁶ is a monomial
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Could someone kindly give me a detailed explanation with step-by-step instructions for the solution? I would greatly appreciate it.
Let f: N → Q be defined by f(x) = x / 1 + x for any x ∈ N. Prove or disprove each of the following:
(a) The function f is injective.
(b) The function f is surjective.
A. The function f is injective.
B. The function f is not surjective, as there are values in Q (e.g., y = 1) for which there is no corresponding x ∈ N.
How to prove it is injectiveTo prove that the function f is injective, we need to show that if f(x) = f(y), then x = y.
Let f(x) = f(y). Then we have:
x / (1 + x) = y / (1 + y)
Cross-multiplying, we get:
x(1 + y) = y(1 + x)
x + xy = y + xy
Now, subtract xy from both sides:
x = y
Since x = y when f(x) = f(y), we can conclude that the function f is injective.
(b) To prove or disprove that the function f is surjective, we need to determine whether for every y ∈ Q, there exists an x ∈ N such that f(x) = y.
Consider the case where y = 1/2. We need to find x ∈ N such that:
f(x) = x / (1 + x) = 1/2
Cross-multiplying, we get:
2x = 1 + x
Subtract x from both sides:
x = 1
In this case, there exists an x ∈ N (x = 1) such that f(x) = 1/2. However, we need to consider all y ∈ Q. Let's try another case.
Consider the case where y = 1. There is no x ∈ N that satisfies the following equation:
f(x) = x / (1 + x) = 1
Cross-multiplying, we get:
x = 1 + x
Subtract x from both sides:
0 = 1
This is a contradiction, so there is no x ∈ N such that f(x) = 1. Therefore, the function f is not surjective, as there are values in Q (e.g., y = 1) for which there is no corresponding x ∈ N.
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I really need help doing this Constructing an Angle Bisector. please help me.
The bisector of angle RQP is angle PQT and angle RQT, both angles are equal and their sum is equal to angle RQP.
What is the bisector angle RQP?Angle bisector or a bisector angle is a type of angle obtained after dividing the initial angle into two equal parts.
The bisected angle can be obtained using a pair of compass and a pencil attached to it.
To bisect the given angle RQP; we will take the following steps;
Place the compass on exactly point Q.Expand the radius of the compass such that the pencil attached to the compass will be in between R and P.Strike an arc with the pencil clock wiseStrike another arc with the pencil anti clock wise such that the two arc intersects.Draw a line from point Q to intersect the two arcs.Label the point of intersection of the two arcs TFinally, angle PQT is equal to angle RQTLearn more about bisector angles here: https://brainly.com/question/24334771
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I don’t know the solution too this math problem
Answer:
Step-by-step explanation:
x° + 2x° + 9° = 180°
3x° + 9° = 180°
x° + 3° = 60°
x = 57°
in a water tank there's a depth of 9cm, imagine the tank is sealed and put onto it's side, whats the depth of the water now (photo included)
The depth of water when the tank is on its side is 4.2 cm.
We are given that;
tank measurement is 13*8*17
Now,
A cube is a three-dimensional representation of a square. it has 6 faces 2 on the bottom and top, 4 on the sides faces.
To find the volume of water in the tank when it is upright. To do this, you multiply the depth of water by the area of the base:
Volume = Depth * Area Volume = 9 cm * (13 cm * 8 cm) Volume = 936 cm^3
This volume does not change when you put the tank on its side. However, the area of the base does change. Depending on which side you put the tank on, the area of the base will be either 13 cm by 17 cm or 8 cm by 17 cm. Let’s assume you put the tank on its longer side, so that the area of the base is 13 cm by 17 cm.
Now, you can find the depth of water by dividing the volume by the area:
Depth = Volume / Area Depth = 936 cm^3 / (13 cm * 17 cm) Depth= 4.2 cm
Therefore, by the cube answer will be 4.2cm.
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A survey of 45 people was conducted to compare their self-reported height to their actual height. The difference between reported height and actual height was calculated.
You're testing the claim that the mean difference is greater than 0.
From the sample, the mean difference was 0.3, with a standard deviation of 0.8.
Calculate the test statistic, rounded to two decimal places
The test statistic is given as follows:
t = 2.52.
How to calculate the test statistic?We have the standard deviation for the sample, thus, the t-distribution is used. The test statistic is given by the equation presented as follows:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested at the null hypothesis.s is the standard deviation of the sample.n is the sample size.The parameters for this problem are given as follows:
[tex]\overline{x} = 0.3, \mu = 0, s = 0.8, n = 45[/tex]
Hence the test statistic is given as follows:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{0.3 - 0}{\frac{0.8}{\sqrt{45}}}[/tex]
t = 2.52.
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PLEASE HELP TIMED
The amount that two groups of students spent on snacks in one day is shown in the dot plots below.
Group A
A dot plot titled Group A. A number line going from 0 to 5 labeled Amount in Dollars. There are 0 dots above 0, 5 above 1, 4 above 2, 1 above 3, and 0 above 4 and 5.
Group B
A dot plot titled Group B. A number line going from 0 to 5 labeled Amount in Dollars. There are 0 dots above 0, 3 above 1, 2 above 2, 4 above 3, 0 above 4, and 1 above 5.
Which statements about the measures of center are true? Select three choices.
The mean for Group A is less than the mean for Group B.
The median for Group A is less than the median for Group B.
The mode for Group A is less than the mode for Group B.
The median for Group A is 2.
The median for Group B is 3.
The three statements about the measures of center that are true include the following:
A. The mean for Group A is less than the mean for Group B.
B. The median for Group A is less than the median for Group B.
C. The mode for Group A is less than the mode for Group B.
How to calculate the mean for the set of data?In Mathematics and Geometry, the mean for this set of data can be calculated by using the following formula:
Mean = [F(x)]/n
Group A
Mean for Group A = [(1 × 5) + (2 × 4) + (3 × 1)]/(5 + 4 + 1)
Mean for Group A = (5 + 8 + 3)/10
Mean for Group A = 16/10
Mean for Group A = 1.6
Mode for Group A = 1
Median for Group A = (1 + 2)/2
Median for Group A = 3/2
Median for Group A = 1.5
Group B
Mean for Group A = [(1 × 3) + (2 × 2) + (3 × 4) + (5 × 1)]/(3 + 2 + 4 + 1)
Mean for Group A = (3 + 4 + 12 + 5)/10
Mean for Group A = 24/10
Mean for Group A = 2.4
Mode for Group B = 3
Median for Group B = (2 + 3)/2
Median for Group B = 5/2
Median for Group B = 2.5
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
Answer: A,B,C
Step-by-step explanation:
Drag each tile to the correct box.
Arrange the following pairs of coordinates in order from least to greatest based on the differences between the points.
(4,1) and (2,2)
(-5,2) and (-3,-2)
(3,-4) and (-2,1)
(-1,-2) and (1,-4)
(5,-2) and (-1,-1)
The pairs of coordinates arranged from least to greatest based on the differences between the points are:
(-1,-2) and (1,-4)
(4,1) and (2,2)
(-5,2) and (-3,-2)
(3,-4) and (-2,1)
(5,-2) and (-1,-1)
Let's calculate the differences and arrange the pairs accordingly:
(4,1) and (2,2):
Difference in x-coordinates: 4 - 2 = 2
Difference in y-coordinates: 1 - 2 = -1
(-5,2) and (-3,-2):
Difference in x-coordinates: -5 - (-3) = -2
Difference in y-coordinates: 2 - (-2) = 4
(3,-4) and (-2,1):
Difference in x-coordinates: 3 - (-2) = 5
Difference in y-coordinates: -4 - 1 = -5
(-1,-2) and (1,-4):
Difference in x-coordinates: -1 - 1 = -2
Difference in y-coordinates: -2 - (-4) = 2
(5,-2) and (-1,-1):
Difference in x-coordinates: 5 - (-1) = 6
Difference in y-coordinates: -2 - (-1) = -1
Now let's arrange them in order from least to greatest based on the differences in the points:
(3,-4) and (-2,1) (difference: 5)
(-1,-2) and (1,-4) (difference: 2)
(4,1) and (2,2) (difference: 2)
(-5,2) and (-3,-2) (difference: 4)
(5,-2) and (-1,-1) (difference: 6)
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3 1/5x+10 7/9-2 2/5x-10 8/9 (Simplify) I need the answer to this ASAP!
The simplified form of the expression 3 1/5x + 10 7/9 - 2 2/5x - 10 8/9 is 4/5x - 1/9.
To simplify the expression: 3 1/5x + 10 7/9 - 2 2/5x - 10 8/9, we need to perform the addition and subtraction of the terms.
First, let's focus on the x terms: 3 1/5x - 2 2/5x.
The whole numbers can be treated as fractions with a denominator of 1. Thus, we have:
(3 1/5)x - (2 2/5)x.
To perform the subtraction, we need to find a common denominator for the fractions involved, which is 5.
(3 1/5)x - (2 2/5)x = (16/5)x - (12/5)x.
Now we can subtract the terms:
(16/5)x - (12/5)x = (16 - 12)/5x.
Simplifying further:
4/5x.
Now let's simplify the whole number and fraction terms: 10 7/9 - 10 8/9.
10 - 10 = 0.
The fraction terms can be simplified by finding a common denominator, which is 9:
(7/9) - (8/9) = (-1/9).
Now we can combine all the simplified terms:
3 1/5x + 10 7/9 - 2 2/5x - 10 8/9
= (4/5x) + 0 + (-1/9)
= 4/5x - 1/9.
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please help! thank uu ~ :)
Answer:
Impossible
Step-by-step explanation: if a cube is number from 1-6 theirs no chance of getting a number less than 1.
The area of the entire figure below is 1 square unit.
How can we describe the area of the striped rectangle?
Answer:
4/15 square unit (0.2667 rounded)
Step-by-step explanation:
The whole square is one square as
((1/10) x 10 (columns)) multiplied by ((1/3) x 3 (rows)) = 1 multiplied by 1 = 1.
So, with that, the area of the striped rectangles should be:
(1/10) x 4 (columns in the striped area of rects) multiplied by (1/3) x 2 (rows in the striped area of rects) = 0.4 multiplied by 2/3 = 4/15 square unit.
Color Payout
Red $2
Blue $6
Green $6
Yellow $20
The game costs $5 to play. You win money based on the color the spinner lands on (the spinner can land on any color, not just green).
Payouts are as follows:
Find the expected value of the following game to the player.
Express your answer in dollars
rounded to the nearest cent (e.g.
$3.50)
Answer:
$2.25
Step-by-step explanation:
Red: $2
Blue: $6
Green: $6 + $5 (original cost of game) = $11
Yellow: $20
The total number of slots on the spinner is 4, with one slot for each color. Since the spinner can land on any color with equal probability, the probability of it landing on each color is 1/4 or 0.25.
Therefore, the expected value of the game is:
(0.25 x $2) + (0.25 x $6) + (0.25 x $11) + (0.25 x $20) - $5 = $2.25
Find the measure of the red arc or chord in ⊙C.
The calculated measure of the red arc in ⊙C is 11
How to find the measure of the red arc or chord in ⊙C.From the question, we have the following parameters that can be used in our computation:
The congruent circles
From the circles, we have
Centers = C and P
Also, we have
Corresponding segments are equal segments
Using the above as a guide, we have the following:
QR = LM
Where
LM = 11
This gives
QR = 11
Hence, the value of QR is 11
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Solve for x square root of (2x^2+1)=0
Sorry for bad handwriting
if i was helpful Brainliests my answer ^_^
QUICK! 40 points. Consider this cone with the diameter measure of 17 inches.
A cone with diameter 17 inches and slant height of 22 inches.
What is the surface area of the cone?
SA = Pir2 + Pirl
A. 204Pi in.2
B. 259.25Pi in.2
C. 446.25Pi in.2
D. 663Pi in.2
259.25π in² is the surface area of the cone
The surface area of a cone can be calculated using the formula SA = πr² + πrl
where r is the radius and l is the slant height.
Given that the diameter is 17 inches, the radius (r) is half of the diameter, which is 17/2 = 8.5 inches.
The slant height (l) is given as 22 inches.
Substituting these values into the formula:
Surface Area = π(8.5)² + π(8.5)(22)
= 72.25π + 187π
= 259.25π
Therefore, the surface area of the cone is 259.25π in²
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Boyles Law says that the volume of a gas varies inversely with the pressure. When the volume of a certain gas is 5L the pressure is 88kPa ( kilo pascals ). What is the volume of the pressure is 55 kPa?
Help due !!! Asap
The final volume of the gas is 8 litres when the pressure is 55 kilo pascals.
What is the final volume of the gas?Boyle's law simply states that "the volume of any given quantity of gas is inversely proportional to its pressure as long as temperature remains constant.
Boyle's law is expressed as;
P₁V₁ = P₂V₂
Where P₁ is Initial Pressure, V₁ is Initial volume, P₂ is Final Pressure and V₂ is Final volume.
Given that:
Initial volume of the gas V₁ = 5LInitial pressure of the gas P₁ = 88 kPaFinal pressure of the gas P₂ = 55 kPaFinal volume of the gas V₂ = ?Plug the given values into the above formula and solve for the final volume:
88 kPa × 5L = 55 kPa × V₂
V₂ = 440 / 55
V₂ = 8 L
Therefore, the final volume is 8 litres.
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