On the first day, the members earned 90% of their daily goal of $50.00 which is equal to $45.00 (0.9 x $50.00 = $45.00).
On the second day, the members earned 6% more than their daily goal of $50.00 which is equal to $53.00 ($50.00 + 0.06 x $50.00 = $53.00).
On the third day, the members earned 14% less than their daily goal of $50.00 which is equal to $43.00 ($50.00 - 0.14 x $50.00 = $43.00).
Therefore, the members earned a total of $45.00 + $53.00 + $43.00 = $141.00 from ticket sales on all three days.
The members of the school club earned $141.00 from ticket sales over the three days.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
To find out how much money the members of the school club earned from ticket sales on all three days
Let us calculate the amount of money earned each day and then add them together.
On the first day, the members earned 90% of their daily goal, which is:
0.9 x $50.00 = $45.00
On the second day, they earned 6% more than their daily goal, which is:
$50.00 + 0.06 x $50.00 = $53.00
On the third day, they earned 14% less than their daily goal, which is:
$50.00 - 0.14 x $50.00 = $43.00
To find the total amount of money earned over the three days, we simply add the amounts earned on each day:
$45.00 + $53.00 + $43.00 = $141.00
Therefore, the members of the school club earned $141.00 from ticket sales over the three days.
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Quadrilateral JKLM is an isosceles trapezoid. Write each length or angle measure.
The measure of angles JKL, KJM and KRL are -51°, 105° and 51° respectively and the length of diagonal JL is 81 units.
What is a isosceles trapezoid?An isosceles trapezoid is a four-sided polygon with two opposite sides parallel and two other sides of equal length.
In Quadrilateral JKLM,
KR = 42 and JR = 39,
R being the midpoint of diagonal.
Also, angle KMJ = 27° and KML = 78°.
The measure of angle JKL is equal to the difference of given angles KMJ and KML.
Therefore,
Angle JKL = KML-KMJ
= 78°- 27°
= 51°
The measure of angle KJM is equal to the sum of given angles KMJ and KML.
Therefore,
Angle KJM = KMJ + KML
= 27° + 78°
= 105°
The measure of angle KRL is equal to the difference of given angles KML and KMJ.
Therefore,
Angle KRL = KML - KMJ
= 78° - 27°
= 51°
The length of Diagonal JL is equal to the sum of lengths of given sides KR and JR.
Therefore,
Length of JL = KR + JR
= 42 + 39
= 81
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Audrey has $440 to spend at a bicycle store for some new gear and biking outfits. Assume all prices listed include tax.
She buys a new bicycle for $259.52.
She buys 2 bicycle reflectors for $3.07 each and a pair of bike gloves for $29.12.
She plans to spend some or all of the money she has left to buy new biking outfits for $72.61 each.
Write and solve an inequality which can be used to determine oo, the number of outfits Audrey can purchase while staying within her budget.
The inequality is 76.26 - 72.61x ≥ 0 and the value of x is x ≤ 1.05. Audrey can purchase at most 1 biking outfit while staying within her budget.
What is inequality?A mathematical statement called an inequality compares two values, frequently by employing symbols. When there is an inequality, one value is either bigger than or less than the other, not necessarily equal to it. For instance, the inequality x > 5 asserts that x is bigger than, but not necessarily the same as, 5. Relationships between different numbers, such as the sum of money spent on shopping and the sum of money left in a budget, are sometimes described as having inequalities.
Let us suppose the number of outfits = x.
Given that, the total amount Audrey has is $440.
Now, the inequality can be written as:
40 - 259.52 - 2(3.07) - 29.12 - 72.61x ≥ 0
76.26 - 72.61x ≥ 0
-72.61x ≥ -76.26
x ≤ 1.05
Hence, Audrey can purchase at most 1 biking outfit while staying within her budget.
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the mayor of a town has proposed a plan for the construction of an adjoining bridge. a political study took a sample of 800 800 voters in the town and found that 59% 59 % of the residents favored construction. using the data, a political strategist wants to test the claim that the percentage of residents who favor construction is over 54% 54 % . determine the p-value of the test statistic. round your answer to four decimal places.
The p-value of the test statistic is 0.0000 (rounded off to four decimal places).
The p-value of the test statistic can be calculated by subtracting the area under the normal curve from the test statistic to infinity in the direction of the alternative hypothesis.
We are given that a political study has been carried out, taking a sample of 800 voters in the town. The sample shows that 59% of the residents favored construction. A political strategist wants to test the claim that the percentage of residents who favor construction is over 54%.
The hypothesis can be defined as follows:
Null hypothesis (H0): p ≤ 0.54, where p is the proportion of residents who favor the construction of the bridge.
Alternative hypothesis (Ha): p > 0.54, where p is the proportion of residents who favor the construction of the bridge.
To calculate the test statistic, we use the formula given below:
z = (p - P) / √[P(1-P) / n]
Here, P = 0.54, n = 800, p = 0.59
Putting these values in the above formula, we get:
z = (0.59 - 0.54) / √[0.54(1-0.54) / 800] = 5.06
To determine the p-value of the test statistic, we need to calculate the area under the normal curve from 5.06 to infinity in the direction of the alternative hypothesis. As the alternative hypothesis is one-tailed, we use the standard normal distribution table to find the corresponding area under the curve. The area can be calculated as:
P(Z > 5.06) = 0.00000035 (using the standard normal distribution table)
Therefore, the p-value of the test statistic is 0.0000 (rounded to four decimal places).
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the top face of a portable digital device measures 3.01 inches by 1.23 inches. find the area of the face of the device
The area of the face of the portable digital device is approximately 3.7033 square inches.
Area is a measurement of the amount of space inside a two-dimensional figure or shape. It is expressed in square units and can be calculated by multiplying the length and width of a rectangle or the base and height of a triangle, or by using specific formulas for other shapes such as circles, trapezoids, or parallelograms.
The area of the face of the portable digital device can be found by multiplying the length by the width
Area = Length x Width
Area = 3.01 inches x 1.23 inches
Area = 3.7033 square inches (rounded to four decimal places)
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[50 POINTS!!!] I posted a Screen shot of the question down below!
Answer:
C; as x-> infinite, f(x) -> infinite, as x-> neg. infinite, f(x) -> neg. infinite
Step-by-step explanation:
Graphing the equation will help with knowing the end behavior.
X^3 graphs tend to increase infinitely when x is going infinitely positive and decrease infinitely when x is going infinitely negative.
The volume of prism R is 40 m³. Prism R and prism S have the same height. The area of the base of prism S is half the area of the base of prism R. What is the volume of prism S? 1) 10 m³ 2) 20 m³ 3) 40 m³ 4) 80 m³
2) 20 m³ is the answer
it’s a 2 part question
The missing values in the figure is solved using central angle theorem to get
angle FHG = 122 degreesHow to find angle FHGThe measure of an central angle is equal to the measure of the intercepted arc according to the central angle theorem.
From the figure we have that the intercepted arc is FG = 122 degrees. Using the central angle theorem, the central angle is angle FHG
central angle = intercepted arc
angle FHG = arc FG
angle FHG = 122 degrees
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40 mm
34.6 mm
40 mm
Please help me with this question
I remember doing this but I don’t seem to remember sorry
find f0.05 where v1=8 and v2=11
a) 2.95
b) 2.30
c) 4.74
d) 3.66
The correct answer for F-distribution f0.05 is d) 3.66
How to find F-distribution f0.05?To find f0.05 with v1=8 and v2=11, you can use an F-distribution table or an online calculator.
Here's a step-by-step explanation:
1. Locate the row in the F-distribution table corresponding to the degrees of freedom for the numerator (v1), which is 8 in this case.
2. Locate the column corresponding to the degrees of freedom for the denominator (v2), which is 11 in this case.
3. Find the intersection of the row and column to get the critical value for f0.05.
Using an F-distribution table or calculator, you will find that the f0.05 value for v1=8 and v2=11 is approximately 3.66.
So, the correct answer is:
d) 3.66
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What Is the area of the entire plot of land (Including the land occupled by the house, backyard, front yard, side yard, and driveway)?
The total area of the entire plot of land, including the land occupied by the house, backyard, front yard, side yard, and driveway, is 7,701 square feet.
What is area?Area is the measure of the amount of surface that a flat or 2-dimensional shape or object occupies. It is typically expressed in square units such as square feet, square meters, or square inches.
To find the area of the entire plot of land, we need to add up the areas of all the individual sections. Let's calculate the area of each section separately:
Area of backyard MNOV = (MN + NO) x OV = (25 + 20) x 5 = 225 square feet
Area of house ABCD = Base x Height = 66 x 38 = 2,508 square feet
Area of front yard RFEH = (RF + FH) x HE = (35 + 8) x 8 = 344 square feet
Area of side yard BFGC = (BF + FG + GC) x BC = (8 + 30 + 5) x 83 = 3,436 square feet
Area of driveway DEGH = Base x Height = 18 x 66 = 1,188 square feet
Therefore, the total area of the plot of land is:
225 + 2,508 + 344 + 3,436 + 1,188 = 7,701 square feet.
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ME HELP PLEASE JSJS
The complete solution and complete answer of the questions provided are mentioned below respectively.
What is an integer?An integer is a whole number that can be either positive, negative or zero, but does not include fractions or decimals. Examples of integers include -5,-4,-3, -2, -1, 0, 1, 2, 3, 4, 5.
1.To find out how much money is in Lane's account now, we need to substitute x = 0 in the given expression:
500(1.05)⁰ = 500(1) = 500
Therefore, Lane has $500 in his account now.
2.To write an expression for the amount of money in Lane's account in 20 years, we need to substitute x = 20 in the given expression:
500(1.05)²⁰ ≈ 1326.65
Therefore, the expression for the amount of money in Lane's account in 20 years is 1326.65.
3.To write an expression for the amount of money in Lane's account 5 years ago, we need to subtract the amount of interest earned in the last 5 years from the current balance of his account. The amount of interest earned in the last 5 years is:
500(1.05)² - 500(1.05)⁰≈ $154.13
Therefore, the expression for the amount of money in Lane's account 5 years ago is 500 - 154.13 = $345.87.
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1. Lane has $500 in his account now.
2. The given expression: 500(1.05)²⁰ ≈ 1326.65
3. The calculation for Lane's account balance five years ago is $345.87.
What is an integer?An integer is a whole number, which does not include fractions or digits and can be positive, negative, or zero.
Integer examples include -5,-4,-3, -2, -1, 0, 1, 2, 3, 4, 5.
1. The following equation must be changed to read x = 0 in order to determine how much money is currently in Lane's account:
500(1.05)⁰ = 500(1) = 500
Lane now has $500 in his account as a result.
2. We must replace x with 20 in the provided expression in order to create an expression for the sum of money that will be in Lane's account in 20 years:
500(1.05)²⁰ ≈ 1326.65
As a result, the phrase for Lane's account balance in 20 years is 1326.65.
3. We must deduct the amount of interest earned over the previous five years from Lane's account balance in order to calculate the balance five years back. The income earned over the previous five years is:
500(1.05)² - 500(1.05)⁰≈ $154.13
Since there was money in Lane's account five years ago, the phrase is 500 - 154.13 = $345.87.
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if you were to have simply guessed the answer for each of the two questions, four choices each, what is the mathematical probability that you would have gotten them both right?
If you were to simply guess the answer to both questions, you would have a 6.25% chance of getting both answers right according to probability
Assuming that each answer choice is equally likely to be correct, the probability of guessing the correct answer to one question is 1/4 or 0.25. Since there are two questions, the probability of guessing both correctly is the product of the probabilities of guessing each question correctly.
P(guessing both questions correctly) = P(guessing first question correctly) x P(guessing second question correctly)
P(guessing both questions correctly) = (1/4) x (1/4)
P(guessing both questions correctly) = 1/16 or 0.0625
Therefore, the probability of guessing both questions correctly is 1/16 or 0.0625.
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trying to make a box without a top out of a square piece of cardboard by cutting off the corners and folding up the sides. your box must have a height of 3 cm and have a square base. how long do the sides of the piece of cardboard, x, have to be in order for the volume of the box to equal 48 cm3?
The sides of the piece of cardboard have to be 10 cm long in order for the volume of the box to equal 48 cm³
Let us assume that the dimension of the square piece of cardboard = m × m
If we cut a 3 cm square out of each corner, then each side of the square base will be (m - 6) cm.
The height of the box, when folded, will be 3 cm.
The volume of the box is:
V= (height) × (width) × (length)
V = 3 (m - 6) (m - 6)
V = 48 cm³
3(m² - 12m + 36) = 48
m² - 12m + 36 = 16
m² - 12m + 36 - 16 = 0
m² - 12m + 20 = 0
m² - 10m - 2m + 20 = 0
m(m - 10) - 2(m - 10) = 0
(m - 10)(m - 2) = 0
m = 10 OR m = 2
when m = 2, (m - 6) = -4 which is not possible.
So, the dimensions of the base of the box = 10 × 10
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Find the y - intercept of the quadratic function f ( x ) = (x - 2.5)^2 + 0.25.
a. ( 0, 6.5 )
b. (0, - 0.25 )
c. (0, 0.25)
d. ( 0, - 6 )
( it is not c, i tried and got it wrong.)
to get the y-intercept we simply set x = 0 and solve for "y", knowing that the x-coordinate will be, well, 0.
[tex]f(x)=(x-2.5)^2+0.25\implies f(0)=(\stackrel{ x }{0}-2.5)^2+0.25 \\\\\\ f(0)=(-2.5)^2 + 0.25\implies f(0)=6.25+0.25\implies f(0)=6.5~\hfill \boxed{(0~~,~~6.5)}[/tex]
Find X, Y geometry y x 45
In triangle, value of x and y are 10,10 .
What does a triangle in math mean?
Three edges and three vertices make up the three sides of a triangle, which is a three-sided polygon in geometry. The fact that the internal angles of a triangle add up to 180 degrees is the most crucial aspect of triangles.
Triangle's angle sum property is what this characteristic is known as. Three edges and three vertices make up a triangle, which is a polygon. It is one of the fundamental geometric shapes. The symbol represents a triangle with the vertices A, B, and C. triangle with equal sides.
In triangle ,
sin45° = y/10√2
1/√2 = y/10√2
10√2 = √2y
y = 10
tan45° = x/y
1 = x /10
x = 10
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Consider this system of linear equations.
-2x - 5y = 12
3x - 4y = 5
Graph the system, and then mark its solution
Answer:
(-1, -2)
Step-by-step explanation:
Andre studies 7 hours this week for end-of-year exams. He spends 1 hour on English and an equal number of hours each on math, science, and history.
Answer:
Step-by-step explanation:
Which of the following conditions could be used to prove both a||b and c||d?
In other words, if a vector v exists such that an is parallel to v, b is parallel expression to v, c is parallel to v, and d is parallel to v, we may conclude that both a||b and c||d exist.
What is expression ?An expression in mathematics is a collection of representations, numbers, and conglomerates that mimic a statistical correlation or regularity
We need a condition that assures that an is parallel to b and c is parallel to d to verify both a||b and c||d.
If a and b are both parallel to the same vector, and c and d are both parallel to the same vector, this is one such condition.
In other words, if a vector v exists such that an is parallel to v, b is parallel to v, c is parallel to v, and d is parallel to v, we may conclude that both a||b and c||d exist.
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Which triangle congruence theorem can be used to prove the triangles are congruent?
a. SSS
b. SAS
c. AAS
d. ASA
Answer:
a. SSS
Step-by-step explanation:
Answer:
Step-by-step explanation:
qacfascffaafa
Solve the system of equations by graphing on the given coordinate plane. y = 2x – 5 y = –x + 4
Answer:
(3,1)
Step-by-step explanation:
I just graphed it using desmos but I could show you algebraically if you want
:)
Carlos purchased a new computer for $1,350. One year later, a popular tech website valued the same computer at $810. The website predicts that the value of the computer will continue depreciating each year. Write an exponential equation in the form y=a(b)x that can model the value of the computer, y, x years after purchase. Use whole numbers, decimals, or simplified fractions for the values of a and b. y = To the nearest ten dollars, what can Carlos expect the value of the computer to be 3 years after purchase?
Answer:
Step-by-step explanation:
Carlos can expect the value of the computer to be $580 in 3 years after purchase.
To find the exponential equation in the form y=a(b)ˣ that models the value of the computer, we need to determine the initial value and the rate of decay.
The initial value of the computer is $1,350, and its value after one year is $810.
We can use this information to find the rate of decay as follows:
810 = 1350 × b¹
b = 0.6
So the exponential equation is:
y = 1350(0.6)ˣ
To find the value of the computer 3 years after purchase, we can substitute x = 3 into the equation:
y = 1350(0.6)³= 583.2
Hence, Carlos can expect the value of the computer to be $580 in 3 years after purchase.
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twenty five cards are marked with the numbers 1 through 25. amira randomly picks two cards without replacement. blanca then randomly picked two of the remaining cards without replacement. what is the probability that at least one of blanca's cards has a number greater than at least one of amira's cards?
The probability that at least one of Blanca's cards has a number greater than at least one of Amira's cards is 0.705 or approximately 70.5%.
The total number of ways in which Blanca can choose two cards out of 23 is given by the combination formula C(23, 2), which is equal to 253.
The value of k can range from 3 (if Amira's cards are 1 and 2) to 25 (if Amira's cards are 24 and 25). Therefore, the total number of ways in which Blanca can pick two cards that are both greater than Amira's cards is:
C(23, 2) - C(2, 2) - C(3, 2) - ... - C(23, 2) = 23C(23, 1) - (C(2, 2) + C(3, 2) + ... + C(23, 2)) = 253 - 276 = -23
Since the result is negative, it means that there are no ways in which Blanca can pick two cards that are both greater than Amira's cards. Therefore, the probability of this case is 0.
P(Case 2) = (number of ways in which Blanca can pick one card greater than Amira's and one card less than Amira's) / (total number of ways in which Blanca can pick two cards out of 23) = 44,550 / C(23, 2) = 0.705
Finally, the probability of at least one of Blanca's cards having a number greater than at least one of Amira's cards is given by the sum of the probabilities of Case 1 and Case 2:
P(at least one of Blanca's cards is greater) = P(Case 1) + P(Case 2) = 0 + 0.705 = 0.705 or 70.5%
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Directions: The following is an axiomatic system. Answer each question as required. Axiom Set: Axiom 1: Each line is a set of three points Axiom 2: Each point is contained by two lines. Axiom 3: Two distinct lines intersect at exactly one point. Question: 1. What are the undefined terms in this axiom set? 2. Is the axiomatic system consistent? Why? Why not? State what specific property is the given axiomatic system.
Geometry is a branch of mathematics that deals with the study of shapes, sizes, positions, and dimensions of objects in space. It includes the study of points, lines, angles, curves, surfaces, and solids, and the relationships between them.
What is Euclidean geometry?Euclidean geometry is a type of geometry that is based on the work of the ancient Greek mathematician Euclid. It is a branch of mathematics that deals with the properties and relationships of points, lines, angles, and planes in two and three-dimensional space.
In the given question
The undefined terms in this axiom set are "line," "point," and "intersect."The axiomatic system is consistent. To see why, we can use the properties of the axioms to reason about the properties of the system. From Axiom 1, we know that every line is a set of three points, and from Axiom 2, we know that every point is contained by two lines. This means that every point is shared by exactly two lines. If we assume that two lines intersect at two distinct points, then those two points must belong to four distinct lines. But this contradicts Axiom 2, which states that each point is contained by exactly two lines. Therefore, two lines must intersect at exactly one point, which is stated in Axiom 3. Thus, the axioms are self-consistent and do not lead to any contradictions.The specific property of the given axiomatic system is the Euclidean geometry of two-dimensional space. The system specifies the basic properties of points and lines in this geometry, including how they intersect, and serves as a foundation for further geometric reasoning and deduction.
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how many solutions does this have?
x + 5 = 24
5x = 12 − y
In conclusion there is only one solution to the system of equations and that is for x and y that satisfies both equations: x = 19 and y = -83.
How to solve and what does an equation mean?
We have two equations:
x + 5 = 24
5x = 12 - y
For the first equation, we can isolate x by subtracting 5 from both sides:
x = 19
Now we can substitute x = 19 into the second equation:
5(19) = 12 - y
95 = 12 - y
y = -83
So we have found a unique solution for x and y that satisfies both equations: x = 19 and y = -83.
Therefore, there is only one solution to the system of equations.
An equation is a mathematical statement that says that two things are equal. It consists of two expressions separated by an equal sign (=). For example, 2 + 3 = 5 is an equation that says that the sum of 2 and 3 is equal to 5.
Equations can be written in a variety of forms, depending on the type of problem being solved. In algebra, equations often involve variables, which are letters or symbols that represent unknown quantities.
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The make African elephant at the city zoo has a mass of 5450 kg. What is its mass in scientific notation
The mass in scientific notation is [tex]5.45 * 10^3 kg[/tex], this means that the mass of the African elephant is 5.45 multiplied by 1000,
To write the mass of the African elephant in scientific notation, we need to express it as a number between 1 and 10, multiplied by a power of 10. To do this, we can start by moving the decimal point in 5450 kg to the left until we have a number between 1 and 10. This gives us 5.45 kg.
Next, we need to determine the power of 10 that we multiplied by to get this number. To do this, we count the number of places we moved the decimal point, which is three places to the left. Therefore, the mass of the African elephant in scientific notation is:
[tex]5.45 * 10^3 kg[/tex]
This means that the mass of the African elephant is 5.45 multiplied by 1000, which is the same as 5450 kg in standard notation. Writing the mass in scientific notation makes it easier to work with very large or small numbers, as it simplifies the representation of the number and makes it more manageable.
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the equation
4x-2y=4
-4x+2y=-3
have the same/different what slopes and the same/different what y-intercepts?
Answer:
They both have the same slope of 2. Their y-intercepts are different. One is -2 and the other is -3/2.
Step-by-step explanation:
4x-2y=4
4x - 4 = 2y
(divide 2 by both sides)
2x-2=y
-4x+2y=-3
2y=4x-3
(divide 2 both sides)
y = 2x - 3/2
Find the greatest common factor of 509089201 and 509089201.
Answer:
GCF = 509089201
for the values 509089201, 509089201
Solution by Factorization:
The factors of 509089201 are: 1, 107, 1663, 2861, 177941, 306127, 4757843, 509089201
The factors of 509089201 are: 1, 107, 1663, 2861, 177941, 306127, 4757843, 509089201
Then the greatest common factor is 509089201.
Answer: 509089201
Step-by-step explanation: The multiples would be 1, 107, 1663 and so on until 509089201, which makes 509089201 the gcf
Twenty-five students were asked to rate—on a scale of 0 to 10—how important it is to reduce pollution. a rating of 0 means "not at all important" and a rating of 10 means "very important." here is a dot plot of their responses. a dot plot for the "importance of reducing pollution" where the numbers 2 through 10 are indicated. the data for the dot plot are as follows: scale 2, 1 dot scale 3, 1 dot scale 4, 1 dot scale 5, 2 dots scale 6, 2 dots scale 7, 2 dots scale 8, 5 dots scale 9, 5 dots scale 10, 6 dots explain why a rating of 6 is not a good description of the center of this data set.
A rating of 6 is not a good description of the center of this data set because the data is skewed to the right, with more students rating the importance of reducing pollution as 7, 8, 9, or 10.
A rating of 6 is not a good description of the center of this data set because the dot plot is skewed to the right. There are more dots to the right of 6 than to the left, indicating that there are more students who rated the importance of reducing pollution as 7, 8, 9, or 10 than those who rated it as 2, 3, 4, 5, or 6.
The center of a data set is typically measured by its mean, median, or mode. In this case, the median would be a better measure of the center than the mean or mode because the dot plot is skewed. The median would be the middle value when the data set is ordered from smallest to largest.
If we order the data set from smallest to largest, we get
2, 3, 4, 5, 5, 6, 6, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10
The median of this data set is 9, which is higher than 6. Therefore, a rating of 6 is not a good description of the center of this data set.
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Need help with homework, thanks in advance.
Equation of block pattern is: n² + 2n + 4
Define the term equation?A statement that shows the equality of two mathematical expressions is known as an equation. The goal is typically to ascertain the values of the variables that keep the equation true, and it may have one or more variables. In that both sides must be equal for an equation to hold true, it might be likened to a balance scale.
A block pattern is a type of organizational structure used in writing and presenting information. It involves dividing the information into distinct blocks or sections, with each block focusing on a particular aspect of the topic being discussed. This pattern is often used in writing comparison and contrast essays, where the writer wants to explore the similarities and differences between two or more subjects.
Equation of block pattern is: n² + 2n + 4
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11. The velocity, V of a car moving with a constant acceleration is partly constant and partly
varies as the time taken, t. The velocity of the car after 8s and 12s are 9 m/s and 11
m/s respectively. Find
(i)
(ii)
The relationship between the velocity and the time taken.
The time taken when the velocity is 15 m/s.
Based on the information provided, the relationship between velocity and time taken is V = 4 + 0.5t.
How to find the velocity between the two variables?We can start by using the formula for velocity with constant acceleration:
V = Vo + at
where V is the final velocity, Vo is the initial velocity, a is the constant acceleration, and t is the time taken.
We know that the velocity is partly constant and partly varies with time, so we can write:
V = Vc + Vv
where Vc is the constant part of the velocity and Vv is the part that varies with time.
Using the given information, we can set up a system of equations:
9 = Vc + Vv (when t = 8s)
11 = Vc + Vv (when t = 12s)
Subtracting the first equation from the second, we get:
11 - 9 = (Vc + Vv) - (Vc + Vv)
2 = Vv (when t = 12s) - Vv (when t = 8s)
2 = Vv (12) - Vv (8)
2 = 4Vv
Vv = 0.5 m/s
Now we can use either of the two original equations to find Vc:
9 = Vc + 0.5(8)
Vc = 4 m/s
Therefore, the relationship between the velocity and the time taken is:
V = 4 + 0.5t
where V is the velocity in m/s and t is the time taken in seconds.
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