A permutation is a collection of things where the arrangement is important. In general, a permutation of a set in mathematics is the rearranging of its members into a sequence or linear order if the set already has an ordered structure.
What is permutation?A permutation is a grouping of items where the order is crucial.
A permutation of a set in mathematics is, broadly speaking, the rearrangement of its elements if the set already has an ordered structure into a sequence or linear order.
The act or procedure of altering the linear order of an ordered set is referred to as a "permutation."
Contrasted with combinations, which are selections of a few members of a set independent of order, are permutations.
There are six permutations of the set "1, 2, 3," for instance, represented as tuples: (1, 2, 3), (1, 3, 2), (2, 1, 3), (2, 3, 1), (3, 1, 2), and (3, 2, 1).
Therefore, a permutation is a collection of things where the arrangement is important. In general, a permutation of a set in mathematics is the rearranging of its members into a sequence or linear order if the set already has an ordered structure.
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Find the exact value of sin (2x) if tan(x)=-1/5.
Answer: The value of sin(2x) can be found using the identity:
sin(2x) = 2sin(x)cos(x)
Since tan(x) = -1/5, we can use the tangent definition to find the sine and cosine values:
tan(x) = sin(x) / cos(x) = -1/5
Cross multiplying and solving for sin(x), we get:
sin(x) = -5 / sqrt(26)
And using the Pythagorean identity:
cos^2(x) + sin^2(x) = 1
We can find cos(x):
cos(x) = sqrt(1 - sin^2(x)) = sqrt(1 - (-5/sqrt(26))^2) = sqrt(26) / sqrt(26) = sqrt(26) / sqrt(26) = sqrt(26) / 5
Finally, substituting the values of sin(x) and cos(x) into the formula for sin(2x), we get:
sin(2x) = 2sin(x)cos(x) = 2 * (-5 / sqrt(26)) * (sqrt(26) / 5) = -2 sqrt(26) / 5 = -2 sqrt(26) / 5 = -2 sqrt(26) / 5
So the exact value of sin(2x) is -2 sqrt(26) / 5.
Step-by-step explanation:
Compare the rates of change of the following table and graph.
4
2
4
-12
-16
O A. The rate of change of the graph is greater than the rate of change of the table.
O B. The rate of change of the table is equal to the rate of change of the graph.
OC.
There is not enough information to determine the rates of change.
O D. The rate of change of the table is greater than the rate of change of the graph.
There is not enough information to determine the rates of change which is therefore denoted as option C in the table and graph given.
What is a Graph?This is referred to as a pictorial representation or a diagram that represents data or values in an organized manner.
In the graph and table there was no clear representation of the variables in the x and y coordinates which is therefore the reason why there won't be enough information to determine the rate of change which is therefore the correct choice.
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The full question:
Compare the rates of change of the following table and graph. x y 1 -4 2 -8 3 -12 4 -16 A. The rate of change of the table is greater than the rate of change of the graph. B. There is not enough information to determine the rates of change. C. The rate of change of the table is equal to the rate of change of the graph. D. The rate of change of the graph is greater than the rate of change of the table.
Antoine is renting a car for a day to drive to his sister's college and back. He estimates that the college is about 60 miles away. Low Price Rentals charges a $49 rental fee plus $0.16 per mile driven. Easy Rental charges a $25 fee plus $0.50 per mile.
Compare the two rental options.
Which company offers a better deal? How do you know?
Select the option that correctly answers both questions.
Responses
Easy Rental, because it will charge $55.00 for the trip, while Low Price Rentals will charge $58.60 (wrong answer)
Easy Rental, because it will charge $34.60 for the trip, while Low Price Rentals will charge $79.00
Low Price Rentals, because it will charge $68.20 for the trip, while Easy Rental will charge $85.00
Low Price Rentals, because it will charge $44.20 for the trip, while Easy Rental will charge $109.00
Answer:
(c) Low Price Rentals, because it will charge $68.20 for the trip, while Easy Rental will charge $85.00.
Step-by-step explanation:
You want to compare two car rental options for a 120-mile trip. Low Price charges $49 and $0.16 per mile; Easy charges $25 and $0.50 per mile.
GraphWe find it convenient to use a graphing calculator to plot the rental charges versus mileage. We find the charges to be ...
Low Price Rentals: $68.20 . . . . better deal (lower price)Easy Rental: $85.00CalculatorYou can also evaluate the charges by adding the fixed fee to the mileage cost for each option, as in the second attachment.
what is 2 divided by 1/8
Answer:
[tex] \frac{1}{16} [/tex]
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Answer:
16 is correct
Step-by-step explanation:
Your welcome
A Set of 4 parallel line intersect with another 2 lines set of 5 paralel lines . how many parallelograms are formed
question this rectangular prism was built with cubes that each have a volume of one cubic centimeter. what is the volume of the rectangular prism?'
The volume of the rectangular prism is 400 cubic centimeters which we can calculate using formula: Volume = L * W * H
The volume of rectangular prism can be computed by simply multiplying their dimensions. If the rectangular prism was built with cubes that each have a volume of one cubic centimeter, then the volume of the rectangular prism can be calculated by multiplying the number of cubes in each dimension.
Let's assume that the rectangular prism has a length of "L" cubes, a width of "W" cubes, and a height of "H" cubes. Then, the volume of the rectangular prism can be calculated as follows:
Volume = L * W * H
Each cube has a volume of one cubic centimeter, so the volume of the rectangular prism is equal to the number of cubes it contains. In other words, if the rectangular prism has 10 cubes along its length, 5 cubes along its width, and 8 cubes along its height, then its volume would be:
Volume = 10 * 5 * 8 = 400 cubic centimeters
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a car dealership sells SUVs and passenger cars for a recent year 20 more suvs were sold than passenger cars if a total of 480 were sold determine the number of each type of vehicle sold
if a total of 480 were sold then the number of each type of vehicle sold is,
250 SUVs230 passenger carsWhat is an Equation ?An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.
For example, 3x+2y=0.
Types of equation
1. Linear Equation
2. Quadratic Equation
3. Cubic Equation
Given that,
A car dealership sells SUVs and passenger cars
the number of each type of vehicle sold = ?
Let x be the number of passenger cars sold.
Then, the number of SUVs sold = x + 20
The combined total of the two types of vehicles sold was 480, so we can write an equation:
x + (x + 20) = 480
Expanding the right side:
2x + 20 = 480
Subtracting 20 from both sides:
2x = 460
Dividing both sides by 2:
x = 230
The number of SUVs sold = 230 + 20
= 250
So, 230 passenger cars were sold and 250 SUVs were sold.
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Take a moment to review classifying polynomial expressions  then classify each polynomial based on its degree and number of terms .  drag the descriptions to the correct location on each table. Each description can be used more than once Polynomial 5x, -7, x^2+4, x^2-3x + 11, 2x-9 liner, quadratic, constant, monomial, binomial, trinomial
Answer:
5x linear monomial
-7 constant monomial
x^2+4 quadratic binomial
x^2-3x+11 quadratic trinomial
2x-9 linear binomial
Step-by-step explanation:
Linear indicates a line, the power of x in the equation is 1 (which we never write the power one, so it looks like just x)
Quadratics have an x to the power of 2
A constant is a plain number with no variable.
The prefixes mono-, bi-, and tri- can help you with these. Mono- means one. Monomials have one term, such as 5x or -7
Bi- means two. Binomials have two terms such as x^2+4 or 2x-9.
Tri- means three. Trinomials have three terms such as x^2-3x+11.
what is the rate of change of the function y=3x+3
The rate of change of the function y=3x+3 is 3
How to determine the rate of changeFrom the question, we have the following parameters that can be used in our computation:
y = 3x + 3
The above function is a linear function
A linear function is represented as
y = mx + c
Where
m = slope = rate of change
Using the above as a guide, we have the following:
rate of change = 3
Hence, the rate of change is 3
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Suppose the heights (in inches) of adult males in a country are normally distributed with a mean of 68 and a standard deviation of 2. Find the percent of men who are no more than 64 inches tall. What is the % of the men in the country are no more than 64 inches tall.
Answer:
So, about 2.28% of men in the country are no more than 64 inches tall.
Step-by-step explanation:
First, we need to standardize the value of 64 inches to a z-score:
z = (64 - 68) / 2 = -2
We can use a standard normal distribution table or a calculator to find the percentage of men who are no more than 64 inches tall:
P(Z ≤ -2) = 0.0228
1. Let the angle between two unit vectors u and v be 3.14/3 Then determine ||u + v||
2. Determine the value (s)of k such that the system x - 3z = -3 2x + ky-z = -2 x + 2y + kz = 1 has i. unique solution ii. No solution iii. Infinite solution
3. Determine the eigen value (s) and the corrosponding eigen vector (s) of
2 1 -1
3 2 -3
3 1 -2
4. Let f(x) be a polynomial of degree 4 with roots 1,2,3,4 and leading coefficient 1 and g(x) be a polynomial of degree 4 with roots 1, 1/2,1/3,1/4 and leading coefficient 1. Then find lim 1 f(x)/g(x)
Answer:
If the angle between two unit vectors u and v is 3.14/3, then using the law of cosines, ||u + v||^2 = 2 + 2cos(3.14/3) = 2 + 2(0.5) = 3. Hence ||u + v|| = sqrt(3).
To find the value of k such that the system has a unique solution, no solution, or an infinite number of solutions, we can use the determinant of the coefficient matrix. If the determinant is nonzero, then the system has a unique solution. If the determinant is zero and the system of equations is inconsistent, then the system has no solution. If the determinant is zero and the system of equations is consistent, then the system has an infinite number of solutions. In this case, the determinant of the coefficient matrix is zero, which implies that the system has an infinite number of solutions.
The eigen values and eigen vectors of the matrix can be found by solving the characteristic equation, which is obtained by det(A - λI) = 0, where A is the matrix and I is the identity matrix.
For the matrix
2 1 -1
3 2 -3
3 1 -2
the characteristic equation is
(2 - λ)(3 - λ) - 3 = 0
which gives us λ = 1 and λ = 3 as the eigen values.
The corresponding eigen vectors can be found by solving the system of equations (A - λI)x = 0, where x is the eigen vector.
For λ = 1, the eigen vector is (1, -1, 1).
For λ = 3, the eigen vector is (-1, 2, 1).
If f(x) is a polynomial of degree 4 with roots 1, 2, 3, 4 and leading coefficient 1, and g(x) is a polynomial of degree 4 with roots 1, 1/2, 1/3, 1/4 and leading coefficient 1, then the limit of 1/f(x)/g(x) as x approaches infinity does not exist. This can be seen by noting that f(x) and g(x) both grow without bound as x grows without bound, so the ratio of the two polynomials also grows without bound.
Which expression is a factor of -2x2 - 11x - 20
Answer:
no real factors
Step-by-step explanation:
-2x² - 11x - 20
try use the first 3 answers as factor, you'll see non works.
Can someone help? CROWN FOR BEST
Can you write me a quantitative survey or simulation question(s)? Making it a little bit complex and not too simple?
This is relating to probability and statistics and I have to answer and do data on them.
If you write a very good one you get a crown!! but it must be well written and a good question not just how much cars are there each morning?
The question is:
How many Syrian citizens choose to leave the country every year for better opportunities?
What is a quantitative survey?A survey that is collected through the facts and numbers from the data is a quantitative survey.
We have to write a quantitative survey or simulation question(s)?
For that,
we will form the variable and target group.
The question:
How many Syrian citizens choose to leave the country every year for better opportunities?
Variable: Number of citizens looking for better opportunities
Target Group: Syrian citizens.
Hence, the question is given above.
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Curtis wears a uniform number that rounds to 50 to the nearest ten and 0 to the nearest hundred. What is the least uniform number that curtis can have
Least number of uniform = 45
What is rounding numbers?Rounding a number means the process of making a number simpler such that its value remains close to what it was. The result obtained after rounding off a number is less accurate, but easier to use. While rounding a number, we consider the place value of digits in a number.
Given,
Curtis wears a uniform number that rounds to 50 to the nearest ten and 0 to the nearest hundred.
Whole numbers, that can be rounded to 50 to the nearest ten are
45, 46, 47, 48, 49, 50, 51, 52, 53, 54
Smallest number is 45
Hence, 45 is the least uniform number Curtis can have.
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Identify the correct graph of the system of equations. 3x − y = 12 x + 4y = 4
more information needed. no graphs to choose.
no multiple choice given..
in the fall of 2014, 1 U.S. dollar was worth 1.10 canadian dollars. an automobile in toronto sells for 26,000 canadian dollars. you found the same car on sale for 23,000 U.S. dollars on the internet. Which is the better buy?
This would be in contemporary math, converting fractions.
A car is through internet is better to buy.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
In the fall of 2014,
1 U.S. dollar = 1.10 Canadian dollars.
Here, An automobile in Toronto sells for 26,000 Canadian dollars.
And, The same car on sale for 23,000 U.S. dollars on the internet.
Thus, The cost of car on internet is,
⇒ 23,000 U.S. dollars
⇒ 23,000 × 1.10 Canadian dollars.
⇒ 25,300 Canadian dollars.
Thus, A car is buy through internet is better to buy.
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Determine the monthly principal and interest payment for a 15-year mortgage when the amount financed is $75,000 and the annual percentage rate (APR) is 8.0%.
The monthly principal and interest payment is $_____?
(Round to the nearest cent as needed.)
The monthly principal and interest payment is $916.6.
What is simple interest?We know simple interest (SI) is given by SI = (p×r×t)/100, where
p = principle, r = rate in percentage, and t = time in years.
From the given information SI = (75000×8×15)/100.
SI = 750×8×15.
SI = $90000.
Therefore, A = P + SI = 75000 + 90000 = $165000.
In 15 years there is 15×12 = 180 months.
Therefore, the monthly payment is,
= $(165000/180).
= $916.6
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Aidan and Bella each plan to open a savings account. Aidan starts with $90 and plans to save $20 every month. Bella starts with $15 and plans to save $35 every month.
Aidan and Bella will have the exact same amount of savings in 5 months.
What are simultaneous equations?We know two simultaneous equations have a unique solution when they intersect at a point,
when they are parallel they have no solution and when they are coinciding they have an infinite no. of solutions.
From the given information, Let the number of months be 'm'.
And, The two equations are 90 + 20x and 15 + 35x.
Therefore, The number of months in which they will have the same amount of savings would be,
90 + 20x = 15 + 35x.
75 = 15x.
x = 5.
So, In 5 months they will have the same amount of savings.
Q. Aidan and Bella each plan to open a savings account. Aidan starts with $90 and plans to save $20 every month. Bella starts with $15 and plans to save $35 every month, in which month they will have the same amount of savings?
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Shelter A has a capacity of 300 beds and is 20% occupied. Shelter B is 60% occupied. The ratio of the occupancy of Shelter A to Shelter B is 1 : 15. How many beds are in Shelter B?
Answer:
1,500 beds
Step-by-step explanation:
Occupancy rate shelter A = 300 x 20/100 = 60
Let capacity of shelter B be X
60% occupancy ==> 60/100 x X = 0.6X
Occupancy rate of A to rate of B is 1: 15 can be expressed as fraction 1/15
Therefore
60/0.6X = 1/15
1 x 0.6X = 60 x 15
0.6X = 900
X = 900/0.6 = 1,500 beds
Use the simple interest formula to determine the missing value.
p = ? r = 6% t = 3 months i= 21$
Answer:
p = 1,400
Step-by-step explanation:
Simple Interest Formula:In the simple interest rate formula, each year the same amount of interest is applied, as it's based off the initial amount invested and the interest rate.
[tex]I=P*r*t[/tex]
Where "r" is the interest rate, "t" is time, and "p" is the principle amount, or initial amount invested.
We're given the following values:
r = 6% = 0.06t = 3 monthsi = 21Now the only thing is generally speaking, interest is applied annually rather than monthly. So we would need to convert the 3 months into years, which we can do by dividing by 12, giving us: 0.25 years
So we actually have: t = 0.25 years
Now from here we can plug in known values, and leave anything we don't know alone. So we start with our initial formula of:
[tex]I=P*r*t[/tex]
Now from here we plug in i = 21, t = 0.25, r = 0.06 and leave "P" as "P"
[tex]21=P*0.25*0.06[/tex]
Now let's simplify the multiplication on the right side:
[tex]21 = 0.015P[/tex]
Divide both sides by 0.015:
[tex]1,400=P[/tex]
And now we have our missing value!
Find mLY and WY.
И
12
7 in.
7 in.
60°
X
Look at the image below, can anyone help me?
Answer:
∠ Y = 60° , WY = 7 in
Step-by-step explanation:
the sides WX and YX are congruent then the triangle is isosceles with base angles congruent, that is
∠ Y = ∠ W = (180 - 60)° ÷ 2 = 120° ÷ 2 = 60°
Since all 3 angles in the triangle are congruent , all 60° then the triangle is equilateral with 3 congruent sides, then
WY = 7 in
Find the quotient.
42,543 divided by 87
Answer:489
Step-by-step explanation:just divide 42,543 by 87
Answer489 I hope this helps
Step-by-step explanation:
The answer is 489 use a calculator
Pls help me figure it out
The volume of the concrete required to be poured for a rectangular prism floor slab are;
11. 5 1/3 cubic yards
12. 74 2/27 cubic yards
What is a rectangular prism?A rectangular prism is a polyhedron that consists of six rectangular faces, in which the adjacent faces are perpendicular and opposite faces are parallel.
11. The dimensions of the floor slab = 18' × 24' × 4''
Where the shape of the slab is a rectangular prism, we get;
Width of the floor slab = 24 feet
Length of the floor slab = 18 feet
Height of the floor slab = 4 inches
4 inches = (1/3) ft
The volume of the cement is therefore;
V = 24 ft × 18 ft × (1/3) ft = 144 ft³
The volume of the concrete required to pour a floor slab of the dimensions: 18' × 24' × 4'' is 144 cubic feet
1 yard = 3 feet
The dimensions of the slab are therefore;
Length = 24/3 yards = 8 yards
Width = 18/3 yards = 6 yards
Height = (1/3)/3 yards = (1/9) yards
The volume of the slab = 8 yards × 6 yards× 1/9 yard = 16/3 cubic yards
Volume of the concrete slab = 16/3 cubic yards = 5 1/3 cubic yards12. The dimensions of the slab are;
Length of the slab = 80 feet = 80/3 yards
Width of the slab = 60 feet = 60/3 yards = 20 yards
Height of the slab = 5 inches = 5/12 ft = 5/(12 × 3) yard = 5/36 yard
The volume of the concrete slab is therefore;
(80/3) yards × 20 yards × (5/36) yard = 74 2/27 cubic yards
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A student decides to solve at least 20 math problems every day to better their grade if they self and math problems every day which inequality is true
For the given condition the correct inequality is,
⇒ x ≥ 20
Where, x represent the number of questions.
What is Inequality?A relation by which we can compare two or more mathematical expression is called an inequality.
Given that;
A student decides to solve at least 20 math problems every day to better their grade if they self and math problems every day.
Let number of questions done by a student = x
So, The inequality for the given condition is,
⇒ x ≥ 20
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A standard piano keyboard has 88 different keys. Find the probability that a cat, jumping on 7 keys in sequence and at random (possibly with repetition), will strike the first seven notes of Beethoven's Fifth Symphony. (Leave your answer as a formula.)
The probability that a cat, jumping on 7 keys in sequence and at random (possibly with repetition), will strike the first seven notes of Beethoven's Fifth Symphony is; P = 2.45 * 10⁻¹⁴
How to find the probability of selection?The parameters expressed are;
Number of Piano Keyboard keys = 88
The following steps can be used in order to determine the probability that a cat, jumping on 7 keys in sequence and at random, will strike the first four notes of Beethoven's Fifth Symphony:
Step 1 - The four notes of the piano are 3 LA's and 1 REb.
Step 2 - The probability that the first key is LA is 1/88.
Step 3 - The probability that the second key is LA is 1/88.
Step 4 - The probability that the third key is LA is 1/88.
Step 5 - The probability that the key is REb is 1/88.
Step 6 - So, the probability that a cat, jumping on 4 keys in sequence and at random, will strike the first four notes of Beethoven's Fifth Symphony is:
P = 1/88 * 1/88 * 1/88 * 1/88 * 1/88 * 1/88 * 1/88
P = 2.45 * 10⁻¹⁴
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median home price in the west fell from 203400 to 192300 find the percent decrease
Answer:
Step-by-step explanation:
I took your points looooser hahahaha
Find the outlier of the data 28,18,26,20,22,25,21,22,65,28,17.
Answer: The outlier of the data is 65! Hope this helps you!
In a group of 600 college students, 183 are math majors, 366 are engineering majors, and 56 are dual majors in both math and engineering.
(a) What is the probability that a randomly selected student is neither a math major nor an engineering major?
(b) What is the probability that a randomly selected student from the group is only an engineering major? Round answer to 4 decimal places.
a. probability of neither a math major nor an engineering major is: 0.1783
b. probability is only an engineering major: 0.5167
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. The probability of an occurrence is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty.
Given that,
n(S) = 60
n(math) = n(M) = 183 ⇒ P(M) = n(M)/ n(S) = 183/600
n(engineering) = n(E) = 366 ⇒ P(E) = n(E)/ n(S) = 366/600
n(M∩E) = 56
P (M∩E) = n(M∩E) / n(S) = 56/600
a) probability of neither a math major nor an engineering major is:
P (M' ∩ E') = P (M∪E)'
P (M' ∩ E') = 1 - P (M∪E)
P (M' ∩ E') = 1 - [P(M) + P(E) - P(M∩E)]
P (M' ∩ E') = 1 - [183/600 + 366/600 - 56/600]
P (M' ∩ E') = 0.1783
b)
probability is only an engineering major:
P(E - M) = P(E) - P(M∩E)
P(E - M) = 366/600 - 56/600
P(E - M) = 0.5167
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If a rock is thrown from the ground with an initial velocity of 80 feet per second, then
a) v(t) = -32t + 80 feet/second and a(t)= -32 feet/second²
b. t = 3 seconds.
c. 24 feet/second > 0).
d. the time at which the rock reaches its highest height is 2.5 seconds and 80 feet respectively.
e. the acceleration is given by a(2.5) = -32 feet/second²
How to calculate?The velocity, v(t), of the rock is given by the derivative of the position function s(t) with respect to time,
v(t) = ds(t)/dt = -32t + 80 feet/second.
The acceleration, a(t) = dv(t)/dt = -32 feet/second²
b) v(3) = -32*3 + 80 = 24 feet/second.
This quantity represents the velocity of the rock at t = 3 seconds.
c) At t = 3 seconds, the rock is rising up because the velocity is positive (v(3) = 24 feet/second > 0).
d) the time at which the rock reaches its highest height,
v(t) = 0, we get -32t + 80 = 0, so t = 80/32 = 2.5 seconds.
The height of the rock will be found using the position function s(t), so s(2.5) = -16(2.5)^2 + 80(2.5) = 80 feet.
e) At the highest height, the velocity of the rock is 0, so the acceleration is given by a(2.5) = -32 feet/second².
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If a rock is thrown upward on the planet Mars with a velocity of 17 m/s, its height (in meters) after t seconds is given by H = 17t - 1.86t2.
The velocity of the rock after one second is v(1)=13.28 m/s.
The given equation is
H(t) = 17t - 1.86t² ------(1)
velicity=17 m/s.
(a) the velocity of the rock after one second will be:
v(t) = dH/dt = 17-3.72t
v(1) = 17 - 3.72(1)
v(1)= 13.28 m/s
(b)the velocity of the rock when t=a
v(a) = 17 - 3.72a.
(c)
The rock hits the surface when H(t) = 0
17t - 1.86t² = t(17-1.86t)=0
⇒ t= 0 or 17-1.86t = 0
The first case is launch, the second is returning to the ground.
17 - 1.86t = 0
17= 1.86t
t = 17/1.86
t ≅9.139s
(d)
v at surface = v at the time from part (c).
v(9.139) = 17- 3.72(9.139)
v(9.139) ≅ -17 m/s
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Full question:
if a rock is thrown upward on the planet mars with a velocity of 17 m/s, its height (in meters) after t seconds is given by H=17t-1.86t²
(a) find the velocity of the rock after one second
(b) find the velocity of the rock when t=a
(c) when will the rock hit the surface
(d) with what velocity will the rock hit the surface?