Distance travelled by the particle from time t = 0 to t = 3 in x-direction and y-direction is 27 units and 54 units respectively.
How to get distance/displacement using velocity?
Velocity is defined as the rate of change of position or the rate of displacement.Velocity = dx/dt that is change in position x with respect to time t.Integration is anti derivative for any quantity. Hence to get displacement using velocity, integrate to with respect to 't' and substitute values of t accordingly.According to given data:
A particle moves with velocity (dx)/(dt) = 3t² in x- direction
and (dy)/(dt) = 12t in y-direction
Integrating both sides of these derivatives with respect to t
x= ∫3t² dt = (3t³)/3 + A = t³ + A
where A is integration constant
y= ∫12t d t = (12t²)/2 + B = 6t² + B
where B is integration constant
At t = 0 we get x = A and at t = 3 we get x = 3³ + A = 27 + A.
Therefore, the difference in position of a from t = 0 t = 3 is
27 + A - (0 + A) = 27 units.
Similarly,
At t = 0 , we get y = B and at t = 3 we get
y = 6 * 3² + B = 54 + B
Therefore, the difference in position of y from t = 0 tot t = 3 is
54 + B - (0 + B) = 54 units.
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Is this the right answer?
Answer:
Step-by-step explanation:
Yeah you have the correct answer.
In the original line you solve for y where the slope is given -3.
Then it is up to you but I like using the point slope formula so I'll plug in the values and the result is the same as the picture.
y-y=m(x-x)
y-(-6)=-3(x-1)
-353.92 - (-283.56) -131.29
-353.92-(-283.56)-131.29= -20,165
Last year, the student population at Haley Elementary School was 360 students. After rezoning this year, the student population is 10% smaller. HOW MANY STUDENTS ATTEND HALEY ELEMENTARY THIS YEAR?
Answer: 324
Step-by-step explanation: 10% is the same as 1/10
360/10 is 36
360-36= 324
meaning 324 students now attend Haley elementary school <3
hope this helps <33
what is 2 +2
4+5
0+9
Answer:
Step-by-step explanation:
2+2=4
4+5=9
0+9=9
Answer:
4, 9 , 9 OR 4 + 9 + 9 = 22
Step-by-step explanation:
Creating a Function from a Mapping
The mapping shows a relationship between input and
output values.
Input
Activity
-5
SAING
2
40 Intro
Output
T? 7 NO
-3
-2
2
Which ordered pair could be removed to make this
relation a function?
O (-5,0)
-O (-1, -3)
O (4,-2)
O (6,-1)
Done
The ordered pair could be removed to make this relation a function is (4,-2).
What is an ordered pair?
An ordered pair is made up of the ordinate and the abscissa of the x coordinate, with two values given in parenthesis in a certain sequence.
The numeric values in an ordered pair can be integers or fractions.
Here,
A function is when each input has one output. So, for every x there is one y. The x values can not repeat.
But in the given value x is repeating so the ordered pair (4, -2) can be removed.
Hence, the ordered pair could be removed to make this relation a function is (4,-2).
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plseas help
There are 7 students in grade 11 and 15 students in grade 12 that are part of the VSS robotics club. A committee consisting of a president, vice president, media rep, and accountant is being chosen.
a. In how many ways could the panel be chosen if the president and vice president must be from different grades?
b. In how many ways could the panel be chosen if it must include at least one grade 11 student and at least one grade 12 student?
The number of ways to form the committees, using the Fundamental Counting Theorem, are given as follows:
a) President and vice from different grades: 79,800.
b) At least one from each: 141,960.
What is the Fundamental Counting Theorem?It is a theorem that states that if there are n independent trials, each with [tex]n_1, n_2, \cdots, n_n[/tex] possible results, the total number of outcomes is calculated by the multiplication of the factorials as presented as follows:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
For item a, there are two possible cases for the parameters, as follows:
[tex]n_1 = 7, n_2 = 15, n_3 = 20, n_4 = 19[/tex]: President from grade 11, vice from grade 12, the remaining two roles can be chosen from any student.[tex]n_1 = 15, n_2 = 7, n_3 = 20, n_4 = 19[/tex]: President from grade 12, vice from grade 11, the remaining two roles can be chosen from any student.Hence the number of ways is:
N = 7 x 15 x 20 x 19 + 15 x 7 x 20 x 19 = 79,800.
For item b, the total number of outcomes is obtained as follows:
N = 22 x 21 x 20 x 19 = 175,560.
The number of outcomes with only grade 11 students is:
N = 7 x 6 x 5 x 4 = 840.
The number of outcomes with only grade 12 students is:
N = 15 x 14 x 13 x 12 = 32760.
Hence the number of students with at least one of each is:
N = 175,560 - (840 + 32,760) = 141,960.
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Write the expression 3a+2y+5ay-2y-+-52-3y in simplest form. Then, answer the following questions
using complete sentences.
a. How many terms are in the simplified expression?
b. How many of the terms in the simplified expression are negative?
The simplified expression is 3a + 5ay - 3y -52 .
(a) There are 4 terms in the simplified expression
(b) there are 2 negative terms in the simplified expression .
In the question ,
the algebraic expression is given as 3a+2y+5ay-2y-52-3y
to simplify it , we first group them in like terms
the expression becomes .
= 3a [tex]+[/tex] 2y [tex]+[/tex] 5ay -2y - 52 -3y
= 3a + 5ay + 2y - 2y - 3y - 52
= 3a + 5ay - 3y -52
Part(a)
the number of terms in the simplified expression is 4 ,
Part(b)
as we can see that the terms -3y and -52 are negative
So , there are 2 negative terms in the expression.
Therefore , (a) There are 4 terms in the simplified expression
(b) there are 2 negative terms in the simplified expression .
The given question is incomplete , the complete question is
Write the expression 3a+2y+5ay-2y-52-3y in simplest form. Then, answer the following questions using complete sentences.
a. How many terms are in the simplified expression?
b. How many of the terms in the simplified expression are negative?
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what is the answer to
$224.50- $225.00
i already did calculator many different wayss
i will report wrong answers UNLESS you actually tried
Answer:_______________________________________________
-0.5
Answer:
224.50
-225.00
$0.50
- 50 cents
Pls help urgent someone hurry please
Proved that the triangle ABW ≅ triangle DCW
In the given question,
The length of WA = The length of WD
The measure of angle 5 = The measure of angle 7
Here we have to prove that one angle and two sides of the triangle ABW is equal to the one angle and two sides of the triangle DCW
Consider the triangle ADW,
In the triangle ADW the length of the WA is equal to the length of WD.
Therefore the measure of angle A is equal to the measure of angle D.
So in triangle ABW and the triangle DCW, one side and two angles are equal.
Therefore the triangle ABW and triangle DCW are congruent
Hence, proved that the triangle ABW ≅ triangle DCW
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7. In one week, Sabrina received 18 letters and
8 bills. What was the ratio of bills to letters?
What is the sum?
3
+
x+3x+3x+3
X
2
Mrs B invested $30,000, part at 5%, part at 8%. The total interest on the investment was $2100, how much did she invest at each rate?
(Please show working)
Answer:
$10,000 invested at 5%
$20,000 invested at 8%
Step-by-step explanation:
1. Let x = the amount of money invested at 5%, and y = the amount of money invested at 8%.
x + y = 30,000 (the total amount invested)
0.05x + 0.08y = 2,100 (the total interest earned)
2. Solve the system by whatever method you choose.
how do i factor (x + 2)^2 - (y - 2)^2???
The factor of the difference of two squares (x + 2)² - (y - 2)² is (x + y)(x - y + 4).
Difference of two squaresIf for any two squares say a² and b², then their difference a² - b² = (a + b)(a - b).
Given the two squares (x + 2)² and (y - 2)²
then their difference will yeild the factors derived as follows;
(x + 2)² - (y - 2)² = [(x + 2) + (y - 2)][(x + 2) - (y - 2)]
open brackets
(x + 2)² - (y - 2)² = (x + 2 + y - 2)(x + 2 - y + 2)
collect like terms
(x + 2)² - (y - 2)² = (x + y + 2 - 2)(x - y + 2+ 2)
so
(x + 2)² - (y - 2)² = (x + y)(x - y + 4)
Thus, by application of the rule of difference of two squares, we have the factors of (x + 2)² - (y - 2)² to be (x + y 2 - 2) and (x - y + 2+ 2).
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A person is selected at random. A is the event “the person selected earns more than $100,000 per year” and B is the event “the person selected earns more than $250,000 per year.”
The pairs of events, A and B, that are disjoint include option A and B.
What are disjoint events?It should be noted that disjoint events simony means the events that are mutually exclusive as they can't occur at the same time.
For option A, because a person can be either male or female but not both, events A and B are disjoint.
For B, because the person already earns more than $100,000, events A and B are not disjoint.
For C, because the sum of two dice cannot be three when one die is three, events A and B are disjoint.
Therefore, A and C are disjoint.
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Complete question
Which of the following pairs of events, A and B, are disjoint?
(a) A person is selected at random. A is the event "sex of the person selected is male" and B is the event "sex of the person selected is female."
disjoint / not disjoint
(b) A person is selected at random. A is the event "the person selected earns more than $100,000 per year" and B is the event "the person selected earns more than $250,000 per year."
disjoint / not disjoint
(c) A pair of dice are tossed. A is the event "one of the dice is a 3" and B is the event "the sum of the two dice is 3."
disjoint / not disjoint
The graph of g(x) is the graph of f(x)=x−2reflected across the y-axis. Which equation describes function g?
The required equation of g(x) for reflection of f(x)=x-2 across the y-axis is g(x)=-x-2.
What is reflection?Reflection is basically a mirror image of the shape, in which the image of a given figure changes accordingly to a given line or axis.
Given that,
f(x)=x-2
To find the required equation for g(x) that is reflected across the y-axis, Use reflection property,
According to reflection property,
Reflection Across the y-axis, the x change in -x and the remaining part of the equation remains same.
The equation of f(x) changes in g(x) as g(x)=-x-2,
So, the equation of g(x)=-x-2 .
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Simplify the fraction
Answer:
Step-by-step explanation:
Define rational number in your own words.
Answer:A rational number is a number thats a quotient or fraction
Step-by-step explanation:
4\6 would be a rational number 8 over 4 as well.
What will be the rule for a negative fraction?
Maybe like -m/n instead of just m/n?
The generalized rule of the indices to be negative fraction can be written as [tex]a^{-m/n} =(\sqrt[n]{a})^{-m}[/tex].
What is the law of indices?Index (indices) in Maths is the power or exponent which is raised to a number or a variable.
An algebraic expression is a quantity made up of symbols and processes + - / and multiplication Expressions utilizing indices are made simpler using the laws of indices.
Let's consider a negative fraction exponent as, [tex]a^{-m/n}[/tex]
[tex]a^{-m/n}=1/a^{m/n}[/tex]
Since,[tex]a^{-m/n} =(\sqrt[n]{a})^{-m}[/tex]
Therefore, the above expression converts as,
[tex]a^{-m/n} =1/(\sqrt[n]{a})^{-m}[/tex]
[tex]a^{-m/n} =(\sqrt[n]{a})^{-m}[/tex]
Hence "The generalized rule of the indices to be negative fraction can be written as [tex]a^{-m/n} =(\sqrt[n]{a})^{-m}[/tex].".
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To determine the size of the county's moose population, naturalists catch 65 moose, tag them and
then set them free. Months later, 48 moose are caught, of which 14 have tags.
The estimated size of the moose population is___?
. (Round to nearest whole moose.)
The size of the moose population, 65 + (48-14)=99.
What is unitary method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. What can be values and units.Let's say you go to the store to buy six apples. You are informed by the shopkeeper that he is offering 10 apples for Rs 100. In this instance, the value and the units are the price of the apples.Recognizing the units and values is crucial when using the unitary technique to a problem.Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things. We are aware of the quantity of apples and the amount of money in the aforesaid problem.acc to our question-
naturalists have = 65 moosetheycatch and tag = 48set them free and catch them later,= 14now total moose= 65 + (48-14)99learn more about unitary method click here:
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A motorboat maintained a constant speed of 11 miles per hour relative to the water in going 10 miles upstream and then returning. The total time for the trip was 5.5 hours. Use this information to find the speed of the current.
The speed of the current is 9 miles per hour
How to determine the speed of the current?
Given that: the motorboat maintained a constant speed of 11 miles per hour relative to the water in going 10 miles upstream and then returning.
Total time = 5.5 hours
Let s = speed of the current
speed downstream relative to land = 11 + s
speed upstream relative to the land = 11 - s
speed = distance/time
time = distance/speed
upstream time + downstream time = total time
10/11-s + 10/11+s = 5.5 (find LCM of 11-s and 11+s)
10(11+s) + 10(11-s) /(11-s)(11+s) = 5.5
110+10s+110-10s /(11-s)(11+s) = 5.5
220 = 5.5(11-s)(11+s)
220 = 5.5(121 - 11s + 11s - s²)
220 = 5.5(121 - s²)
220 = 665.5 - 5.5s²
5.5c² = 665.5 - 220
5.5c² = 445.5
s² = 445.5/ 5.5
s² = 81
s = √81 = 9
Therefore, the speed of the current is 9 miles per hour
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A stock’s price fluctuations are approximately normally distributed with a mean of $26.94 and a standard deviation of $3.54. You decide to sell whenever the price reaches its highest 20% of values. What is the highest value you would still hold the stock?
The highest value you would still hold the stock is $23.97
How to determine the highest value you would stock??From the question, the given parameters about the distribution are
Mean value of the set of data = $26.94
Standard deviation value of the set of data = $3.54
Proportion = Highest 20%
This means that the p value is
p = 20%
Express as decimal
p = 0.2
At a p value of 0.2, the z-score is
z = -0.84
The z-score of the data value is calculated using the following formula
z = (x - mean value)/standard deviation
Substitute the given parameters in the above equation
-0.84 = (x - 26.94)/3.54
Cross multiply in the above equation
So, we have
x - 26.94 = -0.84 * 3.54
Evaluate the products
x - 26.94 = -2.97
Add 26.94 to both sides of the equation
So, we have the following representation
x = 26.94 -2.97
Evaluate the difference
x = 23.97
Hence, the highest value is 23.97
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14 subtracted from the product of x and -3 is 25
Answer:
14-3x=25
Step-by-step explanation:
-3x=25+14
-3x=39
-3 -3
x = -13
There are 10 applicants applying for 3 positions Hostess server and busier how many ways
The number of ways to select 3 position out of 10 applicant is 120 ways
What is combination?Combinations implies the selection of things from a given set of things. In this case, we intend to select the objects. Combination formula is illustrated as:
nCr = n! / ((n – r)! r!)
n = the number of items.
r = how many items are taken at a time.
Since there are 10 applicants applying for 3 positions. This will be:
= 10! / (10 - 3)!3!
= 10! / 7!3!
= 10 × 9 × 8 / 3 × 2
= 120
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Evaluate the given function for f(2).
Answer:
3
Step-by-step explanation:
You want the value of f(2) for the graphed function.
Function valueThe value of the function f(a) is the y-coordinate of the point that has 'a' as its x-coordinate.
Finding the function value requires you locate x=a on the horizontal axis. Where the graph crosses that vertical line, the y-coordinate is the function value.
ApplicationHere, the vertical line x=2 meets the function graph at the dot with coordinates (2, 3). The y-value there is 3, so ...
f(2) = 3
Answer: [D]: " 3 " ; [that is; f(2) = 3 ].
____
We are asked to:
Evaluate the given function for f(2) ; within the given image.
By examination of the graph, we can verify that the graph is, in fact, a function—by using the vertical line test.
We find that no value for x shares more than one y-value; which means that the graph is a function.
____
Note that for a function: f(x) = y .
So; To find f(2) :
____
Note: f(2) = the "[ y - coordinate/corresponding value for y ]" ;
⇒ when " x = 2 ".
So; looking at the graph: We see that when " x = 2 " ; → " y = 3 " .
→ {Examine the co-ordinate/point: (2, 3) —that is part of the graph.}
So; f(2) = 3 ; which is Answer choice: [D]: " 3 ."
______
Hope this is helpful to you. Best wishes!
______
Rohan bought some tiles for a kitchen floor. 3/5 of the tiles were white, 1/4 of the
remainder were yellow, and the rest were blue. There were 60 more white
tiles than blue tiles. Each tile cost $3. What was the total cost of the tiles?
The cost the tiles are = $182.55
what is unitary method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. What can be values and units.Let's say you go to the store to buy six apples. You are informed by the shopkeeper that he is offering 10 apples for Rs 100. In this instance, the value and the units are the price of the apples. Recognizing the units and values is crucial when using the unitary technique to a problem.Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things. We are aware of the quantity of apples and the amount of money in the aforesaid problem.acc to our question-
white tiles =W = 1/4
3/5 = yellow
each tile costs= $3
= 0.25+ 0.6+ 60
= 60.85*3
$182.55
hence,The cost the tiles are = $182.55
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How does knowing the x-intercepts and the vertex of a
function help you graph a quadratic function?
A graph of a quadratic function is a parabola, making an equation of a parabola with help of an x-intercept and vertex can be formed.
The graph is a demonstration of curves that gives the relationship between the x and y-axis.
Here,
With the help of the vertex and the x-intercept, the equation of the parabola can be formed which helps to graph a quadratic function because the equation of the parabola resembles the quadratic function,
Thus, a graph of a quadratic function is a parabola, making an equation of a parabola with help of an x-intercept and vertex can be formed.
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If the pediatric floor of the hospital has 165 beds how many rooms are there if each room holds 3 beds?
PLEASE HELP
19- 4x + x² can be written in the form
(x + a)² + b, where a and b are numbers.
Work out the values of a and b.
Step-by-step explanation:
so, let's do the multiplications and squaring. and then compare the result with the target.
(x + a)² + b = x² + 2ax + a² + b
and the original expression is
x² - 4x + 19
x² = x² done
2ax = -4x
2a = -4
a = -2
a² + b = 19
(-2)² + b = 19
4 + b = 19
b = 15
so, the result is
(x - 2)² + 15
Answer: (x-2)^2+15
Step-by-step explanation:
Given x^2-4x+19
=here b=-4 and c=19
B=b/2=-4/2=-2
C=c-B^2=19-(-2)^2=19-4-15
so
(x-B)^2+C
(x-2)^2+15
3. Round 134.76821 to the nearest hundredth.
Answer:
134.77
Step-by-step explanation:
Round 134.76821 to the nearest hundredth
by placing each number in reference to what they represent.
1 - hundreds
3 - Tens
4 - units
.7=Tenth
.76=Hundredth
.768=Thousandth
.7682=Ten Thousandth
.76821= Hundred Thousandth
Nearest hundredth will be
134.[76]821
since 2,1 are both round down numbers they will produce approximately 0
since 8 is a round off number it will produce approximately 10
134.77000
or 134.77
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Madison needs to order some new supplies for the restaurant where she works. The restaurant needs at least 474 spoons. There are currently 246 spoons. If each set on sale contains 6 spoons, use the drop-down menu below to write an inequality representing s, the number of sets of spoons Madison should buy.
38 sets
474 - 246 = 228
228 ÷ 6 = 38
