Answer: y = -3x + 5
Step-by-step explanation:
We are given that the line passes through the point (1,2) and has a slope of -3. To find the y-intercept, we can use the point-slope form of a line:
y - y1 = m(x - x1)
where (x1, y1) is the point the line passes through.
Substituting the values we have:
y - 2 = -3(x - 1)
Expanding the brackets and rearranging:
y - 2 = -3x + 3
y = -3x + 5
Therefore, the equation of the line is y = -3x + 5, in slope-intercept form.
Colton is building a new shed for his backyard. The shed has a right rectangular prism for the base and triangular prism for the roof component. Colton included the dimensions of the shed in his diagram.
1.) How much can Colton store inside the new shed? Explain your reasoning.
2.) Colton wants to paint the outside of the shed including the door to match his house. Explain how much paint Colton will need to paint the shed.
3.) A gallon of paint covers 200 square feet and cost $16.99.
-How many cans of pain are needed?
-How much will it cost Colton to paint the shed?
The volume Colton store inside the new shed is 640 cubic feet.
We are given that;
length=10, width=8, height=6
Now, we can calculate the volumes of each part:
Volume of base prism = lwh Volume of base prism = (10)(8)(6) Volume of base prism = 480 cubic feet
Volume of roof prism = Bh Volume of roof prism = (0.5)(8)(4)(10) Volume of roof prism = 160 cubic feet
Volume of shed = Volume of base prism + Volume of roof prism Volume of shed = 480 + 160 Volume of shed = 640 cubic feet
Therefore, by the given prism the answer will be 640 cubic feet.
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Which of the following transformations maps triangle JKL to triangle MNO? What is the relationship between the triangles? Reflect triangle JKL over the x-axis; triangle JKL and triangle MNO are similar Rotate triangle JKL 180° clockwise about the origin; triangle JKL and triangle MNO are congruent Translate triangle JKL left 1 unit and downward 10 units; triangle JKL and triangle MNO are congruent Dilate triangle JKL by a scale factor of 2 from the origin; triangle JKL and triangle MNO are similar
Translate triangle JKL left 1 unit and downward 10 units; the triangles are congruent
Describing the transformations that map triangle JKL to triangle MNO?From the question, we have the following parameters that can be used in our computation:
Triangle JKL to triangle MNO
From the figure, we can see that translating the triangle JKL left 1 unit and downward 10 units would give triangle MNO
The above also implies that the triangles are congruent
This is because translation is a rigid transformation
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Hanna spells her name using 5 letter tiles. She places the tiles in a bag.
She randomly draws a tile, and then she draws a second tile from those
that remain. What is the probability that Hanna draws two tiles having
the same letter?
A. 2/15
B.1/6
C.1/5
D.4/5
Answer:
I'd assume D
Step-by-step explanation:
Hanna has 5 letters and 4 are 2 letters that are the same therefore 4 letter out of 5 chance
barb covered each of the playroom "s for walls with a large piece of white board for kids to draw on. each board measured 7ft × 3ft. what was the total area of all 4 board?
The total area of all four white boards is 84 square feet, obtained by multiplying the dimensions of one board (7ft × 3ft) by the number of boards (4)
What is area?Area is the measure of the size of a two-dimensional surface, usually expressed in square units such as square inches, square feet, or square meters.
What is square feet?Square feet is a unit of area commonly used to measure the size of a surface in the US customary and Imperial measurement systems. One square foot is equal to the area of a square with sides of one foot in length.
According to the given information:
Barb covered 4 walls with white boards, and each board measured 7ft × 3ft. To find the total area of all 4 boards, we need to multiply the area of one board by the number of boards:
Total area = area of one board × number of boards
Total area = (7 ft × 3 ft) × 4
Total area = 21 ft² × 4
Total area = 84 ft²
Therefore, the total area of all four white boards is 84 square feet.
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What is the volume of the sphere? Use 3.14 for pi. Round to the nearest whole number.
423 m³
423 m³
2144 m³
2144 m³
1582 m³
1582 m³
985 m³
Write an equation in slope-intercept form for the line with a slope -4/3 and a y-intercept 9.
Answer:
[tex]y=\frac{-4}{3}x+9[/tex]
Step-by-step explanation:
[tex]y=slope*x+y intercept[/tex]
Given a slope of -4/3 and y-intercept of 9, the equation will be:
[tex]y=\frac{-4}{3}x+9[/tex].
I will give brainliest and ratings if you get this correct
The firm should produce 4 units of the first good and 2 units of the second good to maximize its profits.
How to calculate the valueProfit = 15Q1 + 18Q² - (-2Q1² + 2Q1Q2+ 3Q2²)
Simplifying, we get:
Profit = 2Q1² - 2Q1Q2 - 3Q2² + 15Q1 + 18Q2
Now, we need to find the values of Q1 and Q2 that maximize this profit function. we need to take the partial derivatives of the profit function with respect to Q1 and Q2, and set them equal to zero:
dProfit/dQ1 = 4Q1 - 2Q2 + 15 = 0
dProfit/dQ2 = -2Q1 - 6Q2 + 18 = 0
Solving these equations simultaneously, we get: Q1 = 4 and Q2 = 2
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Select all of the equations that represents a nonlinear function.
The equations of nonlinear functions from the options are y = 3x^2 + 9x = 6 and y = x(3x + 10)
Selecting the equations of nonlinear function.From the question, we have the following parameters that can be used in our computation:
The list of options
As a general rule:
Nonlinear function are functions that have a degree not equal to 1
using the above as a guide, we have the following as nonlinear functions
y = 3x^2 + 9x = 6
y = x(3x + 10)
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HELP!!!! I need to know the Measure of Center and the Measure of spread to this set of variables please
The value mean of variable 1 is approximately 170.42 and the median is 153.75.
We are given that;
Variable 1 = 190,187,186,183,182,182,181,181,180,164,161,160,140,158,156,155,152.5,151
Now,
To Find the mean by adding up all the values and dividing by the number of values
Mean = (190 + 187 + 186 + 183 + 182 + 182 + 181 + 181 + 180 + 164 + 161 + 160 + 140 + 158 + 156 + 155 + 152.5 + 151) / 18 Mean = (3067.5) / 18 Mean ≈ 170.42
Find the median by arranging the values in ascending order and locating the middle value
Median = (140 ,151 ,152.5 ,155 ,156 ,158 ,160 ,161 ,164 ,180 ,181 ,181 ,182 ,182 ,183 ,186 ,187 ,190) Median = (152.5 + 155) / 2 Median = (307.5) / 2 Median = 153.75
Therefore, by mean and median answer will be 170.42 and 153.75.
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A rectangular retaining wall has an area of 36 square feet. The height of the wall is 5 feet less than it’s length. Find the height and length of the wall in feet.
Answer:
Length = 9 feet
Height = 4 feet
Step-by-step explanation:
Length = x
Height = x-5
36 = (x-5) * x
36 = x^2 - 5x
0 = x^2 - 5x - 36
Find the zeroes of the equation:
[tex]x^2-5x-36[/tex]
We get:
[tex]x= -4;\ x=9[/tex]
Since length cannot be negative, we choose "x = 9"
Therefore,
Length = x = 9
Height = x - 5 = 4
A number when rounded to the nearest 100 gives 1200. When rounded to the nearest 10 it gives 1250. What could be the number?
Answer:
1247
Step-by-step explanation:
the answer is 1247
I hope this helps
What is the qualificat
The probability that a student randomly chooses to play drums is 34.29%
The total number of students in seventh grade = 35
The number of students who choose drums in seventh grade is 14
The total number of students in eighth grade = 35
The number of students who choose drums in eighth grade is 10
Total number of students who play drums = 14 + 10 = 24
Total number of students = 35 + 35 = 70
The probability that a student randomly chooses to play drums is:
Probability = Total number of students who play drums / Total number of students
Probability = 24 / 70
Probability = 0.342857 (rounded to 6 decimal places)
probability = 34.29%
Hence, the probability that a student randomly chooses to play drums is 34.29%
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Function f has a domain of _____
range of _____
the function approaches ________( y= 0, positive infinity, or negative infinity)
The domain and the range of the function are given as follows:
Domain: All real values.Range: y > 0.The function approaches y = 0 as x approaches positive infinity.
What are the domain and range of a function?The domain of a function is the set that contains all possible input values of the function, that is, all the values assumed by the independent variable x in the function.The range of a function is the set that contains all possible output values of the function, that is, all the values assumed by the dependent variable y in the function.More can be learned about the domain and the range of a function at https://brainly.com/question/2264373
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NEED HELP WILL GIVE BRAINLIEST AND 5 STARS I HAVE 20 MINUTES PLEASE HELP!
For this rational function, Use algebra to find the x intercepts and y intercepts.
Consider the function f(x) = (x² - 4)/(x - 2).
For x gives us x = -2 and x = 2 which are the x-intercepts of f(x) and we have f(0) = -4/2 = -2 which is the y-intercept of f(x)
What is meant by function?
A function is a mathematical rule that assigns a unique output value for each input value in a specified domain. It is a relationship between two or more variables that describes how one variable depends on the others.
What is meant by the x-intercept?
The x-intercept of a function is the point where the graph of the function intersects the x-axis. It is the value of the input variable (usually denoted as x) that makes the output of the function equal to zero.
According to the given information
Consider the function f(x) = (x² - 4)/(x - 2). To find the x-intercept, we set f(x) = 0 and solve for x. We get (x² - 4)/(x - 2) = 0 which means that x² - 4 = 0 since division by zero is undefined. Solving for x gives us x = -2 and x = 2 which are the x-intercepts of f(x). To find the y-intercept, we set x = 0 and solve for y. We get f(0) = -4/2 = -2 which is the y-intercept of f(x)
The complete question is:
For this rational function, Use algebra to find the x-intercepts and
y-intercepts. The given function is f(x) = (x² - 4)/(x - 2)
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If the Banquete Middle School sells 120 drinks during breakfast on Thursday, which
prediction for Thursday is NOT supported by the data in the table?
The number of cartons of apple juice sold will be 6 more than the number of
cartons of orange juice sold.
The number of cartons of apple juice sold will be 3 times the number of cartons
of orange juice sold.
The number of cartons of chocolate milk sold will be 4 times the number of
cartons of white milk sold.
There will be a total of 86 cartons of milk sold.
If the Banquete Middle School sells 120 drinks during breakfast on Thursday, the prediction for Thursday that is NOT supported by the data in the table is option B: "The number of cartons of apple juice sold will be 3 times the number of cartons of orange juice sold."
What is the prediction?Ten boxes of apple juice and seven boxes of orange juice were purchased on Wednesday. In order for this forecast to come to truth, the sale of 21 apple juice cartons and 7 orange juice cartons on Thursday is needed. The information available above does not back up this view.
Hence, The absence of any indication regarding the presence of a relationship on Wednesday in the table implies that there is no logical rationale for presuming that this connection would abruptly manifest on Thursday.
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See full text below
Banquete Middle School cafeteria on Wednesday.
Drinks Sold at Breakfast on Wednesday
Kind of Drink Number Sold
Apple juice 10
Chocolate milk 24
Orange Juice 7
Strawberry milk 13
White milk 6
If the Banquete Middle School sells 120 drinks during breakfast on Thursday, which prediction for Thursday is NOT supported by the data in the table?
The number of cartons of apple juice sold will be 6 more than the number of cartons of orange juice sold.
The number of cartons of apple juice sold will be 3 times the number of cartons of orange juice sold.
The number of cartons of chocolate milk sold will be 4 times the number of cartons of white milk sold.
There will be a total of 86 cartons of milk sold.
A store is having a sale on almonds and jelly beans. For 5 pounds of almonds and 3 pounds of jelly beans, the total cost is $27. For 7 pounds of almonds and 9 pounds of jelly beans, the total cost is $51. Find the cost for each pound of almonds and each pound of jelly beans.
Answer:
For this question you can use simultaneous equation, both elimination method or substitution method. In math when you are trying to solve for something but you don't have the answer to it, you can always use x.
soooo
5x + 3y = 27 (equation 1)
7x + 9y = 51 (equation 2)
soo im using substitution method
From equation 1, we can solve for y in terms of x:
y = (27 - 5x) / 3
Substitute this expression for y into equation 2 and solve for x:
7x + 9[(27 - 5x) / 3] = 51
Multiplying both sides by 3 to eliminate the fraction:
21x + 27 - 15x = 153
Simplifying and solving for x:
6x = 126
x = 21
Now, we can substitute this value for x into either equation 1 or equation 2 to solve for y:
5(21) + 3y = 27
105 + 3y = 27
3y = -78
y = -26
Since a negative cost doesn't make sense, we need to double-check our work. We made an error by switching the signs of the cost variables in our equations. So, the correct answers are:
The cost per pound of almonds is $21.
The cost per pound of jelly beans is $26.
find the circumference of a cirlce with diameter d=9.7cm
Answer:
circumference of a circle = 30.473 cm
Step-by-step explanation:
solution: given diameter- 9.7cm
so radius (pie) = d/2 = 9.7/2 = 4.85
circumference of a circle is 2(pie)r
circumference = 2 × 22/7 × 4.85
circumference = 30.47345 = 30.473 to 3 sf.
circumference of a circle = 30.473 cm
The depth at which dolphins dive, y, in feet, as related to the duration of the dive, t, in seconds, is represented by the linear model ŷ = 0.25 + 5.78t.
If the dive duration is 3 seconds, what is the predicted depth of the dive?
Answer:
17.59 feet
Step-by-step explanation:
Daniels new book has 240 pages in it. After he read it. Daniel counted all the pages with pictures. If 1/12 of the pages had pictures, how many pages of daniels book had pictures
20 pages of Daniel's book had pictures.
If 1/12 of the pages in Daniel's book had pictures, we can calculate the number of pages with pictures by multiplying the total number of pages in the book by 1/12:
240 pages x (1/12) = 20 pages
To find the number of pages with pictures in the entire book, we need to determine how many groups of 12 pages there are in the book and then multiply that number by the number of pages with pictures in each group (which is one page). We can do this by multiplying the total number of pages in the book (240) by the fraction 1/12, which gives us 20 pages with pictures in the book.
Therefore, 20 pages of Daniel's book had pictures.
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Calculate 50% of 42m
Directions: Simplify the following by subtracting the exponents.
1.
8r6
__
8r
2.
s5t4
____
s2t3
3.
3q2r2s
____
3qrs
4.
x3y6z
_____
x2y2z
5.
m7n3o
_____
m2n2o
6.
x4
___
x
7.
z3
___
z5
8.
a3b2
_____
ab2
9.
d4f3
_____
df
10.
mn2
_____
mn2
11.
10c5d6
______
10c4d3
12.
b8c4d2
________
b5c4d2
13.
xy
___
xy
14.
s2t4
_____
st
15.
m2n2
______
m4n4
The value of expression using Exponents and power is shown below.
We have to find the value of expression using Exponents and power.
Using the Exponents and power
[tex]a^m / a^n = a^{m-n[/tex]
1. 8[tex]r^6[/tex] / 8r
= 8[tex]r^{6-1[/tex]
= 8[tex]r^5[/tex]
2. [tex]s^5t^4[/tex] / s²t³
= [tex]s^{5-2}t^{4-3[/tex]
=s²t
3. 3q²r²s / 3qrs
= qr
4. x³[tex]y^6[/tex]z / x²y²z
= x [tex]y^{6-2[/tex]
=x[tex]y^4[/tex]
5. [tex]m^7[/tex]n²o / m²n²o
= [tex]m^{7-2[/tex]
= [tex]m^5\\\\[/tex]
6. [tex]x^4[/tex] /x
= x³
7. z³ / [tex]z^5[/tex]
= [tex]z^{3-5[/tex]
= [tex]z^{-2[/tex]
8. a³b² / ab²
= a²
9. [tex]d^4[/tex]f³ / df
= d³f²
10. mn² / mn²
= 1
11. 10 [tex]c^5d^6 / 10c^4d^3[/tex]
= cd³
12. [tex]b^8c^4d^2 / b^5c^4d^2[/tex]
= b³
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By observing a set of data values, Tina used a calculator for the engine speed (rpm) and predicted horsepower (hp) to get an equation for the least-squares line: ŷ = 10 + 30x. Based on the data that Tina collected, select the statement that is TRUE. a.) The horsepower associated with an engine speed of 2.5 rpm would be 85 hp. b.) The horsepower associated with an engine speed of 3.5 rpm would be 110 hp. c.) The horsepower associated with an engine speed of 0.5 rpm would be 40 hp. d.) The horsepower associated with an engine speed of 1.5 rpm would be 70 hp. SUBMIT MY ANSWER
The statement that is true is a) The horsepower associated with an engine speed of 2.5 rpm would be 85 hp.
To use the equation ŷ = 10 + 30x, we need to plug in the value of x (engine speed in rpm) to find the predicted value of y (horsepower).
a) For x = 2.5, ŷ = 10 + 30(2.5) = 85. Therefore, the horsepower associated with an engine speed of 2.5 rpm would be 85 hp.
b) For x = 3.5, ŷ = 10 + 30(3.5) = 115. Therefore, the statement is false.
c) For x = 0.5, ŷ = 10 + 30(0.5) = 25. Therefore, the statement is false.
d) For x = 1.5, ŷ = 10 + 30(1.5) = 55. Therefore, the statement is false.
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Pls help me (its in the png below)
Based on the expression, the answer to the question is, and the condensed expression is 1/(25k²).
What is Expression?A value is represented by an expression, which is made up of symbols, variables, constants, and operators. Expressions are used in computer programming to alter data and carry out calculations. Expressions may be straightforward or intricate, and they may contain arithmetic, logical, or conditional assertions. Expressions in mathematics can stand in for equations, functions, and other abstract ideas. Expressions can be used to describe actual phenomena, such as how things move or how systems behave.
To simplify the expression (1/5k)², we square the numerator and denominator separately, as follows:
(1/5k)² = (1²) / (5k)²
= 1 / (25k²)
Therefore, the simplified expression is 1/(25k²).
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A sample of 100 gadgets is selected from one day’s production of 5,000 gadgets. In the sample, 7 are defective. Predict the number of gadgets in the day’s production that are not defective.
We can use the proportion of defective gadgets in the sample to estimate the number of defective gadgets in the entire production, and then subtract that from the total number of gadgets produced to estimate the number of non-defective gadgets.
The proportion of defective gadgets in the sample is:
7/100 = 0.07
We can assume that this proportion is representative of the entire production, so we can estimate the number of defective gadgets in the entire production as:
0.07 x 5000 = 350
Therefore, we can estimate the number of non-defective gadgets in the production as:
5000 - 350 = 4650
Therefore, we can predict that there are 4,650 gadgets in the day's production that are not defective.
Use the formulas in the table to the right to answer the following question.
A competition swimming pool is 60 meters long, 40 meters wide, and 3.5 meters deep How much water does the pool hold?
Thanks! :)
Answer:
Step-by-step explanation:
What integer can be added to -27 to result in zero
Answer:
+ 27
Step-by-step explanation:
-27 +27 = 0
Answer: +27
Step-by-step explanation:
If you think of a number line -27 is 27 units left of 0
so you would need to move 27 units in the positive direction to get to 0
+27
There have been two especially important shifts in how markets are defined in recent decades: one involves _________________ and the other involves _____________.
The complete statement is -
There have been two especially important shifts in how markets are defined in recent decades: one involves technology and the other involves globalization.
Given is that there have been two especially important shifts in how markets are defined in recent decades. It is asked to fill in the blanks with correct values.
We can fill the statement as -
There have been two especially important shifts in how markets are defined in recent decades: one involves technology and the other involves globalization.
Therefore, the complete statement is -
There have been two especially important shifts in how markets are defined in recent decades: one involves technology and the other involves globalization.
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The circle below has a center at point and a radius of 4.5 cm. Find the measurement of the line segments that you can determine. For any one you cannot determine, explain your reasoning why.
For the given figure the measurement or lengths are:
AB = 4.5 cm.
ED = 9 cm.
DF = cannot be determined since it is a chord and it needs more information.
CA = 4.5 cm.
We have the radius of the given circle is 4.5 cm.
Now we have to find the lengths of the mentioned line segment from the circle figure.
A is the center of the circle and B is a point on circumference of circle.
So, AB is a radius of the circle. So, AB = 4.5 cm.
Now, E and D are two points on circumference of circle and segment ED passes through the center A.
So, ED is a diameter for the circle.
We know that Diameter = 2*Radius
So, ED = 2*4.5 = 9 cm.
F and D are two points on circumference of circle but segment DF does not pass through the center A. So it is not diameter it is a general chord.
So we cannot determine this due to inadequate information.
A is the center of the circle and C is a point on circumference of circle.
So, CA is a radius of the circle. So, CA = 4.5 cm.
Hence, AB = 4.5 cm.; ED = 9 cm.; DF = cannot be determined; CA = 4.5 cm.
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The question is incomplete. The complete question will be -
"The circle below has a center at point A and a radius of 4.5 cm.
Find the measurement of the line segments that you can determine. For anyone you cannot determine, explain your reasoning why.
Segment AB
Segment ED
Segment DF
Segment CA"
What is the total capacity of all the servings that are two and two fourths cups? A line plot titled Servings of Lemonade. The bottom label is Capacity in cups. There is a number line from 1 to 2 and 2 fourths, partitioned into fourths. There is one mark above 1. There are 4 marks above the first tick mark after 1. There is 1 mark above the second tick mark after 1. There are 2 marks above the third tick mark after 1. There are 3 marks above the first tick mark after 2. There are 2 marks above the second tick mark after 2. three and three over four cups 4 cups four and three over four cups 5 cups
The correct answer is option D. 250 milliliters, is the capacity of a small cup.
It is given that, the total capacity of two large cups and two small cups is 1,500 milliliters. If the total capacity of one large cup and two small cups is 1,000 milliliters.
To find the capacity of a small cup
Let small cup capacity be 's' and large cup capacity be 'l'
From the given information we can write,
2l + 2s = 1500
Then l + s = 750
one large cup and two small cups is 1,000 milliliters.
l + 2s = 1000
l + s + s = 1000
(l + s) + s = 1000
750 + s = 1000
s = 1000 - 750 = 250
The correct answer is option D. 250 milliliters
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complete question:
The total capacity of two large cups and two small cups is 1,500 milliliters. If the total capacity of one large cup and two small cups is 1,000 milliliters, what is the capacity of a small cup?
A. 375 milliliters
B. 200 milliliters
C. 500 milliliters
D. 250 milliliters
please help me with this question!!
Particles P and Q travel in consonance whenever: 0 < t < 10/g or t > 10/g
How to explain the velocityAssuming particle P is launched downwards, its velocity shifts according to the equation:
vP = gt,
where g is the acceleration due to gravity (roughly 9.81 ms^-2).
Conversely, particle Q emerges vertically with a speed of 10 ms^-1, thus making its velocity at a later point t :
vQ = 10 - gt.
It should be noted that to spot the points in time where both particles transit in the same direction, we arm ourselves by finding out when vP and vQ yield the equivalent sign. This happens when either:
The two velocities are positive (i.e., upwards motion for both) or;
Velocities of each particle yields negative signal (transiting downwards for both).
Case 1: Both velocities are positive
In this case, we have:
gt < 10
t < 10/g
Considering that t stands for time beginning from the projection of particle P, we must follow the condition t > 0. Thinking thus, the set of values which ensure simultaneous upward motion for both particles is:
0 < t < 10/g
Case 2: Both velocities are negative
As per our hypothesis:
gt > 10
t > 10/g
At the same time, noticing that particle Q starts 5 m approx. above the land surface, it will experience its maximum height when:
10 - gt = 0
t = 10/g
Which means, the set of values useful to determine downwards movement of both particles ought to be:
t > 10/g
In conclusion, to sum up, Particles P and Q travel in consonance whenever: 0 < t < 10/g or t > 10/g
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