According to the separable differential equation, the family of implicit solution is 1/2 (x² - y²)
The term separable differential equation is defined as in which the variables can be separated from each other are called separable differential equations.
As per the definition the general form to write separable differential equations is dy/dx = f(x) g(y), where the variables x and y can be separated from each other.
Here we have given that (dy/dx) = (x/y)
When we cross multiply the terms, then we get,
=> y dy = x dx
When we differentiate the terms, then we get the following,
=> ∫y dy = ∫x dx
The solution of this integral can be written as,
=> y²/2 + C = x²/2 + C
When we simplify this one then we get the resulting expression as,
=> x²/2 - y²/2 = 0
=> 1/2 (x² - y²)
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Write an equation for the line that passes through (9, 12) and is perpendicular to y=4 .
The linear function that passes through (9, 12) and is perpendicular to y=4 is given as follows:
x = 9.
What is a linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
For which the parameters are given as follows:
m is the slope, representing the rate of change of the function.b is the intercept, representing the value of y when x = 0.The line y = 4 is an horizontal line, hence a perpendicular line will be a vertical line, which has the format given as follows:
x = c.
The point is (9,12), meaning that the x-coordinate is of 9, and thus the constant c is given as follows:
c = 9.
Hence the equation is:
x = 9.
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Why is 1 U and 1 V graph a straight line?
A 1-U, 1-V graph is a special type of graph that has only one vertex of degree 1 (U) and one vertex of degree 2 (V). The edge connecting the two vertices is called the "bridge" of the graph.
Because the graph has only one vertex of degree 2, it forms a simple path (a straight line) between the two vertices. The vertex of degree 1 is a leaf, which means it is only connected to one vertex, and the vertex of degree 2 is the other end of the path. The path is a simple one, meaning it has no loops or multiple edges between the two vertices.
In a 1-U, 1-V graph, the vertex of degree 1 (U) can be thought of as the start of the path and the vertex of degree 2 (V) as the end of the path. Because there are no other edges or vertices in the graph, the path is the only structure in the graph and it's a straight line.
It's important to note that a 1-U, 1-V graph is a special case of a graph and it's not a general representation of all possible graphs. Most graphs have more than one vertex and multiple edges, making them more complex than a simple straight line.
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A regular hexagon is inscribed in a circle of radius 2 units. In square units, what is the area of the hexagon
The area of inscribed regular hexagon is 6[tex]\sqrt{3\\[/tex] unit square using the properties of equilateral triangles which combined, form the hexagon.
In a circle, a regular hexagon can be inscribed with all the six vertices of hexagon touching the circumference of the circle. The center of the circle is the center of the hexagon itself.
Now, if we join the center with all the vertices of the hexagon, we see six equilateral triangles are formed. The other two sides of each triangle apart from the ones joining the vertices of hexagon, are radii of the circle and all the sides are equal in length. The attached image can be referred for better understanding.
To find the area of the hexagon, we need to find the area of single equilateral triangle and multiply it by 6, as six triangles make a regular hexagon.
Radius of the circle ([tex]r[/tex]) = 2 units
Area of a single equilateral triangle = [tex]\sqrt{3} /4[/tex] [tex]r^{2}[/tex]
=( [tex]\sqrt{3} /4[/tex] ) × [tex]2^{2}[/tex]
= [tex]\sqrt{3}[/tex]
Area of hexagon = Area of 6 equilateral triangles = 6 × [tex]\sqrt{3}[/tex]
Area of hexagon = [tex]6\sqrt{3}[/tex] [tex]units^{2}[/tex]
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-7x7^-4 can someone explain it to me pls
an experimenter had participants exercise much, a little, or not at all and then measured how much they ate at dinner two hours later. what was the dependent variable in this experiment?
The amount of food eaten was the dependent variable in this experiment.
What is dependent variable?Everything that track in the study and what is impacted by it are both considered dependent variables. Depending on the independent variable, the dependent variable will change. Because it "depends" on the independent variable, it is known as a dependent variable. The dependent variable on other measurable variables As a result of an experimental modification of the independent variable or variables, these variables should change.
The amount of study one did, how much sleep one got the night before the test, or even how hungry he or she were can all affect your test result, which makes it a dependent variable. As an example, the test score might be a dependent variable.
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Q3. There are 5 red sweets, 6 blue sweets and 9 yellow sweets in a bag.
Sarah takes a sweet at random.
She replaces it back and then
Take another sweet at random.
Work out the probability the both the sweets the same colour.
Answer:
Step-by-step explanation:There are a total of 20 sweets in the bag (5 red + 6 blue + 9 yellow).
To find the probability that Sarah takes two sweets of the same color, we need to find the probability of her choosing a sweet of a specific color on her first pick and then the probability of her choosing another sweet of that same color on her second pick.
For example, if she chooses a red sweet on her first pick, the probability of that happening is 5/20, or 1/4. Then the probability of her choosing another red sweet on her second pick, given that she already picked one, is 4/20, or 2/10. Therefore the probability of her choosing two red sweets in a row is (1/4) * (2/10) = 1/20.
Similarly, the probability of her choosing two blue sweets in a row is (6/20) * (5/20) = 3/50.
The probability of her choosing two yellow sweets in a row is (9/20) * (8/20) = 9/100.
The probability of her choosing two sweets of the same color is the sum of the probability of her choosing two red sweets, two blue sweets, or two yellow sweets in a row.
P(Two same color) = 1/20 + 3/50 + 9/100 = 11/50
So, the probability of her choosing two sweets of the same color is 11/50.
6. 21 and 22 form a linear pair. If m/1 = (5x + 9) and m/2 = (3x + 11), find the measure of
each angle.
7. 21 and 22 are vertical angles. If mZ1 = (17x + 1) and m/2 = (20x-14), find m22.
8. ZK and ZL are complementary angles. If mZK = (3x + 3) and mL = (10x-4), find the
measure of each angle.
Answer:
Since 21 and 22 are vertical angles, they are congruent. Therefore, m/1 = m22.
Using the equation m/1 = (17x + 1) we can find the measure of the angle m22.
m22 = (17x + 1)
Since ZK and ZL are complementary angles, the sum of their measures is 90 degrees.
mZK + mL = 90
Using the equations mZK = (3x + 3) and mL = (10x-4) and substituting them in the equation, we can find the measure of each angle.
3x + 3 + 10x - 4 = 90
13x - 1 = 90
13x = 91
x = 7
Therefore, mZK = (3x + 3) = (3(7) + 3) = 24 and mL = (10x-4) = (10(7) - 4) = 66
Step-by-step explanation:
what restrictions must be made on , and so that the triple will represent a point on the axis? on the axis? in the plane? in the plane?
If we fix x = 0 and z = 0 only y coordinate can change. So triple (0, y, 0) can only represent a point in y axis.
What do you mean by a plane?
In geometry, a plane is a surface made up of all the lines that are parallel to one another and connect any two locations on it. It is, in other words, a level or flat surface.
A plane is defined uniquely through any of the following in a Euclidean space of any number of dimensions: with the aid of three non-collinear points.
For the triple (x,y,z ) to represent the point on the y - axis .
x must be 0 y must be a real number
and z must b 0
For the triple (x,y,z ) to represent the point on the y - axis .
x must be 0 y must be 0
and z must be a real number
For the triple (x,y,z ) to represent the point on the y - axis .
x must be real number y must be 0
and z must be a real number
For the triple (x,y,z ) to represent the point on the y - axis .
x must be 0 y must be real number
and z must be a real number
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in chicago, there is a probability of 30% that it will snow on any given day from january to march. what is the probability that it will snow on 3 consecutive days?
The probability that it will snow on 3 consecutive days is 2.7 %
What is Probability?Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty.
The probability formula is defined as the possibility of an event to happen is equal to the ratio of the number of favorable outcomes and the total number of outcomes.
Probability of event to happen P(E)
= Number of favorable outcomes/Total Number of outcomes
Given, probability of 30% rain that it will snow on any day,
The probability of snow over a 3-day period is the product of the probabilities of rain for each day:
P3-day = (P1-day)(P1-day)(P1-day)
= (30/100)³
= (3/10)³
= 27/1000
= 2.7%
Hence, 2.7% is the probability that it will snow on 3 consecutive days.
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Find the area of an ellipse with equation [tex]\frac{x^2}{100} +\frac{y^2}{64} = 1[/tex]
On solving the provided question, we can say that area of the ellipse equation = [tex]\pi ab[/tex] = 3.14*10*8 = 251.2 cm sq.
What is equation?A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.
area of an ellipse with equation = [tex]x^2/100 + y^2/64 = 1\\[/tex]
here, a = 10 and b = 8
area of the ellipse equation = [tex]\pi ab[/tex] = 3.14*10*8 = 251.2 cm sq.
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PLSSS HELP IF YOU TURLY KNOW THISS
To simplify the expression 3k + 9 - 2k + 11, we need to combine like terms and simplify the expression.
The first step is to combine the constants (numbers without variables)
3k + 9 - 2k + 11 = 3k - 2k + 9 + 11
The next step is to combine the variable k
3k - 2k = k
Now we have
k + 9 + 11 = k + 20
The final simplified expression is k+20
Answer:
20
Step-by-step explanation:
3k+(-2k) = 1k or just k
+9+11 = +20
= k+20
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Find the volume of this shape
The volume of the given shape would be = 410cm³
What is a rectangle?A rectangle is defined as the type of quadrilateral that has two pairs of equal sides that are parallel to each other with angles equal to 90°.
From the shapes given above,
it is made up of three rectangles combine together with different lengths, width and height.
The volume of a rectangle = l×w×h
Rectangle A = 10×3×8 = 240
Rectangle B = 6×5×3 = 90
Rectangle C = 2×5×8 = 80
Therefore the volume of the shape = 240+90+80= 410cm³.
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At a local play, student tickets cost $6 each and adult tickets cost $11 each. if ticket sales were $3,000 for 400 tickets, how many students attended the play?
As per the unitary method the number of students who attended the play is 280.
The unitary method is a mathematical method used to find the value of a single unit in a given set of values. In this case, we will be using it to find the number of student tickets sold at the local play.
Let's say that "x" represents the number of student tickets sold.
The cost of each student ticket is $6, so the total cost of student tickets is $6x. The total cost of adult tickets is $11y, where "y" represents the number of adult tickets sold. The total ticket sales for the play was $3,000, so we can write the equation:
$6x + $11y = $3,000
We already know the cost of student tickets and adult tickets, so we can substitute those values into the equation:
$6x + $11y = $3,000
$6x = $3,000 - $11y
Now we can divide both sides of the equation by $6 to find the value of x:
x = ($3,000 - $11y) / $6
Since the total ticket sales were $3,000 for 400 tickets, we can use that information to solve for y:
$3,000 = $6x + $11y
$3,000 = $6x + $11(400 - x)
Expanding the equation:
$3,000 = $6x + $4400 - $11x
Combining like terms:
$3,000 = $-5x + $4400
Adding $5x to both sides:
$3,000 + $5x = $4400
Subtracting $3,000 from both sides:
$5x = $4400 - $3,000
$5x = $1400
Dividing both sides by 5:
x = $1400 / $5
x = 280
So, 280 students attended the play.
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PLSSSS HELLPPPPPPP
How far is it across the lake?
Answer:
9 km
Step-by-step explanation:
By making use of the tangent function, we can calculate the angle inside the right triangle formed with the Lake and the 6km as two of the sides. See the attached worksheet for the detailed steps.
Can someone help me solve this?
[tex]f(t)=0.4(1.16)^{t-1}\qquad \begin{cases} x=0.4\\ y=1.16 \end{cases}\implies f(t)=xy^{t-1} \\\\[-0.35em] ~\dotfill\\\\ xy^{t-1}\implies xy^t y^{-1}\implies x\cfrac{y^t}{y}\implies \cfrac{x}{y}y^t\implies \stackrel{\textit{substituting back}}{\cfrac{0.4}{1.16} ~~ (1.16)^t} \\\\\\ \stackrel{\textit{"r" is positive, \Large Growth}}{\cfrac{0.4}{1.16} ~~ (1+0.16)^t \implies f(t)~~ \approx ~~ 0.34 ~~ (1+0.16)^t}\qquad \begin{cases} a\approx 0.34\\\\ r=0.16 \end{cases}[/tex]
Solve for X, Leave in simplest radical form.
By the concepts of trigonometric ratios, the value of x in the right angle triangle is 1.
What are trigonometric ratios in terms of a right-angle triangle?We know a right-angled triangle has three sides they are -: Hypotenuse,
Opposite and Adjacent.
We can remember SOH CAH TOA which is,
sin = opposite/hypotenuse, cos = adjecen/hypotenuse and
tan = opposite/adjacent.
If we take the reference angle of 60°, Then the hypotenuse is x and the adjacent is 2.
We know, cos = adjacent/hypotenuse.
Therefore,
cos60° = 2/x.
x = 2cos60°.
x = 2×1/2.
x = 1.
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What is meant by absolute term?
The absolute value or modulus |x| of a real number x is the non-negative value of x without regard to its sign.
The absolute value is always a positive value and not a negative number. so those numbers are called absolute values.
It is represented as |a|, which defines the magnitude of any integer ‘a’.
It defines removing any negative sign in front of a number and thinking of all numbers as positive.
Absolute value is a term used in mathematics to indicate the distance of a point or number from the origin (zero point) of a number line or coordinate system.
When x itself is negative (x<0), then its absolute value is necessarily positive
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what is the most descriptive name for a quad with all congruent sides and two sets of parallel sides
The most descriptive name would be a rhombus.
What is a rhombus?
A rhombus is a geometric shape that is a type of parallelogram. It is defined as a quadrilateral with all four sides congruent (equal in length). The opposite angles of a rhombus are also congruent. A rhombus can also be thought of as a square that has been stretched or compressed in one direction, so all its angles are right angles.
The most descriptive name for a quadrilateral with all congruent sides and two sets of parallel sides is a parallelogram. Specifically, a parallelogram with all congruent sides is called a rhombus.
Hence, The most descriptive name would be a rhombus.
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How many unique triangles can be drawn with side lengths 5 inches 15 inches and 30 inches
Answer:
Step-by-step explanation:
The idea is, for each triangle, sort all of its sides and then store it in a map, if all those three sides are already present in the map then increase the frequency by 1, else its frequency will be 1. The count of elements of the map which have frequency 1 in the end will be the answer.
URGENT, pls answerr!!
Answer:
15/16
Step-by-step explanation:
In a dice, there are 3 even and 3 odd numbers.
So, to calculate the required probability, we will have to calculate the probability of getting an odd number in all of them.
Probability of getting odd number in 1 dice = 3/6 = 1/2
Probability of getting odd number in 4 dice =
1/2 x 1/2 x 1/2 x 1/2 = 1/16
Therefore, probability of getting atleast one even number is 1 - 1/16 = 15/16
15/16 is the answer.
Pls mark as brainliest. Cheers
Can anyone help me with this question?
Answer: Side SK
Step-by-step explanation:
A jar contain ome marble. {frac(1/2)} of the marble are blue. 3 BLACK marble are added to the jar. What fraction of marble in the jar are BLUE NOW?
The fraction of blue marble in the jar is [(1/2)x]/ (x+3) where x+3 is the total marbles.
This question involves basic arithmetic and fractions.
We know that a fraction means a part of a whole. It is of the form a/b where b is not equal to zero and a, b are numbers.
Now, here let the total number of marbles in the bar is x .
Then , the number of blue marbles is (1/2)x i.e. 1/2 of x.
Now, if three black marbles are added to the jar, the total number of marbles = x + 3.
So, fraction of blue marble in the jar = (no. of blue marble)/(no. of total members)
= [(1/2)x]/ (x+3).
Thus, the fraction of blue marble in the jar is [(1/2)x]/ (x+3) where x+3 is the total marbles.
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What is density?
The number of
particles in an
chject or
substance
The amount of
matter in an
object or
substance
The amount of
space an object
or substance
takes up
A measure of how
much matter is ha
certain volume
The Scale On A Map Is 1 Inch = 60 Miles. If Two Cities Are 2 3/4 Inches Apart On The Map, How Many Miles Are They Apart?
As you answer the following questions, write explanations for why your current answer is correct
A - 58.3 mi
B - 165 mi
C - 120 mi
D - 21.8 mi
The Scale On A Map Is 1 Inch = 60 Miles. If Two Cities Are 2 3/4 Inches Apart On The Map, the number of miles they are apart is, 165 Miles
So, Option B is correct.
What is the scale factor ?Scale factor is a mathematical term, which we use to scale 2-dimensional and 3-dimensional shapes. Scale factor is a measure of similar figures. Those figures who look the same but are in different sizes.
For example, Two spheres look similar but could have different radii.
Given that,
The Scale On A Map Is 1 Inch = 60 Miles
Two Cities Are 2 3/4 Inches Apart On The Map
The number of miles they are apart =?
1 Inch = 60 Miles
11/4 Inch = 60 × 11/4 Miles
= 165 Miles
So, The actual distance is 165 Miles
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What are the top 15 Excel functions?
The top 15 Excel functions are SUM, AVERAGE, COUNT, MAX, MIN, IF, VLOOKUP, CONCATENATE, INDEX, MATCH, ROUND, TEXT, OFFSET, TODAY, and RAND.
1. SUM: Add up the values in a range of cells
2. AVERAGE: Calculate the mean of a range of cells
3. COUNT: Count the total number of cells in a range
4. MAX: Find the maximum value in a range of cells
5. MIN: Find the minimum value in a range of cells
6. IF: Perform different actions based on whether a condition is met
7. VLOOKUP: Look up the value of a cell in another table
8. CONCATENATE: Join two or more cells together
9. INDEX: Return a value from a given range of cells
10. MATCH: Find the position of a value in a range of cells
11. ROUND: Round a number to a specified number of decimal places
12. TEXT: Format a number or value as text
13. OFFSET: Return a range of cells at a given offset from another cell
14. TODAY: Return the current date
15. RAND: Generate a random number
The top 15 Excel functions are SUM, AVERAGE, COUNT, MAX, MIN, IF, VLOOKUP, CONCATENATE, INDEX, MATCH, ROUND, TEXT, OFFSET, TODAY, and RAND, which are used for various tasks such as adding up values, calculating the mean, counting cells, finding maximum/minimum values, looking up values in another table, joining cells together, returning a value from a given range, finding the position of a value, rounding numbers, formatting values as text, generating a random number, and returning the current date.
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The velocity function v(t) (in meters per second) is given for a particle moving along a line.
V(t)= 5t-8, 0
Find the Total distance d2 traveled by the particle during the time interval given above?
The particle's total d2 distance for the course of the time period indicated above, in accordance with the supplied assertion, was -3/2 m.
What exactly are function and example?An example of a utility rule is one that generates a single output from a single input. The picture was obtained from Alex Federspiel. The equation y=x2 serves as an example of this. There is only one output for y for every input for x. We may assert that y appears to be a time variable given that x remain the source value. A function, according to a technical definition, is a relationship between a set of inputs and a set of potential outputs, where each input is connected to precisely one output.
dx(t)/dt = 5t-8
[tex]\int_0^{x(t)} \mathrm{dx}(t)=\int_0^3 5 t-8 \mathrm{~d} t[/tex]
[tex]x(t)=\left.\left[\frac{5}{2} t^2-8 t\right]\right|_0 ^3[/tex]
f(0) = 0
[tex]f(3)=\frac{5}{2} * 3^2-8 * 3=-\frac{3}{2} m[/tex]
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The complete question is-
The velocity function v(t) (in meters per second) is given for a particle moving along a line.
V(t)= 5t-8, 0 <equal to 't' <equal to 3
Find the Total distance d2 traveled by the particle during the time interval given above?
I need help solving this problem, i know how to solve it but i keep getting the wrong answer. My answer is 457/10.. how do you solve this problem
Please help quickly! Use the rectangle below to answer questions 27-31
The measure of angle BAC from the given rectangle ABCD is 39°.
What is a rectangle?A rectangle is a closed two-dimensional figure with four sides. The opposite sides of a rectangle are equal and parallel to each other and all the angles of a rectangle are equal to 90°.
In the given rectangle ABCD, diagonals AC and BD bisect each other E.
27) m∠DAC=2x+4 and m∠BAC=3x+1,
Here, m∠DAC+m∠BAC=90°
2x+4+3x+1=90°
5x+5=90°
5x=85
x=17
So, m∠BAC=3x+1=52
28) m∠BDC=7x+1 and m∠ADB=9x-7,
Here, m∠BDC+m∠ADB=90°
7x+1+9x-7=90
16x-6=90
16x=96
x=6
So, m∠BDC=7x+1=43°
29) m∠ABD=7x-31 and m∠CDB=4x+5,
Here, 7x-31=4x+5
3x=36
x=12
m∠ABD=7x-31 =53°
30) m∠BAC=x+3 and m∠CAD=x+15
Here, m∠BAC+m∠CAD=90°
x+3+x+15=90
2x+18=90
2x=72
x=36
m∠BAC=x+3=39°
Therefore, the measure of angle BAC from the given rectangle ABCD is 39°.
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can someone help me with this? thanks
Answer:
a. y = 2x - 6
To find the slope of the equation, we need to find the coefficient of x which is 2. So the slope of this equation is m=2
To find the y-intercept, we can substitute x = 0 into the equation:
y = 2(0) - 6
y = -6
So the y-intercept of this equation is b = -6
b. y = 1/2 * x + 12
To find the slope of the equation, we need to find the coefficient of x which is 1/2. So the slope of this equation is m=1/2
To find the y-intercept, we can substitute x = 0 into the equation:
y = 1/2(0) + 12
y = 12
So the y-intercept of this equation is b = 12
Therefore, the slope-intercept form of the equation is y = 2x - 6 and y = 1/2x + 12 respectively.
2.
D
Answer:
4
Step-by-step explanation:
You and a friend are hiking and find yourselves near the top of a waterfall. There is a path to hike down that takes 1.5 miles to reach the bottom safely and go swimming. There is also a path that is 1.2 miles down to a great place to eat lunch. Your friend wants to stay at the top of the waterfall and fly his drone overhead to take pictures from the sky. A drone is a flying robot that can be remotely controlled with computer software or technology. Draw a vertical number line to help you answer the questions.
Part A: How far would the drone need to fly up in the air to be the opposite distance from you when you are eating lunch? (3 points)
Part B: How far would the drone need to fly up in the air to be the opposite distance from you when you are swimming? (3 points)
Part C: What does the value of zero represent in this problem? (3 points)
Part D: Use absolute value to show that if you hike down to go swimming and then hike back to the top to meet your friend that you hiked the same distance in both directions. (3 points)
if you say the wrong answer i will take my points back
The relative location of the drone are as follows;
Part A: The height of the drone will be 1.2 miles.
Part B: To be opposite distance from the top of the waterfall as the swimming site, the height of the drone should be 1.5 miles above the top of the water fall
Part C: The value 0 represents the location of the top of the water fall from which all other points are measured
Part D: Using the absolute function indicates that the distance to the site for swimming -1.5 miles is the same as the distance back, to the top which is 1.5 miles as |-1.5| = |1.5| = 1.5.
What is number line?
A number line is a diagram of a graduated straight line used to represent real numbers in elementary mathematics. It is assumed that every point on a number line corresponds to a real number, and that every real number corresponds to a point.
The height to which the drone needs to fly up in the air to be the opposite distance from the place for eating lunch is found has follows;
The distance from the location for eating lunch to the top of the water fall = 1.2 miles
The height to which the drone has to fly to be opposite from from where they eat lunch is 1.2 miles above the top of the waterfall
Part B: The height of the drone above the waterfall such that it is the same as the swimming site the to the top of the waterfall is 1.5 miles.
Part C; A zero is a reference point. The reference point in the question is location of the top of the waterfall, from which the distances of other location are sated
Part D: The distance from the water fall to the swimming site = -1.5 miles
Distance from the swimming site back = 1.5 miles
Using the absolute value function. we have;
The distance to the swimming site = |-1.5| = 1.5
The distance back up = |1.5| = 1.5
The absolute value function indicates that the distance in both direction is the same.
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Can you come up with the equation for the graph to the left in y = mx + b form?
Answer:
hope this helps you to understand.
