The potential energy of the ball will be 7200 Joules.
What is potential energy?The energy possessed by a body by virtue of its position relative to others, stresses within itself, electric charge, and other factors.For small height changes, gravitational potential energy can be computed using - E = mgh.Given is a 6-kg bowling ball sits on top of a building that is 120 meters tall.
We can write the potential energy of the ball as -
E = mgh
E = 6 x 10 x 120
E = 60 x 120
E = 7200 Joules
Therefore, the potential energy of the ball will be 7200 Joules.
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dana created a column chart showing four quarters of data, but she no longer wants to display the quarter 1 data series. how can she quickly remove it?
Steps to remove the quarter 1 data series from Dana's column chart in Microsoft Excel are given below.
You might need to add an additional data series to the chart after it has been created. A data series, such as a list of quarterly corporate profits, is a row or column of figures that are input in a worksheet and plotted in your chart.
To remove the quarter 1 data series from Dana's column chart in Microsoft Excel:
Click on the chart to select it.Right-click on the data series you want to remove.Select "Delete" from the context menu.The quarter 1 data series should now be removed from the chart.Note: The steps may vary slightly depending on the version of Excel you are using.
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need the answer asap ! thank you to anyone who helps !
A plate of spring roll is price of $7.5.
What is Linear System?
A linear system is a mathematical representation of a system in systems theory that relies on the application of a linear operator. Compared to nonlinear systems, linear systems often have significantly simpler traits and properties.
Let n, b, and c represent the cost per plate of spring roll, chicken tenders , and pretzel dipper, respectively.
One party spends $23 and purchases two plates of chicken tenders and one plate of pretzel dipper.
i.e. 2b + 1c = 23
2b + c = 23 --------------------- 1
Three plates of spring roll and a plate of chicken tenders are purchased by another group for $30.75.
That is
3n + 1b = 30.75
3n + b = 30.75 ---------------------- 2
A third party spends $22.25 and purchases one of each appetizer.
That is
n + b + c = 22.25 --------------------- 3
On solving;
eqn2 - eqn3
2n - c = 8.5 --------------------- 4
on solving;
eqn 1 + eqn 4
2b+ 2n = 31.5
b + n = 15.75 --------------------- 5
On solving;
eqn 3 - eqn 5
c = 6.5
Substituting in eqn 4
2n - 6.5 = 8.5
n = 7.5
Substituting in eqn 3
7.5 + b + 6.5 = 22.25
b = 8.25
Price of spring roll n = $7.5 .
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X-intercept:
y-intercept:
Answer: I believe your x-intercept is (-7,0) and your y-intercept is (0,2)
Step-by-step explanation: I hope this helps! (It's kind of sad how this is the only bit of math I'm good at)
Given g(x) = − 4x + 8, identify the domain, range, and x-intercept of the function. Domain: −∞ < x < ∞; Range: −∞ < y < ∞; x-intercept (2, 0) Domain: −∞ < x < ∞; Range: −∞ < y < ∞; x-intercept (−2, 0) Domain: −4 < x < 8; Range: − 4 < y < ∞; x-intercept (2, 0) Domain: −4 < x < 8; Range: −∞ < y < 4; x-intercept (−2, 0)
the domain, range, and x-intercept of the function g(x) = − 4x + 8 are Domain: −∞ < x < ∞; Range: −∞ < y < ∞; x-intercept (2, 0) that is the first option.
What is the function?
A relationship between a group of inputs and one output is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function. Typically, f(x), where x is the input, is used to represent a function.
Given a function g(x) = − 4x + 8
The domain of a function means all possible inputs or all the numbers that can be put in place of x to get some output
The range of a function means all possible outputs or all the numbers that are the result of all the inputs or values of y
Intercept is the point on a graph whose one coordinate is zero. There are two types of intercepts - X intercept where the y coordinate is zero and Y-intercept where the value of the x coordinate is zero
The domain of the given function is all real numbers or - infinite < x< infinite
The range of the given function is all real numbers or - infinite < x< infinite
The x-intercept of the given function is where y = 0
so, 0 = -4x + 8
-8 = -4x
x = 2
The x-intercept is (2,0)
Therefore, the domain, range, and x-intercept of the function g(x) = − 4x + 8 are Domain: −∞ < x < ∞; Range: −∞ < y < ∞; x-intercept (2, 0) that is the first option.
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The variable X varies jointly with Y and Z. When Y = 2 and Z = 4, X = 14. What is the value of X when Y = 10 and Z = 16?
The value of x when y = 10 and Z = 16, in the given joint variation is: 1120.
How to Solve a Joint Variation Problem?If X varies jointly with Y and Z, then we can use the formula X = k * Y * Z, where k is the constant of proportionality.
Using the given information, we can find k by plugging in the values of Y, Z, and X and solving for k:
14 = k * 2 * 4
k = 14 / (2 * 4)
k = 7/2
Now that we know the value of k, we can use it to find the value of X when Y = 10 and Z = 16:
X = k * Y * Z
X = (7/2) * 10 * 16
X = 70 * 16
X = 1120
So the value of X when Y = 10 and Z = 16 is 1120.
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I Need Help I’m Desperate
For the graph with points (-2, 2) and (2,0), the slope, linear equation and y-intercept is m = -1/2, y = -1/2x + 1 and y = 1 respectively.
What is a linear equation?
A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.
The first graph shows the points (-2, 2) and (2,0).
The slope-intercept form of an equation/function is - y = mx + b
To find the slope m use the formula -
(y2 - y1)/(x2 - x1)
Substituting the values in the equation -
[0 - 2]/[2 - (-2)]
(-2)/(2 + 2)
-2/4
-1/2
So, the slope point is obtained as m = -1/2.
The equation becomes - y = -1/2x + b
To find the value of b substitute the values of x and y in the equation -
2 = -1/2(-2) + b
2 = 1 + b
b = 2 - 1
b = 1
So, the value for b is 1.
Now, the equation becomes -
y = -1/2x + 1
To find the y-intercept substitute the value of x = 0 in the equation -
y = -1/2(0) + 1
y = 0 + 1
y = 1
Therefore, the slope is 1, equation is y = -1/2x + 1 and y-intercept is y = 1.
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2. Which number is NOT a
common denominator of the
fractions being added?
29
2 + 151/20
9
A 108
B 72
C 36
D 24
2.D movi
Therefore , the solution of the given problem of denominator comes out to be 36.55 is the correct option.
What is an example of common denominator?Common denominators are used to describe fractions with the same denominators. Take a look at the following instances: 1/2 + 1/2 = 1 and 3/4 + 1/4 = 1 The fractions' denominators are both common, making it simple to calculate the variable result in both situations.
Here,
Given :
=>29 + 151/20
=> 580 + 151/20
=> 731/20
=> 36.55
As a zero denominator would result in an infinite fraction, a finite fraction can never have a denominator of 0.
Therefore , the solution of the given problem of denominator comes out to be 36.55 is the correct option.
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Which statements are true for the functions g(x) = x2 and h(x) = –x2 ? Check all that apply.
For any value of x, g(x) will always be greater than h(x).
For any value of x, h(x) will always be greater than g(x).
g(x) > h(x) for x = -1.
g(x) < h(x) for x = 3.
For positive values of x, g(x) > h(x).
For negative values of x, g(x) > h(x).
100 pts: Which of the following tables represents a linear function? x 1 1 0 1 1 y −2 −1 0 1 2 x 0 1 2 3 4 y −3 2 0 −2 3 x −2 −1 0 1 2 y 2 0 −1 0 2 x −2 −1 0 1 2 y 3 1 −1 −3 −5
Table (D) represents a linear function which the graph has been attached below.
What is the Linear function?A linear function is defined as an equation in which the highest exponent of the variable is always one. In mathematics, independent and dependent variables are values that vary in relation to one another.
The table is given in the question, as an option (D)
x: −2 −1 0 1 2
y: 3 1 −1 −3 −5
According to the above table, we plot the graph through the points then we can see that the graph of a function looks linear.
Thus, this table represents a linear function.
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NEED HELP ASAPP :)
this will help with a good answer :p
The inequality shown on the graph is x > -2 and x < 5 or -2 < x < 5
How to translate inequality graph to expression?An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value e.g. 5 < 6, x ≥ 2, etc.
If you examine the graph, you will notice that there is one circle on -2 and another circle on 5. These give you the range of values. Also, notice that circles are not shaded. Thus, this can be written as:
x > -2 and x < 5 or -2 < x and x < 5
Which can then be combined as:
-2 < x < 5
Note: The reason we did not use ≤ is because the circles are not shaded.
Thus, the inequality is x > -2 and x < 5 or -2 < x < 5
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If you help you get a cookie :)
Niles spent $42 on three kites. Which equation will tell you how much each kite cost?
Responses
A x3
= 42x 3 = 42
B x + 3 = 42x + 3 = 42
C 3x = 423x = 42
D 42x = 3
Answer:
3x = 42
Step-by-step explanation:
The correct equation is
3x = 42
However, because your formatting has been scrambled, I cannot tell you which choice it is
Compare this equation with your original question and see which is the correct choice
3x = 42 means
each kite = 42/3 = $14
but the question is only asking for the equation not the solution
You can mail the cookie to brainly :)
Please help Due in 20 min
Evaluate
1/6x+7/12 when x= 1/2.
Answer: 8/12
Step-by-step explanation:
First you multiply 1/6 with 1/2 that would give us 1/12
Then you add 1/12 with 7/12
Our answer would be 8/12
Answer:
2/3 or in Decimal its 0.6
Step-by-step explanation:
1/6x+7/12 when x= 1/2.
1/6(1/2)+7/12
Can someone help please
The coordinates of point A are given as follows:
A(19, 23).
How to obtain the coordinates of point A?The coordinates of point A are obtained applying the proportions in the context of this problem.
The segment AB is represented as follows:
AB = B - A.
Hence the segment 5AB is given as follows:
5AB = 5(B - A) = 5B - 5A.
Then the x-coordinate of A is obtained as follows:
5(16) - 5A = -15
5A = 95
A = 19.
The y-coordinate of A is obtained as follows:
5(30) - 5A = 35
5A = 115
A = 23.
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A spinner with repeated colors numbered from 1 to 8 is shown. Sections 1 and 8 are purple. Sections 2 and 3 are yellow. Sections 4, 5, and 6 are blue. Section 7 is orange.
Which statement about probability is true?
The probability of landing on orange is greater than the probability of landing on purple.
The probability of landing on yellow is less than the probability of landing on orange.
The probability of landing on orange is equal to the probability of landing on yellow.
The probability of landing on purple is equal to the probability of landing on yellow.
The correct statement is : The probability of landing on purple is equal to the probability of landing on yellow.
What is probability?Probability is a measure of the likelihood of an event occurring. The probability formula is defined as the possibility of an event happening 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 here: A spinner with four different colors purple, yellow, blue and orange.
Now Section 1&8 = Blue
Section 2&3 = yellow
Section 4,5,6 = blue
Section 7 = orange
Total=8
Thus probability for each section are as follows
P(purple)=2/8
=1/4
P(yellow)=2/8
1/4
P(Blue)=3/8
P(orange)=1/8
∴ The probability of landing on purple is equal to the probability of landing on yellow.
Hence, The probabilities of all the individual sections are 1/4,1/4,3/8,1/8 for purple, yellow, blue and orange respectively.
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Subti
0-9
3)
Number of
tickets won
0
123
2
4
5
6
7
8
Frequency
2
11
28
18
11
15
223
10
a) Work out the total
number of tickets won
(2)
b) Calculate the mean
number of tickets per game
(2)
Answer:
Step-by-step explanation:
0-2-0
1-11-11
2-28-56
3-18-54
4-11-44
5-15-75
6-10-60
7-2-14
8-3-24
total number of tickets won - 100
mean number - 336 divided by 100 = 3.36
Simplify
45y/30y (7x+49)
Plsss help
By simplifying 45y/30y (7x+49) this we get 3 / 2(7x + 49).
What is the simplifying?Simple implies to make anything easier to understand. Reducing an expression, fraction, or mathematical problem to its simplest form is known as simplification. Using calculations and solving the problem makes it simple. simplify fractions by cancelling all the common factors from both the numerator and the denominator and writing the fraction in its lowest/simplest form. simplify mathematical expressions by grouping and combining similar terms. This makes the expression easily understandable and solvable.45y/30y (7x+49)
45y / 30y(7x +49) : 3 / 2(7x + 49)
45y / 30y(7x + 49)
45y / 30(7x + 49)
Factor the number :45 = 15 . 3
=15.3 / 30(7x + 49)
Factor the Number : 30 = 15 . 2
15.3 / 15.2(7x + 49)
Cancel the common factor : 15
= 3 / 2(7x + 49).
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The results of a study show that a college graduate makes on average $52,000 a year 10 years after graduating high school and a high school graduate makes on average $32,000 a year 10 years after graduating high school. The results are summarized in the graph shown. Which of the statements is true?
I'd really appreciate the answer to this.
The area of each box would be proportional to the salaries of each group. Option C.
What is the summary of the statements?The use of models to represent data in mathematics is well known. In the case of the data we have, the salaries of the college graduates and the high school graduates have been shown by the use of squares.
We can see that the sizes of the squares respectively show the magnitudes of the salries of the high school graduate and that of the college graduate. The area of the boxes would be proportional to the salaries.
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56) a player who is off the field of play to receive medical treatment trips a player who is on the field of play. what decision does the referee make?
If a player who is off the field of play to receive medical treatment trips a player who is on the field of play , then (c) the referee cautions the player and the play is restarted with a indirect free kick.
On the field of play of football , the medical treatment of any player is not permitted under any circumstances.
When the player is bleeding, the player is required to leave the field immediately.
When the play has been restarted, only time the injured player is allowed to return to field of play is after game has started again.
It is exclusive responsibility of match referee to decide whether or not an injured player may return to the game.
The given question is incomplete , the complete question is
A player who is off the field of play to receive medical treatment trips a player who is on the field of play. what decision does the referee make?
(a) A. The referee shows a red card and sends off the player. Play is restarted with an indirect free kick.
(b) The referee shows a yellow card and cautions the player. Play is restarted with an indirect free kick.
(c) The referee cautions the player and Play is restarted with an direct free kick.
(d) The referee cautions the player and restarts with a dropped ball.
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Write the ratio 60:145 in the form 1:n
Answer:
1:2.42
Step-by-step explanation:
145/60 = 2.42
Answer: 1 : 29/12
Step-by-step explanation:
60/60 = 1
145/60 = 29/12 in simplest form
therefore 1 : 29/12
Here’s the other ones
The value of side length PS is found as 4 units for the given right angled triangles.
Define the term congruent triangles?Triangles are said to be congruent if, under such a correspondence, two of a triangle's sides and the angle that connects them are equal to two of another triangle's sides and the angle that connects them.Congruent refers to something that is "absolutely equal" in terms of size and shape. The shapes hold true regardless of how we rotate, flip, or turn them. Draw two circles with the same radius, for instance, cut them out, and stack them on top of one another.For the stated question:
PQ = 3x - 3
QR = 6x - 9
PS = 5x - 6
As, Q is the mid point of PR.
PQ = QR
3x - 3 = 6x - 9
On solving.
x = 2
Then,
PS = 5*2 - 6
PS = 4
Thus, the value of side length PS is found as 4 units for the given right angled triangles.
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The correct question is attached.
Write the pair of fractions as a pair of fractions write a common denominator 6/9 and 1/3
Levi buys eggs and lemons at the store.
• He pays a total of $29. 33.
• He pays a total of $5. 39 for the eggs.
• He buys 6 bags of lemons that each cost the same amount.
How much does each bag of lemons cost?
Each bag of lemons costs $3.99
Let m represents the cost of eggs and n represents the cost of each bag of lemons.
He buys 6 bags of lemons that each cost the same amount.
so, the cost of six bags of lemons would be 6n
He pays a total of $29. 33
so, we get an equation,
m + 6n = 29. 33 ............(1)
Levi pays a total of $5. 39 for the eggs
So, m = 5.39
We need to find the value of n.
substitute above value of m in equation (1)
m + 6n = 29. 33
5.39 + 6n = 29. 33
6n = 23.94
n = 23.94 / 6
n = 3.99
Thus, the cost of each bag of lemon = 3.99 dollars
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Given right triangle ABC with altitude BD drawn to hypotenuse AC. AC = 20 and DC=18, what is the length of BC in simplest radical form?
The length of BC in simplest radical form is 2√19
How to determine the length of the lengthThe Pythagorean theorem states that the square of the hypotenuse side of a right angled triangle is equal to the square of the other sides.
It is represented mathematically as;
a² = b² + c²
Given that the parameters;
a is the hypotenuse sideb is the opposite sidec is the adjacent sideFrom the information given, we have that;
Hypotenuse side, a = 20
Adjacent side = 18
Substitute the values
20² = 18² + b²
Find the squares
400 =324 + b²
collect like terms
b² = 400 - 324
b² = 76
Make 'b' the subject of formula
b = 2√19
Hence, the value is 2√19
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A
B
D
C
If m/ABC = 130° and m/DBC = 30°,
then m/ABD = [?]°
The measure of the angle m∠ABD is 100°.
What is the measure of angle?
In mathematics, an angle is defined as the amount of rotation between two lines or planes that share a common point. The measure of an angle is typically given in degrees or radians. A full rotation is equal to 360 degrees or 2π radians, and the size of an angle can range from 0 degrees (no rotation) to 360 degrees (a full rotation).
In the given figure, m∠ABC = 130° and m∠DBC = 30° is given.
And we have to find the m∠ABD
so
m∠ABC = m∠ABD + m∠DBC
130° = m∠ABD + 30°
m∠ABD = 130° - 30°
m∠ABD = 100°
Hence, the measure of the angle m∠ABD is 100°.
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A parcel box has a height of 3 centimeters and the volume is expressed as 6x2 + 24x + 18. Write
the area of the base. Then determine the dimensions (length and width) of the base.
(HINT: Volume / height = area of the base)
Area of the Base_______
Dimensions of the base_______
and______
The area of the base of the parcel box is given by the expression A=2x²+8x+6. The dimensions (length and width) are determined from this expression as (2x+2) and (x+3).
In general, the volume of a rectangular box is calculated by the product of the height, width, and length of the box. From the given hint, we can write the volume of the parcel box as a product of the height and the area of the base. This is written as,
[tex]\begin{aligned}V&=A\times h\\6x^2+24x+18&=A\times 3\\A&=\frac{1}{3}(6x^2+24x+18)\\A&=2x^2+8x+6\end{aligned}[/tex]
The above equation gives the area of the base
Now solving the above quadratic equation to find dimensions, we get,
[tex]\begin{aligned}A&=2x^2+8x+6\\&=2x^2+6x+2x+6\\&=2x(x+3)+2(x+3)\\&=(2x+2)(x+3)\end{aligned}[/tex]
The dimensions are (2x+2) and (x+3).
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Express tan Y as a fraction in simplest terms.
a maintenance firm has gathered the following information regarding the failure mechanism for 100 air conditioning systems: evidence of gas leaks yes no evidence of electrical failure yes 55 5 no 34 6 the units without evidence of gas leaks or electrical failure showed other types of failure. if this is a representative sample of ac failure, find to 3 decimal places the probability (a) that a failure involves a gas leak. enter your answer in accordance to the item a) of the question statement (b) that there is evidence of electrical failure given that there was a gas leak. enter your answer in accordance to the item b) of the question statement (c) that there is evidence of a gas leak given that there is evidence of electrical failure. enter your answer in accordance to the item c) of the question statement
There is a 0.81 Probability that the breakdown entails a gas leak. Given that there is a gas leak, there is a 0.63 percent chance that there is evidence of electrical failure. Given that there is evidence of an electrical failure, the likelihood of a gas leak is 0.77.
A)
Total number of units
= 55 + 32 + 17 + 3
= 107
Hence the Probability that failure involves a gas leak
= ( 55 + 32 ) / 107
= 0.8131
B) Probability that there is a evidence of electrical failure given that there is a gas leak
P ( A / B ) = P( A∩B ) = 55/107 = 0.5140
P ( B ) = ( 55 + 32 ) / 107 = 0.8131
Hence P ( A / B ) = 0.5140 / 0.8131 = 0.6322
A = failure due to electrical
B = failure due to gas leak
C) Probability of a gas leak given that there is evidence of electrical failure
P ( B / A ) = P ( B ∩ A ) = 0.5140
P( A ) = ( 55 + 17 ) / 107 = 0.6729
Hence P ( B / A ) = 0.5140 / 0.6729 = 0.7639
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Identify the lower class limits, upper class limits, class width, class midpoints, and class boundaries for the given frequency distribution. Also identify the number of individuals included in the summary.
Age (yr) when award was won Frequency
15-24 27
25-34 33
35-44 14
45-54 4
55-64 6
65-74 1
75-84 1
Lower class limits are 15, 25, 35, 45, 55, 65, 75, Upper class limits are 24, 34, 44, 54, 64, 74, 84, Class width are 10 (all classes have a width of 10), Class midpoints are 19.5, 29.5, 39.5, 49.5, 59.5, 69.5, 79.5, Class boundaries are [15, 25), [25, 35), [35, 44), [45, 54), [55, 64), [65, 74), [75, 84) and Number of individuals included in the summary is 76.
Here are the details for the given frequency distribution:
Lower class limits are the least number among the pair
Here, Lower class limits are 15, 25, 35, 45, 55, 65, 75 respectively.
Upper class limits are the greater number among the pair
Here, upper limit class are 24, 34, 44, 54, 64, 74, 84 respectively.
Class width is the difference between the Lower class limits and Upper class limits which is 10 (all classes have a width of 10).
Class midpoints is the middle point of the lower class limits and Upper class limits which is 19.5, 29.5, 39.5, 49.5, 59.5, 69.5, 79.5 respectively.
Class boundaries are the extreme points of the classes which are [15, 25), [25, 35), [35, 44), [45, 54), [55, 64), [65, 74), [75, 84) respectively.
Number of individuals = 27 + 33 + 14 + 4 + 6 + 1 + 1
= 76
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What is the value of x
Answer: 1
Step-by-step explanation:
Anything to the power of 0 is 1
i need help with all a b and c.
second attachment are the correct answers, please explain how to get to those answers.
Answer:
(a) A(x) = (12 -2x)√(3x -9)
Step-by-step explanation:
You want a formula for the area (a(x)) of an isosceles triangle with congruent sides of length x and perimeter 12. You also want its maximum value, and a graph and the maximum value of z = 2a(3x+3)+1.
(a) Heron's formulaHeron's formula for the area of a triangle with side lengths a, b, c is ...
A = √(s(s -a)(s -b)(s -c)) . . . . . . where s = (a+b+c)/2, the semiperimeter
Given a perimeter of 12, and two sides x, this becomes ...
A(x) = √(6(6 -x)(6 -x)(6 -(12-2x))) = √(6(6 -x)²(2x -6))
A(x) = 2(6 -x)√(3(x -3)) . . . . . . factor out perfect squares
A(x) = (12 -2x)√(3x -9) . . . . . . domain: 3 ≤ x ≤ 6
The domain is such that the radical and the area are non-negative.
(b) MaximumThe derivative of the area function is ...
[tex]A'(x)=-2\sqrt{3x-9}+\dfrac{3(6-x)}{\sqrt{3x-9}}=\dfrac{-2(3x-9)+3(6-x)}{\sqrt{3x-9}}\\\\A'(x)=\dfrac{-9x+36}{\sqrt{3x-9}}[/tex]
The derivative is zero at the maximum, so ...
-9x +36 = 0 ⇒ x = 4 . . . . . . . an equilateral triangle
The maximum area is ...
A(4) = (12 -2·4)√(3·4 -9) = 4√3
The maximum area is 4√3.
Since the maximum of A(x) is 4√3 at x=4, the maximum of 2A(3x+3) +1 will be ...
2(4√3) +1 = 8√3 +1 . . . . . . . where 3x+3 = 4 ⇒ x = 1/3
The maximum of 2A(3x+3)+1 is 8√3 +1 at x = 1/3.
(c) Scaled and translatedThe function ...
z = 2A(3x+3) +1 = 2A(3(x+1)) +1
Compare this to ...
z = p·A(q(x -r)) +s
which is vertically expanded by p, horizontally compressed by q, then translated right r and up s.
We see that the parent function A(x) is vertically expanded by a factor of 2, compressed horizontally by a factor of 3, then translated left 1 and up 1.
Applying these transformations to the original A(x) domain and range, we find the domain is ...
1/3[3, 6] -1 = [0, 1] . . . . . domain of z
And the range is ...
2[0, 4√3] +1 = [1, 8√3 +1] . . . . . range of z