Data set 2 is not a function, while data set 1 is a function. To turn the data set that is not a function into a function, the point (3,0) can be changed so the x-value is not equal to 1, 3, 5 or 7.
When does a relationship represents a function?To verify whether a relation represents a function, we need to observe if each input is mapped to only one output.
In input-output format, the points in these relations are given as follows:
(x,y).
Hence a data-set will represent a function if each value of x is mapped to a single value of y.
This means that data-set 1 represents a function, while data-set 2 does not, as the value of x = 3 is mapped to both y = 2 and y = 0.
The data-set 2 will represent a function if one of the x-coordinates of 3 is changed to another x-coordinate, that is also different of the other x-coordinates of the table.
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HELP FOR BRAINLIEST!! ASAP PLS
Using the linear function, the monthly cost for 6 HCF is $36.72.
What is the monthly cost for 6 HCF?If the monthly water bill is a linear function with a slope of 1.65, it means that for every additional HCF used, the cost increases by $1.65.
Let's denote the monthly cost as C(HCF) and the number of HCF used as HCF. We know that C(12) = $46.62.
Now, to find the monthly cost for 6 HCF (C(6)), we can use the slope information:
C(12) = $46.62
C(12) - C(6) = $46.62 - C(6) = (12 HCF - 6 HCF) * 1.65
C(6) = $46.62 - (6 HCF * 1.65)
Now, let's calculate:
C(6) = $46.62 - (6 * 1.65)
C(6) = $46.62 - 9.90
C(6) = $36.72
So, the monthly cost for 6 HCF is $36.72.
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3.4.Sarah, Lilly and Paula make R1 200 profit from selling cakes. Determine how much profit each girl receives if they invested in the ratio 1:2:3.
Profit made by each girl Sarah, Lilly and Paula respectivly are R 200 , R 400 and R 600
What is Ratio and Proportion ?A ratio displays the multiplicity of two numbers. For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. The ratio of oranges to the overall amount of fruit is 8:14, while the ratio of lemons to oranges is 6:8.
An ordered pair of integers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. For instance, you might express the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls) There are 1 in 4 boys and 3 in 4 girls.
A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. Indicators of proportions include "::" and "=".
The amount of investment done by each girl Sarah, Lily and Paula respectivly is x, 2x and 3x
So, the profit will be
x + 2x + 3x = 1200
⇒6x =1200
⇒ x = 200
Profit made by each girl respectivly are x = R 200 , 2x = R 400 and 3x = R 600.
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An employee at a construction company is ordering interior doors for some new houses that are being built. there are 6 one-story houses and 2 two-story houses on the west side of the street which require a total of 72 doors. on the east side there are 5 one-story houses and 7 two-story houses which require a total of 124 doors. assuming that the floor plans for one-story houses are identical and so are the two-story houses, how many doors does each type of house have?
The number of doors in one-story building are 8 and the number of doors in two-story building are 12.
What is a linear system of equations?A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.
Given that, an employee at a construction company is ordering interior doors for some new houses that are being built.
Let the number of doors in one-story houses be x and the number of doors in two-story houses be y.
There are 6 one-story houses and 2 two-story houses on the west side of the street which require a total of 72 doors.
Here, 6x+2y=72 -------(I)
On the east side there are 5 one-story houses and 7 two-story houses which require a total of 124 doors.
5x+7y=124 -------(II)
Multiply equation (I) by 7, we get
42x+14y=504 -------(III)
Multiply equation (II) by 2, we get
10x+14y=248 -------(IV)
Subtract equation (IV) from (III), we get
32x=256
x=8
Substitute x=8 in equation (I), we get
48+2y=72
2y=24
y=12
Therefore, the number of doors in one-story building are 8 and the number of doors in two-story building are 12.
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work out the area of this shape
Answer: 127
Step-by-step explanation:
the image has steps
Answer:
the answer is 127 cm^2 ig
!!!!!!!!!!!!Sorry im just so tired from so much work but I need some help with this one quickly while I finished other assignments!!!!!!Question How do you graph an inequality? Use 2 or more sentences
Answer: To graph an inequality, treat the <, ≤, >, or ≥ sign as an = sign, and graph the equation. If the inequality is < or >, graph the equation as a dotted line. If the inequality is ≤ or ≥, graph the equation as a solid line.
Step-by-step explanation:
a household having 0.5 inch pipe consumed 45 units of water in a month. Calculate the payment of bill including 50% sewage service charge if the payment is made within one month of bill issued.
Answer:Volume of Pipe Formula. The pipe volume formula is: Volume = pi x radius² x length. To do piping size calculation, follow these steps: Find the inner diameter and length of the pipe, in inches or millimeters. Calculate the inner diameter of the pipe by measuring
Step-by-step explanation:
Help I have one more try
Answer: The answer is 4
Step-by-step explanation: Firstly you want to convert the whole number into a fraction, the fraction will be 24/1. Then you multiply 1/6 by 24/1 or 1x24/6x1 which equals 26/6. This fractio can be simplified, by finding the greatest common factor. The GCF of 24 and 6 is 6.
24/6 = 4
6/6 = 1
So our full answer is 4/1 which simplifies to 4
Answer:
4
Step-by-step explanation:
take 24 divided by 6 you'll get
Tara has read 95\%95%95, percent of the books she owns. If Tara owns 160160160 books, how many of her books has she not read?
The number of the books owed by Tara which she has not read would be = 152 books.
What is percentage?Percentage is defined as the part of the value that can be expressed as per 100 of the whole given value. This can be represented with a symbol such as %..
The number of books owned by Tara = 160 books
The percentage of books read by Tara = 95%
Therefore, 95% of her books = 95/100 × 160
= 15200/100
= 152 books.
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select the correct answer. a classmate finds that it takes 1.090 seconds for a tossed ball to touch ground. how many significant figures are in this measurement? a. 4 b. 3 c. 2 d. 1
Significant figures are in this measurement 1.090
In a number, to determine the number of significant figures following three rules are used:
The digits which are non-zero are always significant.
Any zeros between two digits which are non-zero are significant.
In the decimal portion, trailing zeros are significant.
Significant figures = Numbers that carry meaning in the measurements of a number.
The number is 1.090, it has two non-zero digits, 1 zero in between two non-zero digit and one trailing zero thus, all of them are significant figures.
Therefore, it has 4 significant figures : 1.090
Significant figures are in this measurement 1.090
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The sum of the perimeters of 2 different regular hexagons is 66 and the difference between their perimeters is 30. If x represents the side length of the larger regular hexagon and y represents the side length of the smaller regular hexagon, which of the following systems of equations can be used to find the dimensions of the regular hexagons?
Perimeter of rectangular hexagon = 6 × length of side, length of side of given hexagon = 30/6 =5 cm and perimeter of new figure = Number of outer sides × length of each side =10×5=50 cm
What is rectangle?A rectangle in Euclidean plane geometry is a quadrilateral with four right angles. You might also describe it as follows: a quadrilateral that is equiangular, which indicates that all of its angles are equal. The parallelogram might also have a straight angle. Squares are rectangles with four equally sized sides. A quadrilateral of the shape of a rectangle has four 90-degree vertices and equal parallel sides. As a result, it is sometimes referred to as an equirectangular rectangle. Because its opposite sides are equal and parallel, a rectangle is also known as a parallelogram.
Perimeter of rectangular hexagon = 6 × length of side
length of side of given hexagon = 30/6 =5 cm
perimeter of new figure = Number of outer sides × length of each side
=10×5=50 cm
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Which of the following is not a polynomial ? a: √3x^2-2√3x+3 , b: 3x^3/2-5x^2-1/√2x-1 , c: x+1/x , d: 5x^2-3x+ √2
A polynomials is a mathematical statement made up of real number coefficients and a sum of power in one or so more parameters (indeterminates) having non-negative integer exponents.
Out of the options given, option "b" is not a polynomial.SOLUTION:
Three terms with non-negative integers exponents (x2, x1) make up Option "polynomial, "'s which has real numbers (x3, -2x3, and 3) as coefficients.
Option "c" x+1/x is a rational function; it is not a polynomials because of the fraction in it. It consist of one polynomials divided by another polynomial. 1/x
Option "d" is a polynomial that has real numbers (5, -3, and 2) as coefficients and terms with non-negative integers exponents (x2, x1) as its exponents.
Consequently, option "b" 3x3/2-5x2-1/2x-1 is not a polynomial due to the fraction and non-integer exponent (3/2).
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Option "b" 3x3/2-5x2-1/2x-1 is not a polynomial due to the fraction and non-integer exponent (3/2). A polynomials is a mathematical statement made up of real number coefficients and a sum of power in one or so more parameters (indeterminates) having non-negative integer exponents.
How to find a polynomial?Three terms with non-negative integers exponents (x2, x1) make up Option "polynomial, "'s which has real numbers (x3, -2x3, and 3) as coefficients.
Option "c" x+1/x is a rational function; it is not a polynomials because of the fraction in it. It consist of one polynomials divided by another polynomial. 1/x
Option "d" is a polynomial that has real numbers (5, -3, and 2) as coefficients and terms with non-negative integers exponents (x2, x1) as its exponents.
Consequently, option "b" 3x3/2-5x2-1/2x-1 is not a polynomial due to the fraction and non-integer exponent (3/2).
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Complete the following probability distribution table: Probability Distribution Table X P(X)20 0.2 49 0.453 ? 80 0.3 Get help: Written Example
0.1 is probability in distribution table.
What are examples and probability?
The quantity of success-producing options. the total number of outcomes that could occur.
For instance, the chance of flipping a coin and obtaining heads is 1 in 2, as there is only one way to acquire a head and there are a total of 2 possible outcomes (a head or tail). We specify P(heads) = 12.
Here X is a random variable. P(X) is its probabilities corresponding to the different values of X.
now according to the properties of probability theory we know that sum of probabilities is 1.
so here to find the value of the probability of X coresponding to the value 53 we should use the following steps:
sum of given probabilities =(0.2+0.4+0.3) = 0.9
required probability = 1 - sum of given probabilities = 1 - 0.9 = 0.1
hence the complete probability table is
X P(X)
20 0.2
49 0.4
53 0.1
80 0.3
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the difference between the two numbers is 3 and their product is 28
Answer:
4 and 7
Step-by-step explanation:
7-4=3
4x7=28
At what point do the curves r1 (t) = t, 4 - t, 35 + t^2 and r2 (s) = 7 - s, s - 3, s^2 intersect? Find their angle of intersection, \theta, correct to the nearest degree.
At point, the parametric curves cross (4, 1, 32).
What are parametric functions?t functions expressed as x = f(y) = y = f(x) = (some function of the variable x) (some function of the variable y).
It is frequently more easier to view functions of two or more variables (although we'll keep it at two here) as parametric functions, particularly in physical science.
The introduction of the idea of time makes parametric functions the most simple to understand.
Imagine tracing a parabola-like function from left to right as time passes.
Then, it is simple to begin considering how the x-coordinate and the y-coordinate change as a function of time: x = f(t), y = g. (t). In this sense, time is actually referred to as the parameter.
We will investigate functions for which a point exists in this section.
Hence, At point, the parametric curves cross (4, 1, 32).
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Na
PRE-ALGEBRA REVIEW
1. An appliance store offers a loan to buy a
refrigerator for $2,700 at an 8% simple interest
rate with equal monthly payments for 2 years.
What is the monthly payment?
A. $124.50
B. $127.50
C. $130.50
D. $132.50
The monthly payment is $130.50. Therefore, option C is the correct answer.
What is the simple interest?Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time.
Simple interest is calculated with the following formula: S.I. = (P × R × T)/100, where P = Principal, R = Rate of Interest in % per annum, and T = Time.
Given that, principal =$2700, rate of interest =8% and time =2 years
Here, SI=(2700×8×2)/100
= 43200/100
= $432
Amount =Principal+Interest
= 2700+432
= $3132
We know that 2 years =24 months
Now, the monthly payment = 3132/24
= $130.50
Therefore, option C is the correct answer.
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Rob is saving to buy a new MP3 player. For every $ 16 he ears babysitting, he saves $9. On Saturday, Rob earned $32 babysitting. How much money did he save?
Applying proportions, the amount of money Bob saved is $18.
How to Apply Proportions to Solve Problems?Proportions can also be used to express a relationship between two or more values in the form of a ratio, such as a:b, where a and b are values being compared.
We can start the problem by using the proportion of saving to earning, which is 9/16.
If for every $16 he earns babysitting, he saves $9, then for $32 that he earned babysitting, he saved:
$9 / (16/32) = $9 * 2 = $18
So Rob saved $18 from the money he earned babysitting on Saturday
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Factor completely:
a^n + a^n+1
Answer:
a^n(a+1)
This is just to reach the minimum character limit.
the perimeter of square $abcd$ is 2. two cars start from $a$ and $b$ simultaneously and drive clockwise on the perimeter of square $abcd$ in the same speed. a drone maintains its location as the midpoint of the two cars. how far did the drone fly after both cars get back to where they started?
The drone has flown a total distance of 4 units, as it has travelled the same distance as the two cars (2 units each).
What is perimeter?Perimeter is the total length of a two-dimensional shape's boundary. It is the sum of all the sides of a shape. Perimeter is used in many areas such as geometry, architecture, landscaping, and more. Perimeter is a measure of the distance around a shape and is often used to measure the size of a space or area.
As the cars have completed a full circuit of the square $abcd$, the drone has also completed a full circuit of the square. The perimeter of the square is 2, so the drone has flown a total distance of 4 units.
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The drone has flown a total distance of 4 units, as it has travelled the same distance as the two cars (2 units each). This can be solved by applying the concept of perimeter.
What is perimeter?Perimeter is the total length of a two-dimensional shape's boundary. It is the sum of all the sides of a shape. Perimeter is used in many areas such as geometry, architecture, landscaping, and more. Perimeter is a measure of the distance around a shape and is often used to measure the size of a space or area.
As the cars have completed a full circuit of the square abcd, the drone has also completed a full circuit of the square. The perimeter of the square is 2, so the drone has flown a total distance of 4 units.
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-10x + 3y = 5
x=y - 4
Answer:
You can use the second equation to substitute the value of x in the first equation and solve for y.
x = y - 4
-10(y - 4) + 3y = 5
-10y + 40 + 3y = 5
-7y = 35
y = 5
Now that you have the value of y, you can use the second equation to find the value of x.
x = y - 4
x = 5 - 4
x = 1
So the solution of the system of equations is x = 1 and y = 5
Step-by-step explanation:
1. how much lower was the 6 a.m. temperature in montreal than in atlanta?
2. by noon, the temperature in milwaukee had risen by 8 degrees. what was the temperature there at noon?
(a) The 6 a.m. temperature in montreal was 84 Fahrenheit lower than in atlanta.
(b) by noon, the temperature in milwaukee was 3 Fahrenheit.
What is arithmetic and simplification?In mathematics, it deals with numbers of operations according to the statements.
The process in mathematics to operate and interpret the function to make the function simple or more understandable is called simplifying and the process is called simplification.
Given that,
City Temperature table (°F)
Montreal -16
Atlanta 68
Dayton 36
milwaukee -5
Juneau -31
Part A- Temperature difference in Atlanta and Juneau
= (-16) - 68
= -84 F
Part B- temperature in milwaukee raise by 8 F at noon
Temperature in noon = - 5 + 8 = +3 F
Thus,
(a) The 6 a.m. temperature in montreal was 84 Fahrenheit lower than in atlanta.
(b) by noon, the temperature in milwaukee was 3 Fahrenheit.
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to change the weight of kilograms into pounds, multiply the weight in kilograms by ____________
1 kilograms is equal to 2.205 pounds, which leads to the conversion factor of 2.205. The conversion factor is based on both the Avoirdupois system of measurement, which is used in the United States and the United Kingdom to measure weight or mass, and the International System of Units (SI).
The basis for the Avoirdupois system is the pound, which is equal to 0.45359237 kilos. Consequently, 0.45359237 kilograms equal one pound.
Finding the weight in pounds of 1 kilograms is necessary to convert kilograms to pounds. We can divide 1 kilograms by 0.45359237 kilograms/pound to get this equivalent weight.
1 kg / 0.45359237 kg/lb = 2.20462262 lb
This is the kilograms to pound conversion factor. The value is rounded to the widely regarded and employed value of 2.205.
Therefore, to convert kilograms to pounds, we multiply the weight in kilograms by 2.205.
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people with acrophobia (fear of heights) sometimes enroll in therapy sessions to help them overcome this fear. typically, seven or eight therapy sessions are needed before improvement is noticed. a study was conducted to determine whether the drug d-cycloserine, used in combination with fewer therapy sessions, would help people with acrophobia overcome this fear. each of 27 people who participated in the study received a pill before each of two therapy sessions. seventeen of the 27 people were randomly assigned to receive a d-cycloserine pill, and the remaining 10 people received a placebo. after the two therapy sessions, none of the 27 people received additional pills or therapy. three months after the administration of the pills and the two therapy sessions, each of the 27 people was evaluated to see if he or she had improved. was this study an experiment or an observational study? provide an explanation to support your answer. when the data were analyzed, the d-cycloserine group showed statistically significantly more improvement than the placebo group did. based on this result, would the researchers be justified in concluding that the d-cycloserine pill and two therapy sessions are as beneficial as eight therapy sessions without the pill? justify your answer. a newspaper article that summarized the results of this study did not explain how it was determined which people received d-cycloserine and which received the placebo. suppose the researchers allowed the therapists to choose which people received d-cycloserine and which received the placebo, and no randomization was used. explain why such a method of assignment might lead to an incorrect conclusion.
(a)- The study was experimental.
(b)- No, the researchers would not be justified in doing so.
(c)- Such a method leads to an incorrect conclusions for justifiable reasons.
This problem involves minute statistical knowledge and assesses the student's ability to differentiate between an experiment and an observation and also his/her potential to make justifiable logics as to draw conclusions for a scientific research. The explainations are-
Part - (a)
The study was not an observation, it was an experiment because the treatments involving D-Cycloserine or placebo were imposed by the researchers on the people with acrophobia.
Part (b) -No, the experiment was designed to compare the D-Cycloserine group with a control group that received a placebo . The researchers can conclude that the D-Cycloserine and two therapy sessions show significantly more improvement than a placebo and two therapy sessions. However, there is no basis for comparison with the other group of people with acrophobia who received eight therapy sessions and no pill.
Part (c)-
We can cite an example that if the therapists were allowed to choose who received a placebo and who received D-Cycloserine, they might assign the people with more severe acrophobia with the other group. Thus, the improvement after only two therapy sessions can be related to the initial severity of the acrophobia rather than to the effects of D-Cycloserine.
Therefore, the answers are -
(a)- The study was experimental.
(b)- No, the researchers would not be justified in doing so.
(c)- Such a method leads to an incorrect conclusions for justifiable reasons.
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The Rockets and the Rangers are in a league where each of the teams plays $100$ games. At some point in the season, the Rockets' ratio of their wins to their losses is $3:2,$ the Rangers' ratio of their wins to their losses is $7:13,$ and both teams have the same number of games left to play. If the Rockets lose all of their remaining games while the Rangers win all of their remaining games, the teams will end the season with the same number of wins. At this point in the season, how many games do the Rockets have left to play?
By solving a linear equation we will see that there are 20 games left.
How many games do the Rockets have left to play?We know that there is a total of 100 games, and the ratio of wins to loses for the rockets is:
3:2
The ratio for the rangers is:
7:13
We know that if the rockets loses all the remaining games, and the rangers win all the remaining games then both teams will win the same number of games.
Let's define X as the number of games left, the number of games won by the rockets is:
(100 - X)*(3/5)
The number of games won by the rangers is:
(100 - X)*(7/20)
We know that if the rangers win the X games left, they will have the same number of wins than the rockets (if the rockets don't win any more game)
Then we can write the linear equation:
(100 - X)*(7/20) + X = (100 - X)*(3/5)
we can solve this for X.
X = (100 - X)*(3/5) - (100 - X)*(7/20)
X = (100 - X)*(3/5 - 7/20)
X = (100 - X)*(12/20 - 7/20)
X = (100 - X)*(5/20)
(20/5)*X = 100 - X
4*X = 100 - X
4*X + X = 100
5*X = 100
X = 100/5
X = 20
There are 20 games left for the rockets.
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how do I work this out and what is the answer
Answer:
54 cm^2
Step-by-step explanation:
calculate the area of each of the 2 rectangles and add them .
area of rectangle = l × w
so let the area of the big rectangle be A1 and the area of the small one A2 :
A1 = l × w = 11 × 4 = 44 cm^2
A2 = l × w = 5 × 2 = 10 cm^2
then , the area of the shape is = A1 + A2 = 44 + 10 = 54 cm^2
What is the absolute value graph called?
Help
need 9 more after this
The simplified form of the given expression is, [tex]\frac{81x^5}{125y^1^8}[/tex].
What is simplifying an expression?
To simplify an expression, create an equivalent expression without any terms that are similar. The expression will then be rewritten using the fewest terms possible.
Solving a math problem is the same thing as simplifying an expression. You basically try to write an expression as simply as you can when you simplify it. At the conclusion, there shouldn't be any more multiplying, dividing, adding, or removing to do.
Consider, the given expression:
[tex](\frac{3x^3y^0}{x^-2} )^4*(\frac{y^2x^-^4}{5xy^-^8} )^3[/tex]
Using the rule: [tex](\frac{a}{b} )^m = \frac{a^m}{b^m}[/tex]
⇒ [tex](\frac{3x^3y^0}{x^-2} )^4*(\frac{y^2x^-^4}{5xy^-^8} )^3 = (\frac{81x^1^2y^0}{x^-^8})(\frac{y^6x^-^1^2}{125x^3y^2^4} ) = \frac{81y^6}{125x^-^5y^2^4} = \frac{81y^-^1^8}{125x^-^5}= \frac{81x^5}{125y^1^8}[/tex]
Hence, the simplified form of the given expression is, [tex]\frac{81x^5}{125y^1^8}[/tex].
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What is the slope of the line that passes through (-4, 7) and (-6, 5)?
also please explain on how you got the answer
The slope of the line that passes through (-4, 7) and (-6, 5) is 1.
What is slope of a line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The formula to find the slope of a line is slope = (y₂-y₁)/(x₂-x₁).
The given coordinate points are (-4, 7) and (-6, 5).
Now, slope m=(5-7)/(-6+4)
m=-2/(-2)
m=1
Substitute m=1 and (x, y)=(-4, 7) in y=mx+c, we get
7=1(-4)+c
c=11
Substitute m=1 and c=11 in y=mx+c, we get
y=x+11
Therefore, the slope of the line that passes through (-4, 7) and (-6, 5) is 1.
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Tabitha’s account balance is $3,800. Of this, $750 is for rent. Tabitha wants to keep a balance greater than $500. Write an inequality describing how much she can withdraw and still meet these conditions
The inequality describing how much she can withdraw is x < 3550
What is an equation?An equation is a expression that shows the relationship between numbers and variables.
Inequalities are used in expression for non equal comparison of variables.
Let x represent the amount of money that can be withdrawn.
Tabitha’s account balance is $3,800. Of this, $750 is for rent. Hence:
Money remaining = 3800 - 750 = 3050
Tabitha wants to keep a balance greater than $500. Hence:
3050 - x > 500
x < 3550
The inequality is x < 3550
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if x is a positive integer, r is the remainder when x is divided by 4, and r is the remainder when x is divided by 9, what is the greatest possible value of r2 r ?
As per the remainder that the greatest possible value of 17
The term remainder in math defined as if a number is not completely divisible by another number then we are left with a value once the division is done
Here we have if x is a positive integer, then r is the remainder when x is divided by 4 and r is the remainder when x is divided by 9.
As we all know that the remainder is always smaller than the divisor.
Here we have also know that it will be 0 if the dividend is evenly divisible or a positive integer less than the divisor.
So, when we divided by 4 then the largest remainder will be 3 and then here we have to divided by 9, then the largest remainder will be written as
=> r² + R = 32 + 8
=> 9 + 8 = 17
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Can someone help me solve the first math problem please in a quadratic model
a) The maximum Height of Projectile is 843.75 m
b) The projectile reach its maximum at t= 12.5 sec.
What is Quadratic Equation?A quadratic equation is a second-order polynomial equation in a single variable x ax²+bx+c=0. with a ≠ 0 .
It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem.
Given:
h(t) = -5t² +120t + 125
a) For the maximum height, h= 0
-5t² +120t + 125 = 0
t² - 24 t - 25 = 0
t² - 25t + t - 25 = 0
t( t- 25) + 1(t-25)= 0
(t-25)(t+1)=0
t= 25, -1
So, Max height is reached after half the total flight time, t= 25/2
So, h(25/2 )= -5(25/2)² +120(25/2) + 125
= -5 x 156.25 + 1500+ 125
= 843.75 m
b) The projectile reach its maximum at t= 12.5 sec.
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