Answer:
To find the equation of a line that is perpendicular to the line y = -x - 2 and intersects the point (-5, 10), we can use the Point-Slope Form of a line: y - y₁ = m(x - X1)
The Point-Slope Form allows us to find the equation of a line when we know the slope of the line (m) and the coordinates of a point on the line (X1, Y1).
In this case, we know that the slope of the line y = -x - 2 is -1, because the coefficient of x is -1. We also know that the line intersects the point (-5, 10), so we can substitute those values into the Point-Slope Form:
[tex]y - 10 = -1(x - (-5))\\[/tex]
Next, we can simplify this equation by distributing the -1:
[tex]y - 10 = -1x + 5[/tex]
Finally, we can write the equation in slope-intercept form by adding 10 to both sides and simplifying:
[tex]y = -1x + 15[/tex]
So, the equation of the line that is perpendicular to y = -x - 2 and intersects the point (-5, 10) is y = 1x+15.
I hope this helps! If you have any questions about this problem or if you need further clarification, just let me know.
2. Chen said that the vertex for any quadratic function f(x) = ax² + bx + c can be
found at the point (-2, c). Do you agree or disagree with Chen? Explain.
Chen was wrong with the explanation the voter of a quadratic equation is at v(h, k) where
h = b/2ak = -(b² - 4ac)/4a How to find the vertex of the quadratic equationThe quadratic equation of the form ax² + bx + c can be compared with the equation of the form a(x - h)² + k which is the vertex form
In the vertex form, the vertex is easily seen an it is
v ( h, k ) and the value of h and k is defined to be
h = b / 2a
k = -(b² - 4ac) / 4a
Hence we can say that k is not equal to c and this makes Chen wrong
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Malcolm got his first job. his wage in his first year was $12.75 an hour. in year 2, it was raised to $13.50 an hour. what was the percent increase in his hourly wage between year 1 and year 2?
a. 0.06% b. 0.75% c. 5.88% d. 7.5%
The percentage increase in his hourly wage between year 1 and year 2 is 5.88 %
Percentage increase describes the eventual increase in the quantity in percent form. The percentage increase formula is used to compare the growth in a quantity from the initial value to its final value, over a period of time. Mathematically, this formula is represented as the difference between the final value and the initial value which is divided by the initial value and then multiplied by 100.
What is a percentage increase?
The percentage increase is the ratio of value increased to the original value and multiplied by 100.
It is expressed in percentage.
If there is an increase in the value of anything, then there is an increase in percentage.
We have,
Wage in the first year per hour = $8.65
Wage in the second year per hour = $10
The percentage increase in hourly wage:
= [ (13.5 - 12.75) / 8.65 ] x 100
= ( 0.75 / 12.75 ) x 100
= 5.88 %
Thus the percentage increase in his hourly wage between year 1 and year 2 is 5.88 %
Option C is the correct answer.
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If Malcom got a raise in his wage from $12.75 an hour to $13.50 an hour in one year, the percent increase in his hourly wage between year 1 and year 2 is 5.88%.
Therefore the answer is c) 5.88%
Malcolm's wage in his first year was $12.75 an hour and in year 2, it was raised to $13.50 an hour. Percentage increase in his hourly wage between year 1 and year 2 can be calculated by
% = ((wage in year 2) - (wage in year 1))/ (wage in year 1) × 100, that is
[tex]% = \frac{(wage\ in\ year\ 2)\ -\ (wage\ in\ year\ 1)}{wage\ in\ year\ 1}[/tex][tex]\% =\ \frac{(wage\ in\ year\ 2)\ -\ (wage\ in\ year\ 1)}{wage\ in\ year\ 1} \ 100[/tex]
% = (13.50 - 12.75)/ 12.75 × 100, that is
[tex]\% =\ \frac{13.50\ -\ 12.75}{12.75} \ 100[/tex]
% = 0.75/ 12.75 × 100
% ≈ 5.88
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Two cars start moving from the same point. One travels south at 52 mi/h and the other travels west at 39 mi/h. At what rate (in mi/h) is the distance between the cars increasing three hours later
Answer:
The answer is 195mile
Step by step explanation:
We've
V(1)=52mi/hV(2)=39mi/ht=3 hourto solve this we need to draw a triangle
then we need to find the distance traveled by each after 3 hours
S = V × tDistance = Speed × TimeS(1) = t × V(1) = 3 × 52 = 156 mile
S(2) = t × V(2)= 3× 39 = 117 mile
the distance between them is our z
S(1) = x
S(2) = y
using the Pythagorean Theorem
z = √x^2 + y^2 = √(156)^2 + (117)^2 = √ 13689+24336 = √38025 = 195 mile
Let x be
At maximum speed, an airplane travels
y be the
2100 miles against the wind in 6 hours.
of the
Flying with the wind, the plane can
travel the same distance in 4 hours.
The speed of the airplane with no wind is 437.5 miles per hour.
What is Speed?Speed is the unit rate in terms of distance travelled by an object and the time taken to travel the distance.
Let x be the maximum speed of the plane and y be the speed of the wind. Speed of the plane with no wind is equal to the maximum speed x.
Total distance travelled = 2100 miles
Time taken to travel the distance against the wind = 6 hours
Time taken to travel the distance with wind = 4 hours
When plane travels against wind, speed of wind becomes negative to get the average speed of both.
x - y = 2100 / 6 = 350 miles/hour
When plane travels with wind, both speeds are added.
x + y = 2100 / 4 = 525 miles/hour
Since x - y = 350 ⇒ y = x - 350
Substituting y = x - 350 in x + y = 525,
x + y = 525
x + (x - 350) = 525
2x - 350 = 525
2x = 875
x = 437.5
Hence the speed of the plane with no wind is 437.5 mph.
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The maximum speed of the plane is 437.5 miles per hour and the speed of the wind is 87.5 miles per hour.
What is the speed?The speed formula can be defined as the rate at which an object covers some distance. Speed can be measured as the distance travelled by a body in a given period of time. The SI unit of speed is m/s.
Given that, At maximum speed, an airplane travels 2100 miles against the wind in 6 hours.
Flying with the wind, the plane can travel the same distance in 4 hours.
Let x be the maximum speed of the plane and y be the speed of the wind.
So, the speed of plane with the wind is x+y
The speed of plane against the wind is x-y
Now, x+y =2100/4
x+y=525 --------(I)
x-y =2100/6
x-y=350 --------(II)
Add equation (I) and (II), we get
x+y+x-y=525+350
2x=875
x=875/2
x=437.5 miles per hour
Substitute x=437.5 in equation (I), we get
437.5+y=525
y=525-437.5
y=87.5 miles per hour
Therefore, the maximum speed of the plane is 437.5 miles per hour and the speed of the wind is 87.5 miles per hour.
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10) Ms. Johnson is throwing the entire class a pizza party.When she places the order from Tony's pizza across the street, she learns that each medium pizza has 6 slices, and each large pizza has 8 slices. If Ms. Johnson orders 9 total pizzas with a total of 66 slices, how many of each size pizza did she buy? Let x represent the number of medium pieces and let y represent the number of large pizzas.
There are 3 medium pizza and 6 large pizza.
How to illustrate the equation?Let medium pizza = x
Let large pizza = y
Since she she places the order from Tony's pizza across the street, she learns that each medium pizza has 6 slices, and each large pizza has 8 slices and Ms. Johnson orders 9 total pizzas with a total of 66 slices
This will be:
x + y = 9 ..... i
6x + 8y = 66 ..... ii
From i, x = 9 - y
Put this into equation ii
6x + 8y = 66
6(9 - y) + 8y = 66.
54 - 6y + 8y = 66.
2y = 12
Divide
y = 12/2
y = 6.
Therefore there are 6 large pizzas
Medium pizza = 9 - 6 = 3
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Your team wins 18 medals at a track meet. The medals are gold, silver, and bronze in a ratio of 2 : 2 : 5. How many of each medal were won by your team?
The gold, silver, and bronze in a ratio of 2 : 2 : 5 will be 4, gold, 4 silver and 10 bronzes.
How to illustrate the ratio?Ratio in Mathematics simply demonstrates how many times one number can be able to fit into another number. It should be noted that ratios contrast two numbers by dividing them. In this case, A/B will be the formula if one is comparing one variable (A) to another variable (B).
In this situation, team wins 18 medals at a track meet. The medals are gold, silver, and bronze in a ratio of 2 : 2 : 5.
Gold = 2/9 × 18
= 4 gold's
Silver = 2/9 × 18
= 4 silvers
Bronze = 5/9 × 18
= 10 bronzes.
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Identify explicit formula for the sequence 3, 6, 9, 12, 15, ...
Answer:
This is an arithmetic sequence since there is a common difference between each term. In this case, adding 3 to the previous term in the sequence gives the next term. In other words, an=a1+d(n−1) a n = a 1 + d ( n - 1 ) . This is the formula of an arithmetic sequence.
Step-by-step explanation:
I hope it's useful for you.
Thank you...
An arithmetic sequence is one in which each phrase grows by adding or removing a certain constant, k. In a geometric sequence, each term rises by dividing by or multiplying by a certain constant k.
We have the Sequence,
3, 6, 9, 12, 15.......
Here the common difference
d = 6-3
d = 3
So, the Explicit formula is
a(n) = a(1) + (n-1)d
a(n) = 3 + (n-1)3
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Which of the following is a type of iterative method of solving non linear equations *?
The Newton-Raphson method is a type of iterative method for solving non-linear equations.
The Newton-Raphson method is an iterative method for finding the roots of a non-linear equation. The basic idea is to start with an initial guess for the root, and then use the information from the derivative of the function to refine the guess in the direction of the root. This process is repeated until the guess is sufficiently close to the root.
The Newton-Raphson method is known to be very fast and efficient, but it does have some limitations. For example, it can only be used for functions that are differentiable, and it may not converge if the initial guess is not close enough to the root.
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What are the 7 properties of logarithms?
Properties of Logarithms are as follows: Product Property, Quotient Property, Power Rule, Change of base rule, Reciprocal Rule, Natural logarithmic Properties and Number raised to log property.
The properties of the logarithms are used to expand a single log expression into multiple or compress multiple log expressions into a single one. Seven logarithmic properties are as follows:
Product Rule : [tex]log_{a}mn = log_{a}m + log_{a}n[/tex]
Quotient Rule : [tex]log_{a}\frac{m}{n} = log_{a}m - log_{a}n[/tex]
Power Rule : [tex]log_{a}m^{n} = n* log_{a}m[/tex]
Change of base rule : [tex]log_{a}m = \frac{log_{n}m}{log_{n}a}[/tex] Where [tex]m, n, a[/tex] are positive integers and [tex]n\neq 1, a\neq 1[/tex]
Reciprocal Rule : [tex]log_{a}m = \frac{1}{log_{m}a}[/tex] where [tex]m,a[/tex] are positive integers other than 1.
Natural logarithmic Properties: [tex]ln(mn) = ln(m) + ln(n)[/tex]
[tex]ln\frac{m}{n} = ln(m) - ln(n)[/tex]
[tex]ln(m^{n}) = n* ln(m)[/tex]
The number raised to log : [tex]a^{log_{a}m} = m[/tex]
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what is the standard form of the equation of this conic
4x² - 5y² - 16x - 30y - 9 = 0
howww heelppp meeee
Answer:
To put this equation in standard form, you need to complete the square for both the x's and the y's.
First, complete the square for the x's by adding and subtracting (16/2)^2 = 16^2/2^2 = 32/2 = 16.
4x² - 16x + 16 - 16 - 5y² - 30y - 9 = 0
4x² - 16x + 16 - 5y² - 30y - 9 = 0
Now, complete the square for the y's by adding and subtracting (30/2)^2 = 30^2/2^2 = 900/2 = 450.
4x² - 16x + 16 - 5y² - 30y + 450 - 450 - 9 = 0
4x² - 16x + 16 - 5(y² - 15y + 225) - 9 = 0
Now, you can simplify the expression inside the parentheses by completing the square for y.
4x² - 16x + 16 - 5(y - 15)^2 + 5*225 - 9 = 0
Now, divide everything by -5 to get the equation in standard form:
-4/5x² + 16/5x - 16/5 - (y - 15)^2 = 0
The standard form of the equation is:
(-4/5)x² + (16/5)x - 16/5 - (y - 15)^2 = 0
how do I solve for there are 16 bacteria in a beaker? four hours later there are 228 bacteria in the beaker. what is the rate of change per hour in the number of bacteria?
Its kind of simple really
first you divide 228 by 4 which give you the amount of bacteria increased each hour which is 57
so the answer is 57 bacteria per hour
Which of the following statements is NOT true?
O The Bayesian approach to calling variants can be run in "real time" meaning you can add data as it arrives rather than waiting for all the data before beginning analysis
O In resequencing, the majority of differences observed between your data (the reads) and the genome are artifacts.
O More coverage provides a higher confidence on called variants.
O The priors used in the Bayesian approach to variant calling do not influence which genotype you infer from your data.
The statement that is NOT true is: "The priors used in the Bayesian approach to variant calling do not influence which genotype you infer from your data."
Bayesian approach is a statistical method that uses prior probabilities to update the probability of an event based on new data. In variant calling, the prior probabilities are used to estimate the likelihood of observing a variant at a certain position in the genome. The priors are chosen based on the prior knowledge of the biology of the organism and the specific variant being called. The priors used in the Bayesian approach will influence which genotype is inferred from the data, as the prior probabilities can bias the variant calling towards certain genotypes.
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What is the scale factor of the dilation? one-fifth two-fifths five-halves 5
The scale factor of the dilation is one-fifth, two-fifths, five-halves, or 5.
The scale factor of a dilation describes the ratio of the lengths of corresponding sides of the image and the preimage. To calculate the scale factor, we must first identify the lengths of the preimage and the image. Let's say that the preimage has a length of 10 units, and the image has a length of 5 units. To calculate the scale factor, we divide the length of the image by the length of the preimage: 5/10 = 1/2.
This tells us that the scale factor of the dilation is 1/2, or one-half. To determine the scale factor in terms of a fraction with a denominator of five, we can multiply the numerator and denominator of the fraction by five, resulting in a scale factor of 2/5, or two-fifths. To express the scale factor as a fraction with a numerator of five, we can multiply the numerator and denominator of the fraction by two, resulting in a scale factor of 5/2, or five-halves. Finally, to express the scale factor as a decimal, we can divide the numerator by the denominator, resulting in a scale factor of 2.5, or 5.
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Answer: C
Step-by-step explanation: 5/2
ty
5
4
3
2
1
-5-4-3-2-1
4
-2
5
2
(0,-3)
(3,4)
3 4 5
X1
x
Choose the answer to complete each statement.
The slope of the line is
The y-intercept is at
The graph represents the function
The slope of the line is 7/3 the y-intercept is -3 and the function is y = 7/3x - 3.
What is an equation of the line?An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.
The general form of the equation of the line:-
y = mx + c
m = slope
c = y-intercept
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
The slope of the line will be calculated as,
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
Slope = ( -3 - 4 ) / ( 0 - 3 )
Slope = -7 / -3 = 7 / 3
The y-intercept will be,
y = mx + c
y = 7 / 3x + c
-3 = 0 + c
c = -3
The equation of the line will be,
y = mx + c
y = 7/3x - 3
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A survey was given to a random sample of 200 residents of a town to determine
whether they support a new plan to raise taxes in order to increase education
spending. Of those surveyed, 146 respondents said they were in favor of the plan.
Determine a 95% confidence interval for the proportion of people who favor the tax
plan, rounding values to the nearest thousandth.
A 95% confidence interval for the proportion of people who favor the tax plan, rounding values to the nearest thousandth, is 292.
What is a survey?In order to gather information about a service, product, or process, a survey is described as an act of looking at a process or questioning a predetermined sample of people.
Based on the given conditions, formulate: 200 x 146%
Calculate the product or quotient: 292
Round the number: 292.0
Therefore, rounding data to the nearest thousandth, a 95% confidence interval for the percentage of persons in support of the tax plan is 292,
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Use the Pythagorean Theorem to find the distance between (-3, 4) and (6, 1)
The distance between the points (-3, 4) and (6, 1) will be 9.49 units.
What is the distance between two points?It is the measure of distance between the two points and is known as length. The length is measured in meters generally.
Let one point be (x, y) and another point be (h, k).
Then the distance between the points will be
D² = (x - h)² + (y - k)²
The points are given below.
(-3, 4) and (6, 1)
The distance between the points (-3, 4) and (6, 1) will be given as,
D² = (- 3 - 6)² + (4 - 1)²
D² = (-9)² + (3)²
D² = 81 + 9
D² = 90
Take square root on both sides. Then we have
D = √90
D = 9.49 units
The distance between the points (-3, 4) and (6, 1) will be 9.49 units.
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PLEASE HELP IT DUE BY THE END OF CLASS
Answer:
x²= 9² + 7²
x =√81+49
x=√130
x≈11.40
A trial jury of 6 people will be chosen from among 18 candidates. how many juries are possible?
There are 18564 possible juries.
The positive integers that appear as coefficients in the binomial theorem are known as binomial coefficients in mathematics. Typically efficiency is denoted by the display style notation and is indexed by the pair of numbers n k 0. It is the multiplicative formula that may be used to calculate the coefficient of the term in the polynomial expansion of the binomial power (1 + x)n.
There are 18 choose 6 ways to choose a group of 6 people from a group of 18, which is equal to 18564. This means there are 18564 possible juries.
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There are 18564 possible juries.
Now, According to the question:
A trial jury of 6 people will be chosen from among 18 candidates.
This is a combinatoric question. As such, you would have n C r possibilities, where n is equal to the number of distinct objects, in this case 18, and r is equal to the number of things taken at a time, in this case, 6.
When order does not matter (in this case, it doesn’t, since it doesn’t matter who juror 1 and who juror 6 is, as long as there are exactly 6 in the end), it would be:
n C r = n! / r! (n-r)!
[tex]_6C^1^8[/tex] = 18!/ 6! (18 - 6)!
[tex]_6C^1^8[/tex] = 18!/ 6! × 12!
This gives us 18564
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Which equation in slope-intercept form represents a line that passes through the point (5,−1) and is parallel to the line y=2x−7?
Answer:
y = 2x - 11
Step-by-step explanation:
In y = 2x - 7, the slope is 2.
A slope parallel to this would also be 2.
y = 2x + b
-1 = 2(5) + b
-1 = 10 + b
b = -11
y = 2x - 11
When determining the quotient of two numbers written in scientific notation, the base numbers and the exponents of the powers of ten.
When dividing two numbers written in scientific notation, you divide the base numbers and subtract the exponents of the powers of ten.
To determine this :
When performing mathematical operations with numbers written in scientific notation, it is important to remember that the base number and the exponent of the power of ten are treated separately. For example, consider the following problem:
(3.2 x 10³) / (2.4 x 10²)
To solve this problem, you would divide the base numbers 3.2 and 2.4 as you would with any other division problem:
3.2 / 2.4 = 1.3333...
Then, you would subtract the exponents of the powers of ten:
3 - 2 = 1
The result of the division problem is then written as 1.3333... x 10¹.
So, to summarize, when dividing two numbers written in scientific notation, you divide the base numbers and subtract the exponents of the powers of ten.
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Theoretical and Experimental Probability
I need help with these 3 questions PLEASE
4/15
What exactly are flashcards?A flashcard, also known as an index card, is a card with information on both sides that is designed to be used as a memory aid. On one side of each flashcard is a question and on the other is an answer.
The advantages include improved language abilities, increased capacity to produce tales, memorization, issue analysis, and vocabulary enrichment. Aside from cognitive benefits, flashcards may also boost self-confidence, create strong and effective communication skills, and boost creativity. Flashcards are miniature note cards that are used to test and improve memory through repeated information retrieval. Typically, flashcards are two-sided, with the prompt on one side and information regarding the prompt on the other. Names, for example, might be included.
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What is the answer????
Answer: a) [tex]4\frac{3}{5}[/tex]
b) [tex]3\frac{1}{6}[/tex]
Step-by-step explanation: I separately wrote down the steps and explanation please refer to the explanation I wrote down for better understanding.
How many solutions exist for the given equation 3x 13 3 x 6 )+ 1?
There is no solution existing for the given equation 3z + 13 = 3( z + 6 )+ 1.
Solving the equation,
3z + 13 = 3( z + 6 )+ 1
3z + 13 = 3z + 18 + 1
3z + 13 = 3z + 19
Shifting variables to one side of the equation and constants to the other side of the equation so that equation could be solved further:
Now
3z - 3z = 19 - 13
0 = 6, revealing that no solution exists for this equation.
Thus, the result shows that the given equation has no solution because 3z cancels out 3z making both sides unequal.
"
Complete question:
How many solutions exist for the given equation 3z + 13 = 3( z + 6 )+ 1?
"
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7 is subtracted from the square of a number
The expression of 7 is subtracted from the square of a number will be :
x² - 7 .
Given,
7 is subtracted from the square of a number .
Here,
Firstly ,
Let a number be x .
Square of a number will be x² .
Now we have to subtract 7 from the x² .
So,
The expression will be :
x² - 7.
Thus its is the required expression .
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What is a complex root of a polynomial?
The roots of a polynomial are the values of x for which the polynomial evaluates to 0.
A complex root is a root for which the real and imaginary parts are not both 0. If a polynomial has a complex root, that means that there is at least one value of x for which the polynomial evaluates to 0.
This can happen in two ways: either the polynomial has a real root and an imaginary root, or it has two complex roots. In either case, the complex roots must be found in order to determine the polynomial's factorization.
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What are the 4 types of fraction?
Answer:
like fraction
unlike fraction
proper fraction
improper fraction
Step-by-step explanation:
Given, line l and line m are parallel. if m∠1 = 60°, and m∠2 = 125°, what is m∠3? 95° 105° 115° 125°
The value of m∠3 is 95°.
In general, the alternate internal angles created by a transversal at the intersection of two parallel lines are congruent. The Alternate Interior Angles Theorem is the name of this tenet.
Several pairs of congruent angles are created when two parallel lines intersect a transversal. Corresponding angles are the name given to these pairings of congruent angles.
Lines l and m are parallel in the given issue and are interrupted by a transversal. This results in the creation of four angles, denoted as m1, m2, m3, and m4. The problem statement states that m1 is 60° and m2 is 125°.
Since lines l and m are parallel, the alternate interior angles formed by the transversal are congruent. This means that m∠1 is congruent to m∠3 and m∠2 is congruent to m∠4. Therefore, m∠3 is congruent to m∠1, which is 60°. Therefore, m∠3 = 60°.
The answer is therefore 95°.
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What are the factors of xⴠ2x² 9?
After taking the common, the factor of [tex]x^2+2x^2+9[/tex] is [tex]3(x^2+3)[/tex].
In the given question, we have to find the factors of [tex]x^2+2x^2+9[/tex]
(1) Find the expression's numbers' greatest common factor before analyzing each variable or expression separately to identify the GCF. Factor out the least power that arises if the variable or expression appears in every term.
(2) Write the GCF outside the parentheses and divide each term by the GCF inside the parentheses to factor out a GCF.
The given expression is [tex]x^2+2x^2+9[/tex].
In the given term first and second term have the same power of term. So we add them.
[tex]x^2+2x^2+9[/tex] = [tex]3x^2+9[/tex]
Now we take 3 common in both term
[tex]x^2+2x^2+9[/tex] = [tex]3(x^2+3)[/tex]
Hence, the factor of [tex]x^2+2x^2+9[/tex] is [tex]3(x^2+3)[/tex].
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The complete question is:
What are the factors of [tex]x^2+2x^2+9[/tex]?
How many integers are there between 1 and 1000 that are divisible by 3 and 5?
There are 166 integers between 1 and 1000 that are divisible by 3 and 5.
1000/3 = 333.3333
1000/5 = 200
333.3333 * 200 = 66,666.66
66,666.66 / 15 = 4444.444
4,444.444 rounded to 4,445
4,445 - 1 = 4,444
4,444 + 1 = 4,445
4,445 integers between 1 and 1000 that are divisible by 3 and 5.
There are 4,445 integers between 1 and 1000 that are divisible by both 3 and 5. The calculation to determine this is 1000 divided by 3, then 1000 divided by 5, then multiplying the two numbers together, then dividing by 15 and rounding the result to the nearest integer, then subtracting and adding 1 to the result.
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the height h (in feet) of a certain aircraft t seconds after it leaves the ground is modeled by h(t)=-9.1t^2+591.5t+20,288.125. What is the maximum height that the airplane reaches?
Answer:
29900 feet
Step-by-step explanation:
First, we calculate the derivative of the function h(t):
[tex]\frac{d}{dh} = -18.2(t-32.5)\\\\[/tex]
After we have the derivative function - we insert 0 on the left side of the equation to find all possible function local maxima:
[tex]0 = -18.2(t-32.5)\\t = 32.5[/tex]
From above equation we know the plane reached maximum height at time of 32.5 seconds, now we just insert the calculated value into the original function:
[tex]-9.1* 32.5^2+591.5 * 32.5+20288.125 = 29900[/tex]
Voila! :D
