Mathematics College

Physics shows that when an object is thrown upward with an initial velocity of v_0, then its approximate height is given by this quadratic function.

s = -4.9t^2 + v_0^t + h

A ball is thrown upward from the top of a building 15 meters high, at a velocity of 3.1m/sec. Answer the following questions. Be sure to show and explain all work.

A. Find the maximum height and the time in which it was attained (round to 3 decimal places)

B. When does it reach the ground? (round to 3 decimal places)

C. Sketch a graph to illustrate your answers.

Answers

Answer 1

The answers to each part is given above.

Explain Maxima and Minima in mathematics?Maxima and Minima are known as the extrema of a function. Maxima and minima are the maximum or the minimum value of a function within the given set of ranges. For the function, under the entire range, the maximum value of the function is known as the absolute maxima and the minimum value is known as the absolute minima.Local Maxima : A point x = b is a point of local maximum for f(x) if in the neighborhood of b i.e in (b−, b+) where can be made arbitrarily small, f(x) < f(b) for all x ∈ (b−, b+)∖{b}. This simply means that if we consider a small region (interval) around x = b, f(b) should be the maximum in that interval.Local Minima : A point x = a is a point of local minimum for f(x) if in the neighbourhood of a, i.e. in (a−,a+), (where can have arbitrarily small values), f(x) > f(a) for all x ∈ (a−,a+)∖{a}. This means that if we consider a small interval around x = a, f(a) should be the minimum in that interval.

Given is that when an object is thrown upward with an initial velocity of v{0}, then its approximate height is given by this quadratic function -

S = - 4.9t² + [tex]$v_{o} ^{t}[/tex] + h

The approximate height is given by this quadratic function -

S = - 4.9t² + [tex]$v_{o} ^{t}[/tex] + h

{ 1 } - For the maximum height :

dS/dt = 0                                        ... Eq{ 1 }

dS/dt = -9.8t + [tex]$3.1^{t}[/tex] log(3.1) + 0 = 0

- 9.8t + [tex]$3.1^{t}[/tex] log(3.1) = 0

Refer to the graph attached. At t = 3.8 {possible value}, the function is 0.

So we get -

t = 3.8 s                                         ... Eq{ 2 }  

Maximum height achieved -

h{max} = - 9.8t + [tex]$3.1^{t}[/tex] log(3.1) + 15

h{max} = - 9.8 x 3.8 + [tex]$3.1^{3.8}[/tex] log(3.1) + 15

h{max} =  - 37.24 + 73.65 x 0.50 + 15

h{max} =  14.585 m

{ 2 } -

0 = 3.1 t + 9.8/2 t²

0 = 3.1 t + 4.9 t²

Solving graphically, we get -

|t| = 0.6 s

Total time taken to reach ground -

T = 2 x 3.8 + 0.6

T = 8.2 seconds                                       ... Eq{ 3 }

Therefore, the answers to each part is given above.

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Related Questions

A bakery is selling breakfast platters. A platter of 12 bagels costs $10.20. Additionally, it costs $4.65 for a gallon of coffee. What is the slope of this situation? 10.20 4.65 0.85 0.12

Answers

The slope of the given situation of selling breakfast platters is 0.90.

What is slope?

In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line. The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).

here, we have,

Given, the platter of 12 bagels costs $10.20.

The extra cost of  $4.65 for a gallon of coffee.

To find the slope of the situation, we convert the situation into the equation of the line.

y=mx+c

here c is the extra cost that is 4.65

12m=10.20

For 12 bagels , the cost is 10.20,

then the slope will be the cost of each bagel.

m=10.20/12

m=0.85

m=$0.85

Therefore, option c 0.85 is the slope of the given situation of the bakery selling the breakfast platter of 12 bagels and a gallon of coffee.

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PLS HELP ME SOLVE THIS

Answers

Answer:

Below

Step-by-step explanation:

According to the triangle bisector theorem

x/18 = 45/20

x = 40.5 units

Use the graph of f to evaluate the following
The average rate of change of f from 2 to 5

Answers

By using the graph, the average rate of change of the function f from 2 to 5 is equal to -1.

How to determine the average rate of change?

In Mathematics, the average rate of change of f(x) on a closed interval [a, b] is given by this mathematical expression:

Average rate of change = [f(b) - f(a)]/(b - a)

Next, we would determine the average rate of change of the function f from the graph over the interval [2, 5]:

a = 2; f(a) = 4

b = 5; f(b) = 1

Substituting the given parameters into the average rate of change formula, we have the following;

Average rate of change = (1 - 4)/(5 - 2)

Average rate of change = -3/3

Average rate of change = -1.

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20 points!!
A EF = 22
B EF = 11
C EF = 16
D EF = 20

Answers

Answer:

A

Step-by-step explanation:

the midsegment EF of the trapezoid ABCD is half the sum of the parallel bases, that is

EF = [tex]\frac{AB+DC}{2}[/tex] ( substitute values )

x + 6 = [tex]\frac{2x-9+x+5}{2}[/tex]

x + 6 = [tex]\frac{3x-4}{2}[/tex] ( multiply both sides by 2 to clear the fraction )

2x + 12 = 3x - 4 ( subtract 3x from both sides )

- x + 12 = - 4 ( subtract 12 from both sides )

- x = - 16 ( multiply both sides by - 1 )

x = 16

Then

EF = x + 6 = 16 + 6 = 22

Work out 1 1 2 + 2 3 7 Give your answer as a mixed number where appropriate.

Answers

Solution of 1 1/2 + 2 3/7 is 3 13/14

What is mixed number?

A mixed number is formed by combining three parts: a whole number, a numerator, and a denominator. The numerator and denominator are part of the proper fraction that makes the mixed number.

Given expression,

1 1/2 + 2 3/7

it can be written as

= 3/2 + 17/7

= (21 + 34)/14

= 55/14

= 3 13/14

Hence,  3 13/14 is the solution of 1 1/2 + 2 3/7

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−5 × (5 + 15 ÷ 5) − 6

Answers

Answer:

Step-by-step explanation:-46

C, C, R, R, D, R, H, H, C, A, A, R, A, A, A, R, R,
H, H, H, C, H, A, R, D, D, D, D, H, R
What is the relative frequency of the people that chose romance? Show
your calculation.
What is the relative frequency of the people that chose comedies? Show
your calculation.
c. What is the relative frequency of the people that chose horror? Show
your calculation.
g. Use the relative frequencies calculated in parts (b) – (f) to explain which
genre of movies is the most popular with your class. Explain your reasoning.
h. If you were having a party for your class which movie genre would you be
least likely to pick? Explain your reasoning.

Answers

Answer:

a. To find the relative frequency of people that chose romance, we need to count the number of times the letter "R" appears in the given sequence and divide it by the total number of letters in the sequence.

The number of times "R" appears in the sequence is: R, R, R, R, R, R, H, R = 7

The total number of letters in the sequence is: 26

Relative frequency of people choosing romance = 7/26 = 0.269 or approximately 0.27.

b. To find the relative frequency of people that chose comedies, we need to count the number of times the letter "C" appears in the given sequence and divide it by the total number of letters in the sequence.

The number of times "C" appears in the sequence is: C, C, C, H, C, C, H, H, C, C = 9

The total number of letters in the sequence is: 26

Relative frequency of people choosing comedies = 9/26 = 0.346 or approximately 0.35.

c. To find the relative frequency of people that chose horror, we need to count the number of times the letter "H" appears in the given sequence and divide it by the total number of letters in the sequence.

The number of times "H" appears in the sequence is:

H, H, H, H, H, H, H = 7

The total number of letters in the sequence is: 26

Relative frequency of people choosing horror = 7/26 = 0.269 or approximately 0.27.

g. Based on the relative frequencies calculated, it can be seen that comedies is the most popular movie genre among the class, as it has the highest relative frequency of 0.35.

h. Based on the relative frequencies, it can be seen that romance is the least popular movie genre among the class, as it has the lowest relative frequency of 0.27. Hence, if we were having a party for the class, we would be least likely to pick romance as the genre of movie to watch.

Mike bought several packs of lacrosse trading cards to add to his collection
to pay for his cards packs , he paid with 1 quarter, 2 dimes 4 nickels and 4 pennies
What was the cost of the packs of cards that mike bought ?

Answers

The cost of the packs of cards that Mike bought can be calculated by adding up the value of the coins he used to pay for them.

1 quarter is worth 25 cents.

2 dimes are worth 2 * 10 cents = 20 cents.

4 nickels are worth 4 * 5 cents = 20 cents.

4 pennies are worth 4 cents.

So, the total value of the coins that Mike used to pay for the packs of cards is 25 + 20 + 20 + 4 = 69 cents.

Therefore, the cost of the packs of cards that Mike bought was 69 cents.

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