A person standing close to the edge on top of a 48-foot building throws a ball vertically upward.
The quadratic function
h(t) = 16t+52t + 48 models the ball's height about the ground, h(t) in feet, t seconds after it was thrown. What is the maximum height of the ball? (Write the answer to the nearest hundredth)
Answers
After solving, the maximum height of the ball is 90.25 feet.
In the given question,
A person standing close to the edge on top of a 48-foot building throws a ball vertically upward.
The quadratic function
h(t) = -16t^2+52t + 48 models the ball's height about the ground, h(t) in feet, t seconds after it was thrown.
We have to find the maximum height of the ball.
Height is given that;
h(t) = -16t^2+52t + 48
Now comparing the given equation by the standard equation ax^2+bx+c=0
Here b = 52, a = -16
For maximum height put t= -b/2a
t = -52/2(-16)
t = 52/32
t = 1.625
Maximum height
h(1.625) = -16(1.625)^2+52(1.625) + 48
h(1.625) = -42.25+ 84.5 + 48
h(1.625) = 90.25 feet
The maximum height of the ball is 90.25 feet.
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Related Questions
Can someone help me with this pleaseeeeee
Answers
The values of x, y , and z in the matrix equation is 3, 4, 0 respectively.
What is the solution of the matrix equation?The solution of the matrix equation is calculated by applying Cramer's rule as shown below;
[ 1 1 -1 ] [ 7 ]
[ 2 3 0 ] [ 18 ]
[ -5 -7 -1 ] [ -43 ]
The determinant of the matrix is calculated as follows;
[ 1 1 -1 ]
[ 2 3 0 ]
[ -5 -7 -1 ]
Δ = 1 (-3 - 0) - 1(-2 - 0 ) - 1(-14 + 15)
Δ = -2
The x determinant of the matrix is calculated as follows;
[ 7 1 -1 ]
[ 18 3 0 ]
[ -43 -7 -1 ]
Δx = 7 (-3 - 0) - 1 (-18 - 0 ) - 1(-126 + 129)
Δx = -6
The y determinant of the matrix is calculated as follows;
[ 1 7 -1 ]
[ 2 18 0 ]
[ -5 -43 -1 ]
Δy = 1 (-18 - 0 ) - 7(-2 - 0 ) -1(-86 + 90)
Δy = -8
The z determinant of the matrix is calculated as follows;
[ 1 1 7 ]
[ 2 3 18 ]
[ -5 -7 -43]
Δz = 1 (-129 + 126) - 1(-86 + 90) + 7(-14 + 15)
Δz = 0
The values of x, y , and z is calculated as;
x = Δx/Δ = -6/-2 = 3
y = Δy/Δ = -8/-2 = 4
z = Δz/Δ = 0/-2 = 0
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Chad has a rope that is 15 yards long. How many pieces of rope measuring 5/7 of a yard can he divide his rope into?
A. 28
B. 21
C. 35
D. 14
Answers
Answer:
Chad can divide his rope in 21 pieces. (Answer B)
Step-by-step explanation:
To solve we divide.
15 divided by 5/7 is what we need to know.
When dividing fractions it is the same thing as multiplying by the reciprocal (flipped version of the fraction).
\(15\) ÷ \(\frac{5}{7}\) = 15 × \(\frac{7}{5}\)
\(\frac{15}{1}\) × \(\frac{7}{5}\) = \(\frac{105}{5}\)
\(\frac{105}{5}\) = 21
Chad can divide his rope in 21 pieces.
Answer:
21 pieces
Step-by-step explanation:
Divide (5/7 yd / piece) into 15 yds:
15 yds
----------------------- = 21 pieces
(5/7 yd / piece)
Find the limit of the function by using direct substitution. limit as x approaches zero of quantity x squared minus five. A) Does not exist B) 0 C) 5 D) -5
Answers
Answer:
lim as x---->0 of (x²-5) = -5 which is D
Cumulative frequency table is given below. Which type of cumulative frequency is given. Try to build the frequencies of respective class intervals.
Runs 0−10,10−20,20−30, 30−40, 40−50
No of cricketers 3, 8, 19, 25, 30
Answers
Step-by-step explanation:
run No of cricket more cumulative less cumulative
0-10 3 3 85
10-20 8 11 82
20-30 19 30 74
30-40 25 55 55
40-50 30 85 30
CAN SOMEONE PLEASE HELP ME ASAP
(wrong answers will be reported )
Answers
The inequality is solved and the number is x ≥ 12
Given data ,
Let the number be represented as x
Now , sum of three times a number and -4 is at least twice the number plus 8
And , 3x - 4 ≥ 2x + 8
To solve for "x", we can start by isolating the "x" term on one side of the inequality
3x - 4 ≥ 2x + 8
Subtract 2x from both sides , we get
3x - 2x - 4 ≥ 2x - 2x + 8
x - 4 ≥ 8
Add 4 to both sides , we get
x - 4 + 4 ≥ 8 + 4
x ≥ 12
Hence , the inequality is x ≥ 12
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Pls help I’ll brainlest ASAP ASAP
Answers
Answer:
3
Step-by-step explanation:
9 times 3 is 27. 27 plus 8 is 35
Answer:
d=3
Step-by-step explanation:
The figure shows four box-and-whisker plots. These represent variation in travel time for four different types of transportation from the beginning to the end of one route.
Conrad is at one end of the route. He is trying to decide how to get to an appointment at the other end. His appointment is in 30 minutes. Which type of transportation is LEAST likely to take more than 30 minutes?
Select one:
a.
bus
b.
car
c.
subway
d.
train
Answers
Comparing the median of each box-and-whisker plot, the type of transportation that is LEAST likely to take more than 30 minutes is: d. train.
How to Interpret a Box-and-whisker Plot?
In order to determine the transportation that is LEAST likely to take more than 30 minutes, we have to compare the median of each data set represented on the box-and-whisker plot for each transportation.
The box-and-whisker plot that has the lowest median would definitely represent the the transportation that is LEAST likely to take more than 30 minutes, since median represents the typical minutes or center of the data.
Therefore, from the box-and-whisker plots given, the one for train has the lowest median. Therefore train would LEAST likely take more than 30 minutes.
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which of the following inferences are true about the data? select all that apply
Answers
Answer: C
Step-by-step explanation: I did this on an exam
C
A man gave 90000.00 to his two daughters Jane and Lydia, 75.00 was given to Lydia to pay her load. After sharing the money Lydia has twice as
much as Jane. How much did each received?
Answers
Jane received $30025 and Lydia received $60000. Let's assume the amount of money that Jane received as x; then Lydia's share of the money will be twice the share of Jane.
We are to find out the share of each person. Here is the solution in steps:Suppose Jane's share was x dollars, and Lydia's share was y dollars.
Given that the total amount given to the two daughters was $90000. Also, given that Lydia paid off her $75, hence she got $75 less than Jane.
Therefore, y = 2x - 75; this is because we are given that Lydia got twice the share of Jane, and also, she got $75 less than Jane. Hence, x + y = $90000, this is because the total sum of money shared is $90000.
Substituting y = 2x - 75 into x + y = $90000 gives x + (2x - 75) = $90000.
Simplifying, we have :3x = $90000 + 75 = $90075.
Dividing both sides by 3, we get:x = $30025. Hence, Jane's share is $30025 Lydia's share = 2x - 75 = 2($30025) - $75 = $60075 - $75 = $60000.
Therefore, Jane received $30025 and Lydia received $60000.
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(I am giving branlest) (plz help only if you understand )
Solve five ninths plus four sixths.
sixty six fifty fourths
ten fifteenths
nine tenths
thirty ninths
Answers
Answer:
hey mr. one eyed ghoul
Step-by-step explanation:
calculate the molar solubility of cui (ksp= 1.27×10−12).
Answers
CuI's molar solubility is determined to be 1.27 x 10⁻¹².
The quantity of ions dissolved per litre of solution is measured by molar solubility. The quantity of ions that are dissolved in this situation's amount of solvent is represented as solubility.
Think about the equation.
Cu+(aq) CuI.(s) + I- (aq)
Let's assume that CuI (s) has a molar solubility of "S" mol/L.
Thus,
Product of solubility = [Cu+(aq)] + [ I-(aq)] → [Cu+(aq)] Ksp
[ I-(aq)] ———(1)
We are aware of
For CuI, the solubility product Ksp is 1.27 x 10⁻¹².
Consequently, from equation (1)
1.27 × 10⁻¹² = S.S
S² =1.27 × 10⁻¹²
= (1.27 × 10⁻¹² )½ = 1.127 x 10⁻⁶ M
Therefore, CuI has a molar solubility of 1.127 x 10-6 M.
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John wishes to choose a combination of two types of cereals for breakfast - Cereal A and Cereal B. A small box (one serving) of Cereal A costs $0.50 and contains 10 units of vitamins, 5 units of minerals, and 15 calories. A small box (one serving) of Cereal B costs $0.40 and contains 5 units of vitamins, 10 units of minerals, and 15 calories. John wants to buy enough boxes to have at least 500 units of vitamins, 600 units of minerals, and 1200 calories. How many boxes of each cereal should he buy to minimize his cost?
Answers
Let's assume that John buys x boxes of Cereal A and y boxes of Cereal B. Then, we can write the following system of inequalities based on the nutrient and calorie requirements:
10x + 5y ≥ 500 (minimum 500 units of vitamins)
5x + 10y ≥ 600 (minimum 600 units of minerals)
15x + 15y ≥ 1200 (minimum 1200 calories)
We want to minimize the cost, which is given by:
0.5x + 0.4y
This is a linear programming problem, which we can solve using a graphical method. First, we can rewrite the inequalities as equations:
10x + 5y = 500
5x + 10y = 600
15x + 15y = 1200
Then, we can plot these lines on a graph and shade the feasible region (i.e., the region that satisfies all three inequalities). The feasible region is the area below the lines and to the right of the y-axis.
Next, we can calculate the value of the cost function at each corner point of the feasible region:
Corner point A: (20, 40) -> Cost = 20
Corner point B: (40, 25) -> Cost = 25
Corner point C: (60, 0) -> Cost = 30
Therefore, the minimum cost is $20, which occurs when John buys 20 boxes of Cereal A and 40 boxes of Cereal B.
Solve |x-5| > -2. Write your solution in interval notation.
Answers
Answer:
(−∞,∞)
Step-by-step explanation:
Since |x−5| is always positive and −2 is negative, |x−5| is always greater than −2, so the inequality is always true.
All real numbers
So, the answer is (−∞,∞)
Mega Movies hosted a film premiere on Friday night. They charged $7 for adults and $5 for children. One hundred twenty-six adults and children attended, and $854 was made in ticket sales. How many children and how many adults went to the film premiere
Answers
Answer: 839
Step-by-step explanation:
HELP ME PLS stock worth $60 a share dropped in value by 20% on Monday. Then it dropped again by 10$ the next Tuesday. And finally increased by 55% the following Friday. What was the final price of a share?
Answers
Answer:
58.90
Step-by-step explanation:
A cylinder has a height of 5 feet. Its volume is 1,570 cubic feet. What is the radius of the cylinder? Use ≈ 3.14 and round your answer to the nearest hundredth.
Answers
The radius of the cylinder is equal to 10 feet.
How to calculate the volume of a cylinder?In Mathematics and Geometry, the volume of a cylinder can be calculated by using the following formula:
Volume of a cylinder, V = πr²h
Where:
V represents the volume of a cylinder.h represents the height of a cylinder.r represents the radius of a cylinder.By substituting the given parameters into the formula for the volume of a cylinder, we have the following;
V = πr²h
1,570 = 3.14 × r² × 5
1,570 = 15.7r²
r² = 1,570/15.7
r² = 100
Radius, r = √100
Radius, r = 10 feet.
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givien the function 6x+6y=5 rearrange the equation so that x is the independant varible
Answers
Answer:
so 6x = -6y + 5
divide by 6
x = 5
Step-by-step explanation:
The American customer satisfaction index scores of McDonalds restaurants grew from 61 in 2002 to 71 in the year 2014. Find the average rate of change for the data. Show work.
Answers
Answer:
\(\large\sf{average\:rate\:of\:change= \frac{6}{5}\:=\:1.2}\)
Step-by-step explanation:
Given the American customer satisfaction index scores that increased from 61 in 2002, to 71 in 2014:
In order to solve for the average rate of change, we could simply use the average rate of change formula:
Average rate of change = Change in output/Change in input
\(\huge\sf{Average\:rate\:of\:change\:=\:\frac{\triangle{y}}{\triangle{x}}\:=\:\frac{(y_2\: -\: y_1) }{(x_2\: -\: x_1)}}\)
Let (x₁, y₁) = (61, 2002)
(x₂, y₂) = (71, 2014)
Substitute these values into the average rate of change formula:
\(\BIGG\sf{Average\:rate\:of\:change\:=\:\frac{\triangle{y}}{\triangle{x}}\:=\:\frac{(y_2\: -\: y_1) }{(x_2\: -\: x_1)}\:=\frac{2014\:-\:2002}{71\:-\:61}\:=\:\frac{12}{10}\:=\:\frac{6}{5}}\)
\(\large\bf\sf{Therefore,\:the\:average\:rate\:of\:change= \frac{6}{5}\:=\:1.2}\).
Find the value of the polynomial x2–3xy+ 1/2 y2 if x= 1/2 and y= 2/3 .
Answers
The value of the given polynomial x² - 3xy + 1/2y² if x = 12 and y = 2/3 is; -19 / 36.
What is the value of the polynomial for the given variable values?It follows from the task content that the value of the polynomial be determined for the given polynomial expression.
As evident in the task content; the given expression is;
x² - 3xy + 1/2 y².
Hence, since the given values of x and y are: 1/2 and 2/3 respectively.
On this note, we have that;
( 1/2 )² - ( 3 × 1 / 2 × 2 / 3 ) + ( 1 / 2 × (2 / 3)² )
= 1/4 - 1 + ( 2 / 9 )
= -3 / 4 + 2 / 9
= -19 / 36
On this note, the value of the given polynomial is; -19 / 36.
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Task #2:
Alecia has 4 times the amount of
money that her sister has. Together,
they have $40.00. How much money
does Alecia have? How much money
does Alecia's sister have?
Answers
Answer:
32-Alecia and 8-sister
Step-by-step explanation:
4x+x=40
5x=40
x=8
Please help with this question
Answers
Answer:
this is the answer:
Step-by-step explanation:
Hope it helps:
2 x + 10 = 28 please answer it’s due in 4 minutes !!
Answers
Answer:
x=9
Step-by-step explanation:
bc 9x2=18 and 18+10=28
Answer:
x = 9
Step-by-step explanation:
2x + 10 - 10 = 28 - 10
2x = 18
x = 9
What is the value of the expression 4x^3 – 3x when x = 6?
Answers
4(6)^3 - 3(6)
4*(216)- 18
864 - 18
=846.
Hope it helped!
Which choice is equivalent to the expression below?
V25x - V4x + 2 VX
Answers
Answer:
The correct answer is C)
A town’s population of children increased from 376 to 421 during the past year.
Which equation shows how to find the percent increase?
p = 421 - 376 / 376
p = 421 - 376 / 421
p = 376 / 421 - 376
p = 376 + 421 / 376
Answers
Answer:
the 3 answer is the right one
One thousand six hundred fifty tickets
were sold at Friday night's football
game. Each adult ticket cost $3.50,
and each student ticket cost $2.00. The
total revenue for ticket sales was
$4,650. Write the pair of equations that
represent the number of a (adult)
tickets and s (student) tickets.
Answers
Answer:
a+s=1650, 3.5a+2s=4650
Step-by-step explanation:
a=adult, s=student
a+s=1650 equation 1
3.5a+2s=4650 equation 2
Use the two given functions to write y as a function of x.
y = -3a + 3, a = -5x + 1
Answers
Answer:
Step-by-step explanation:
To write y as a function of x using the given functions, we can substitute the value of "a" in the first equation with the expression "-5x + 1" from the second equation.
Given:
y = -3a + 3
a = -5x + 1
Substituting the value of "a" in the first equation:
y = -3(-5x + 1) + 3
Now, let's simplify this expression:
y = 15x - 3 + 3
y = 15x
Therefore, y can be expressed as a function of x as:
y = 15x
what is 1/25 squared?
Answers
Answer: 0.0016
Step-by-step explanation: To find the fraction square root, first, find the square root of the numerator and then find the square root of denominator. After finding the square root values, simplify the fraction.
2,76,212+2628 = ______ +2,76,212
Answers
Answer:
555052
Step-by-step explanation:
\(\sqrt{3x+33+17=20\)
Answers
![[tex]\sqrt{3x+33+17=20[/tex]](https://i5t5.c14.e2-1.dev/h-images-qa/answers/attachments/5jwFNAPhnAi91AozDKn3UbOORHWHtXYi.png)