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A baseball is thrown up in the air. The table shows the heights y (in feet) of the baseball after x seconds. Write an equation for the path of the baseball. Find the height of the baseball after 1.7 seconds.
Answers
The equation of an object in free fall is the equation of a parabola
The equation for the path of the ball is y = -16·x² + 36·x + 4The baseball height, after 1.7 seconds is 18.89 feet.
The reason the above values are correct are as follows:
The known parameters are;
The direction of the baseball is up in the air
The values of the height of the baseball after x seconds is given as follows;
[tex]\begin{array}{ccc}\mathbf{Time, \ x}&&\mathbf{Baseball \ height, \ y}\\0.5&&18\\1&&24\\1.5&&22\\2&&12\end{array}\right][/tex]
Required;To write the equation for the path of the baseball
Solution:
The general equation of the motion of free fall is the equation of a parabola, which can be written as follows;
y = a·x² + b·x + c
From the given table, we have;
18 = a·0.5² + b·0.5 + c = 0.25·a + 0.5·b + c
18 = 0.25·a + 0.5·b + c...(1)
24 = a + b + c...(2)
22 = 2.25·a + 1.5·b + c...(3)
12 = 4·a + 2·b + c...(4)
Subtracting equation (1), from (2), to get equation (5) and subtracting equation (3) from (4) to get equation (6) gives;
6 = 0.75·a + 0.5·b...(5)
-10 = 1.75·a + 0.5·b...(6)
Subtracting equation (5) from equation (6) gives;
-10 - 6 = 1.75·a - 0.75·a = a
a = -16
From equation (5), we get;
6 = 0.75 × (-16) + 0.5·b
b = (6 - 0.75 × (-16))/0.5 = 36
b = 36
From equation (2), we get;
24 = (-16) + 36 + c
c = 24 - ((-16) + 36) = 4
The equation for the path of the ball is y = -16·x² + 36·x + 4
Required;The height of the baseball after 1.7 seconds
Solution:
The height, y, of baseball after 1.7 seconds is given by substituting for the time x = 1.7 in the equation of the baseball as follows;
After 1.7 seconds, y = -16 × 1.7² + 36 × 1.7 + 4 = 18.89
The height of the baseball y, after 1.7 seconds is 18.89 feet.
Learn more about motion of an object in free fall here:
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Related Questions
If 7x = 24 y, find the ratio of x to y.
Answers
Answer:
7:24 or [tex]\frac{7}{24}[/tex]
Step-by-step explanation:
a ratio is usually defined as a fraction ( the first to the next)
The speed of light is approximately 3x10^8 m/s. How far does light travel in
240 seconds?
7.2x10^10 m
7.2x10^-10 m
1.25x10^6 m
1.25x10^-6 m
Answers
Answer:
7.2*10^10m
Step-by-step explanation:
3*10^8 multiplied by 240 gives 72000000000.
In scientific notation, this is 7.2*10^10.
Therefore, 7.2*10^10m.
Answer:
1.25x10^_6 m this my own answe
A window in the shape of a parallelogram has a base of 34 inches and a height of 63 inches. What is the area of the window?
Answers
Answer:
2142 inches^2
Step-by-step explanation:
parallelogram's area: base * height
so, 34*63 = 2142
Find the volume of this cone.
Round to the nearest tenth.
10ft
6ft
Answers
Answer:
433.5
Step-by-step explanation:
The volume of the cone with a radius of 6ft and a height of 10ft is approximately 301.4 cubic feet.
What is the volume of the cone?A cone is simply a 3-dimensional geometric shape with a flat base and a curved surface pointed towards the top.
The volume of a cone is expressed as;
V = (1/3)πr²h
Where r is the radius of the base, h is the height of the cone and π is constant pi ( π = 3.14 ).
From the diagram:
Slant height l = 10 ft
Radius r = 6 ft
Height h =?
Volume V =?
First, we determine the height of the cone using Pythagoras theorem:
h² = 10² - 6²
h² = 100 - 36
h² = 64
h = √64
h = 8
Plug the values into the above formula and solve for the volume:
V = (1/3)πr²h
V = (1/3) × 3.14 × 6² × 8
V = (1/3) × 3.14 × 36 × 8
V = 301.4 ft³
Therefore, the volume is approximately 301.4 cubic feet.
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Darion buys 2 pounds of almonds for $21.98 and 3 pounds of dried apricots for $26.25. Which is less expensitve per pound?
Answers
Answer:
Dried Apricots
Step-by-step explanation:
Divide dollars per pound to find amount per pound and then compare.
George is 6 feet tall and his shadow measured 8 feet long at noon. At the same time, a nearby flagpole cast a 40-foot shadow. What is the height of the flagpole? *
Answers
Answer:
42 I think LOL
Jordan has a bag that contains orange chews, strawberry chews, and lime chews. He performs an experiment. Jordan randomly removes a chew from the bag, records the result, and returns the chew to the bag. Jordan performs the experiment 61 times. The results are shown below: An orange chew was selected 11 times. A strawberry chew was selected 17 times. A lime chew was selected 33 times. Based on these results, express the probability that the next chew Jordan removes from the bag will be strawberry chew as a decimal to the nearest hundredth.
Answers
Answer:
17/61 or 0.27
Step-by-step explanation: 17 out of 61 times Jordan will pull out strawberry so the probability of pulling out a strawberry chew is 17/61 which is 0.27 as a decimal
Answer:
0.28
Step-by-step explanation:
0.278 rounded is 0.28
Multiply polynomials #3
Answers
Multiplying the two together, you get an equation such as
-6x^4 - 12x^3 +33x^2 +12x -27.
Answer:
-6x^4-12x^3+33x^2+12x-27
Step-by-step explanation:
A dance studio requires each dancer to pay a registration fee plus an hourly rate for all lessons. If the total cost, y, of a dancer's lesson is modeled by the equation y = 25x + 50, how could the y-intercept be interpreted?
Answers
Answer:
(0,50)
Step-by-step explanation:
Given the total cost of a dancers lesson modeled by the equation y = 25x + 50, the y intercept occurs at the point where x = 0.
Substitute x = 0 into the expression
y = 25x + 50
y = 25(0) + 50
y = 0+50
y = 50
Hence the y intercept is (0, 50). This shows that the total cost of the dancers lesson registration fee is 50
The relationship between the number of pounds (lb) of trail mix and the price
in dollars is shown in the graph. What is the unit price of trail mix?
A. 1 lb/$8
B. $8/1 lb
C. $1/8 lb
D. $16/2 lb
pls answer quickly since this is a quiz :)) picture included above
Answers
What appears to be the domain of the part of the exponential function graphed? A) x ≤ 1 B) h(x) ≤ 1 C) x ≤ 5 D) h(x) ≤ 5
Answers
Can someone help with this question??
Answers
D 11 1/4
Step-by-step explanation:
3/4 + 1 1/2 is 2 1/4
2 1/4 x 5 is 11 1/4
Choose the set that is the possible side lengths of a right triangle.
a)1,1,2 b)3,5,9 c)3,4,7 d)1,1,square root2
Answers
Answer:
D
Step-by-step explanation:
Mathematically, for us to have a right triangle, Pythagoras’ theorem must be obeyed
From the theorem, the square of the hypotenuse (longest side) equals the sum of the squares of the two other sides
Let us take a look at the given set of numbers:
2 square is not same as 1 squared + 1 squared
9 squared is not equal to 3 squares + 5 squared
7 squared is not equal to 4 squared + 3 squared
But;
root 2 squared equals 1 squared plus 1 squared and that is our answer
please help i’ll give brainliest
Answers
Answer:
the answer is b
Step-by-step explanation:
because only some of the energy is saved into the body while the other leaves as waste
Joann decides to paint one wall in her room with blackboard paint. The wall has the dimensions shown. A can of paint covers 25 square feet. How many cans of blackboard paint does Joann need for the wall.
Answers
*see attachment for the diagram of the wall
Answer:
6 cans
Step-by-step explanation:
First, let's calculate the area of the wall to be painted = area of a rectangle
Area of the rectangle = length*width
From the diagram,
Length = 13 ft
Width = 10 ft
Area = 13*10 = 130 ft²
Given that 1 can of paint covers 25 ft²,
Number of can of paints that will cover 130 ft² = 130/25 = 5.2
This means we will need more than 5 cans. So Joan will need to get roughly 6 cams of blackboard paint.
Which is a solution to the system of linear
inequalities? Select all that apply.
y > 2x + 5
y<-3x+5
a. (-5, -1)
b. (0, 2)
c. (-4,1)
d. (-3,0)
Answers
what the answer of ½ ÷ ½
Answers
Answer:
its 1
Step-by-step explanation:
PLEASE HELP ME Which of the following statements is not supported by the Venn diagram below?
There are 55 students taking biology and geometry.
There are 39 students who are not taking both geometry and biology.
There are more students in biology than students in geometry.
There are more students in geometry than students taking only biology.
Answers
Answer:
the answer is
Step-by-step explanation:
There are more students in biology than students in geometry.
The following statements does not support the given venn diagram:
There are 55 students taking geometry and biology.
There are more students in biology than students in geometry.
What are Venn diagrams?
The components of a set or group are schematically represented by a Venn diagram. It is a diagram that depicts every conceivable logical connection between a finite collection of sets or groups. It is also known as set diagram.
In a Venn diagram, sets of various elements are represented by many overlapping shapes (often circles). It seeks to give a pictorial representation of the components, emphasizing their similarities and differences.
Solution:
If we consider the first statement i.e, there are 55 students taking biology and geometry then through the venn diagram we get:17₊ 22 ₊8 = 47
The result of the addition operation is not equal to the number of students, hence it does not support to the statement.
If we consider the second statement i.e, there are 39 students who are not taking both biology and geometry then through the venn diagram we get:17 ₊ 22 = 39
The result of the addition operation is equal to the number of students, hence it supports the statement.
If we consider the third statement i.e, there are more students in biology than students in geometry then through the venn diagram we get:17 ₊ 8 = 25 and 8 ₊ 22 = 30
where, 25 < 30
Here, we can observe that students are less in biology and more in geometry, hence the result does not support the statement.
If we consider the fourth statement i.e, there are more students in geometry than students taking in biology, then through the venn diagram we get:22 ₊ 8 = 30
30 > 17
Here, we can observe that students are more in geometry than students taking only biology, hence the result supports the statement.
So the following statements does not support the venn diagram given:
There are 55 students taking geometry and biology.
There are more students in biology than students in geometry.
Learn more about "Venn diagrams" here-
brainly.com/question/2099071
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what is 15 2/9 as a whole number
Answers
Answer: Unless you round it to a whole number the answer would be 15.2 but if you round to a whole number it would just be 15 lol.
Determine the best method to solve the system of equations. Then
solve the system. x - 3y = 25 and 2x + y = 64. can you please help!!!!!
Answers
Answer:
(31, 2); Substitution.
Step-by-step explanation:
x - 3y = 25
Use SUBSTITUTION by setting everything in the above equation equal to x...
x = 3y + 25
2(3y +25) + y = 64
6y + 50 + y = 64
7y + 50 (-50) = 64 (-50)
7y = 14
y = 2
Then, substitute y = 2 into the original equation.
x - 3(2) = 25
x - 6 = 25
x = 31
(x, y) = (31, 2)
If you find this answer satisfactory, please give me Brainliest.
4 times 8=
PLEASE!!!! tell me the answer!!!
Answers
Answer:
32
Step-by-step explanation:
4*8=32
8+8+8+8=32
4+4+4+4+4+4+4+4=32
PLZ HELP NOW IM FAILING THIS CLASS (work not needed... just answers)
Answers
Answer:
1.D
2.B
Step-by-step explanation:
question 1
-2(2)²+1/3(2)
-7/6
question 2
(-4x-2)(2x)
-8x²-4x
2-2N=3N+17
help plz thank you
Answers
Answer:
-3 = N
Step-by-step explanation:
2-2N=3N+17
Add 2N to each side
2-2N+2N=3N+2N+17
2 = 5N +17
Subtract 17 from each side
2-17 = 5N+17-17
-15 = 5N
Divide each side by 5
-15/5 = 5N/5
-3 = N
Answer:
N= -3
Step-by-step explanation:
First, bring 3N on to the left side by subtracting 3N with 2N
2-2N-3N=17
Then, move 2 to the right side by subtracting 17 and 2: -2N-3N= 17-2
Solving the like terms gives us -5N= 15
N= 15/-5
N= -3
What is the distance between (-3, 5) and
(-7,5)
Answers
the distance is 4 units down
Answer:
The distance between these two coordinates is 4.
Step-by-step explanation:
[tex]x_{2} - x_{1}[/tex]
[tex]y_{2} - y_{1}[/tex]
- 7 - (-3) = 4
5 - 5 = 0
4 + 0 = 4
find the value of y. 120° y = ?°
Answers
Answer:
240
Step-by-step explanation:
360 minus 120 degree give 240 degree
Answer: 60
Step-by-step explanation:
120/2= 60
help? ill give brainliest
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Answer: A
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
Hope this helps also I had this on a test and it was right
4.
2
Round off 14.9028 to the nearest
hundredths
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Answer:
14.9000 is the answer
Step-by-step explanation:
round it
Answer:
can you be more clear
Step-by-step explanation:
Please help if you know the answer please
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CAN SOMEONE PLEASE HELP ME!!!!!
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9514 1404 393
Answer:
$7.00 per week
Step-by-step explanation:
The balance at the end of week 1 is $39-32 = $7.00 higher than at the start. The rate of change is $7.00 per week.
Answer:
$ 7.00 per weekStep-by-step explanation:
#CarryOnLearningGuys pls help me!!!!!
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Answer:
13 1/5 Kilometers
Step-by-step explanation:
you times 4 1/2 by 3 because if she runs 4 1/2 in a third of an hour then she runs 4 1/2 3 times every hour.