Tara and Mallory are practicing their passing at a volleyball practice. Tara bumps the ball from a height of 3 feet above the ground with an initial upward velocity of 12 feet/second. at the same time, mallory serves the ball from a height of 3.25 feet above the ground with an initial upward velocity of 9 feet/second.
if x represents the number of seconds since each ball is passed and y represents the height of the ball, which system of equations models the projectile motion of the two balls? recall that the acceleration due to gravity is -32 feet/second
Answers
Answer:
The system of equation that models the projectile of the two balls is option;
C. y = -16·x² + 12·x + 3
y = -16·x² + 9·x + 3.25
Step-by-step explanation:
The general equation for vertical (upward) motion under gravity is presented as follows;
h - h₀ = u·t + 1/2·g·t²
Where;
h = The final height reached
h₀ = The initial height
u = The initial velocity
g = The acceleration due to gravity ≈ -32 feet/second
t = The time taken
We can rewrite the above equation with different letters for the variables as follows;
h = y,
h₀ = y₀, and
t = x
Therefore, we have;
y - y₀ = u·x - 1/2 × 32 × x²
y = u·x - 1/2 × 32 × x² + y₀ = u·x - 16· x² + y₀
y = u·x - 16· x² + y₀ = -16·x² + u·x + y₀
y = -16·x² + u·x + y₀
For Tara, we have;
u = 12 feet/second
y₀ = 3 feet
Therefore, we get;
y = -16·x² + 12·x + 3
For Mallory, we have;
u = 9 feet/second
y₀ = 3.25 feet
Therefore, we get;
y = -16·x² + 9·x + 3.25
The correct option is therefore;
y = -16·x² + 12·x + 3
y = -16·x² + 9·x + 3.25
Related Questions
14 club members have birthdays in summer. This is 20% of the birthdays in the club. How many club members are there? How do you do this, for kids?
Answers
Answer:
70 club members in all
Step-by-step explanation:
we know that 14 people is equal to 20%
we also know that to get 20% to 100% you multiply by 5
So, what I did was mmultiply 14 by 5 therefore bringing 14 (20%) to 70 (100%)
hope this makes sense. for other values you could just see what to multiply the percent by to get to 100 and multiply the known number by that value.
hope this helps <3
Answer:
70 members
Step-by-step explanation:
Whatever the % is, the answer on the right side of the equation must by 14
So 20% of some number = 14.
20/100 x = 14 Remember 20% = 20 / 100. Multiply by 100
20x = 14*100
20x = 1400 Divide by 20
x = 1400/20
x = 70
There are 70 members in the club.
Kids are done no differently.
The number of people who fulfill the condition goes on the right. The left contains the % and an unknown.
evaluuate 9-b when b=8
Answers
Answer:
[tex]\huge\boxed{\sf 1}[/tex]
Step-by-step explanation:
Given the expression:
= 9 - b
Given that b = 8
= 9 - 8
= 1
[tex]\rule[225]{225}{2}[/tex]
Hope this helped!
~AH1807Okay so we are asked to solve 9 - b, and we are told that b=8
Therefore this is just a matter of substitution:
9 - b
Substitute 8 for b:
9 - 8
Now just finish solving:
1
Therefore, the answer is 1
Hope this helped :)
PLEASE HELP ITS DUE IN AN HOUR!!!!!!
Answers
Answer:
3 units to the right of -5
Step-by-step explanation:
Help me please!!!! I’ll give you brainliest!! :)
Answers
Answer:
399
Step-by-step explanation:
28.5 × 3.5 × 4
Any help would be appreciated. Thank you
Answers
=14-9 x (-2)
=14- (-18)
=32
Use slopes and y-intercepts to determine if the lines 4x−3y=6 and y=43x−1 are parallel.
Answers
Answer:
Since they have the same slope, they are parallel.
Step-by-step explanation:
Equation of a line:
The equation of a line has the following format:
[tex]y = mx + b[/tex]
In which m is the slope. If two lines are parallel, they have the same slope.
4x−3y=6
Placing into the above format:
[tex]3y = 4x - 6[/tex]
[tex]y = \frac{4x - 6}{3}[/tex]
[tex]y = \frac{4x}{3} - 2[/tex]
The slope [tex]m = \frac{4}{3}[/tex]
y=4/3x−1
The slope is [tex]m = \frac{4}{3}[/tex]
Since they have the same slope, they are parallel.
The attendance at a baseball game was 400 people. Adult seats sold for $15 and children seats sold for $10. Total ticket sales were $4560. How many of each type of ticket were sold?
Answers
Answer:
112 adult and 288 children
Step-by-step explanation:
x= adult seats
y= children seats
15x + 10y = 4560
x + y = 400 --> y=400-x
so plug 400-x for y in the other equation
15x + 10(400-x)= 4560
now solve this equation
15x + 10(400-x)= 4560 --> 15x + 4000-10x= 4560 --> 15x -10x = 560 --> 5x=560 --> x = 560/5 --> x= 112
now plug in 112 for this equation (x+y=400) --> 112+y=400 --> y= 288
3
What is the median number of volunteer service hours? *
(5 Points)
Volunteer Service Hours
.
10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
13
20
23
27
Answers
Help me answer the question
Answers
Answer:
cubic
Step-by-step explanation:
you can eliminate all of the other ones
Answer:
cubic
Step-by-step explanation:
quadratic = makes a parabola - U shaped
linear = makes a straight line
cubic = makes a shape just like the one in the picture
square root = makes a curved shape and its also a shape that looks like half of a parabola lying on its side
Help Me Please.............................(7)
Answers
Answer:
Step-by-step explanation:
The first step contains the error.
2x - 10 = 22 Add 10 to both sides
+ 10 +10
2x = 32 Divide by 10
2x/2 = 32/2
x = 16
8. Find F-1 for the function f(x) = (x + 1)3 + 4.
A.f-'(x) =V7-4+1
B. f(x)=x+4+1
C.f(x) = x+4-1
D. g(x)=√x-4-1
Answers
Answer:
Answer is B
Step-by-step explanation:
What is the 38th term of 459,450,441,..
Answers
{(-3,2),(0,4),(2,0)}*{(-2,2),(1,2),(2,-5),(5,0)}
Answers
Answer:
Not sure what your asking but theirs a repeating domain so THIS IS NOT A FUNCTION
PLSSS ANSWERRR HAVE TO HAVE IT DONE IN 10 MIN
Answers
Answer:
466.2 ft²
Step-by-step explanation:
10x24=240
1/2[tex]\pi[/tex]12²=226.194671
240+226.194671=466.194671
Solve the system using any method: y = 3x + 4 6x2y=8
Answers
Answer:
y=24,x=20/3
[tex]y = 3x + 4[/tex]
[tex]8 = 6 \times 2y[/tex]
[tex] 2y = 8 \times 6 [/tex]
[tex]y = 24[/tex]
[tex]24 = 3x + 4[/tex]
[tex] - 3x = 4 - 24[/tex]
[tex] x = \frac{20}{3} [/tex]
272 sweets are divided between Ram and Rahim in the ratio of 7 : 9. How many sweets do they get?
Answers
Answer:
let the ratio of ram and hari be 7x and 9x respectively
7x +9x=272
or, 16x=272
or,x=272÷16
or,x=17
ratio of ram=7x=7 × 17=119
ratio pf rahim=9x=9×17=153
Find the equation of the straight line passing through the point (-4,5) and perpendicular to the line y=2x+7.Suppose the equation is y=cx+d.Find c,d.
Answers
Answer:
The equation of the line is:
[tex]y = -\frac{1}{2}x + 3[/tex]
Step-by-step explanation:
Equation of a line:
The equation of a line has the following format:
[tex]y = mx + b[/tex]
In which m is the slope and b is the y-intercept.
Perpendicular lines:
If two lines are perpendicular, this means that the multiplication of their slopes is -1.
Perpendicular to y=2x+7
This means that:
[tex]2m = -1[/tex]
[tex]m = -\frac{1}{2}[/tex]
So
[tex]y = -\frac{1}{2}x + b[/tex]
Passing through the point (-4,5)
This means that when [tex]x = -4, y = 5[/tex]. We use this to find b.
[tex]y = -\frac{1}{2}x + b[/tex]
[tex]5 = -\frac{1}{2}(-4) + b[/tex]
[tex]2 + b = 5[/tex]
[tex]b = 3[/tex]
The equation of the line is:
[tex]y = -\frac{1}{2}x + 3[/tex]
What expression is equivalent to 4y?
Answers
Answer:
4xy=x or ?
Step-by-step explanation:
The base of the pyramid is a right triangle
The volume is ____ cubic cm.
Answers
Answer:
37 cubic cm should be the answer sorry if I am wrong
I am having a baby day so if you write something wrong I’m reporting you
Answers
Answer:
804.25 or based on the choices 803.8
Step-by-step explanation:
Answer:
804.25
Step-by-step explanation:
so the closest thing to that is 803.8
Plz help this is 400 points. Nancy bought a Reuben sandwich and received her change in several coins. The cashier handed Nancy 2 half dollars, 3 quarters, 4 dimes, 4 nickels, and 1 penny. How much money did Nancy get in change?
Answers
Answer:
2.35
Step-by-step explanation:
2x50=100
3x25=75
4x10=40
4x5=20
100+75+40+20=2.35
The product of the third and the sixth terms of an arithmetic sequence is 406. The
ninth term of the sequence divided by the fourth term gives a quotient of 2 and a
remainder of 6. Find the first term and the common difference of the arithmetic
sequence
Answers
Answer:
The product of the third by the sixth term of an arithmetic progression is 406. The division of the ninth term of the progression by the fourth term gives a quotient 2 and a remainder 6. Find the first term and the difference of the progression.
Need help on this question
Answers
Answer:
Step-by-step explanation:
arc between cars = 360°/25 = 14.4°
θ = 14.4° × π/180 ≅ 0.2512 radian
r = 150/2 = 75 ft
s = rθ = 75×0.2512 = 18.84 ft
area of circle = πr² = 75²π ≅ 17,662.5 ft²
area of sector = 17,662.5/25 = 706.5 ft²
Find the missing side of right triangle, where c= 13 in and a= 5 in
Answers
Answer:
b = 12
Step-by-step explanation:
a^2 + b^2 = c^2
25 + b^2 = 169
b^2 = 144
b = 12
5² + b² = 13²
25 + b² = 169
b² = 169-25
b² = 144
b = √144
b = 12
How can 26n - 7m +4(10n - 6m) be rewritten? A. 36n - 13m B. 40n - 9m C. 66n - 31m D. 35mn
Answers
Answer:
C. 66n - 31m
Step-by-step explanation:
26n - 7m + 4(10n - 6m)
26n - 7m + 40n - 24m
26n - 31m + 40n
66n - 31m
What is the probability that the sum is a common multiple of 2 and 3? Please help me ASAP!
Answers
Answer:
what is the question
Step-by-step explanation:
1;3;5 are the first three terms of the first differences of a quadratic sequence. the 7 term of the quadratic sequence is 35. determine the 6th and 5th term of the quadratic sequence
Answers
Answer:
no
Step-by-step explanation:
The 6th and 5th terms of the giving sequence are respectively; 24 and 15
What are the missing terms of an Arithmetic Sequence?
We are given the first 3 terms of the sequence as; 1, 3 and 5.
We are told that the 7th term is 35.
Let xₙ be the nth term number in the quadratic sequence
dₙ is first difference number in the quadratic sequence
From the given sequence, we see that there is a common difference of 2 for the first 3 terms and so they follow an arithmetic sequence which is;
dₙ = 2n - 1
However, when we apply this up to the 7th term, that would not work. Thus, let us use the differences. We see that sum of two consecutive number position of terms is equal to the difference between the two consecutive terms.
Thus;
difference between 3rd and 4th term = 3 + 4 = 7
difference between 5th and 6th term = 4 + 5 = 9
difference between 6th and 7th term = 5 + 6 = 11
Thus, since 7th term is 35, then;
6th term = 35 - 11 = 24
5th term = 24 - 9 = 15
Read more about Arithmetic Sequence at; https://brainly.com/question/6561461
The two lines graphed on the coordinate grid each represent an equation. (-2, 6) (3,5) (-6, 2) (-6, -6) Which ordered pair represents a solution to both equations?
Answers
Answer:
(-3,3)
Step-by-step explanation:
because it's where the graphs intersect, meaning the point is contained in both solutions
13. Find the measure of arc JK.
J
I
K
70°
L
Answers
180-70=110
Find the volume of the solid
Answers
Answer:
245 yd3
Step-by-step explanation:
Split the solid into two pieces, multiply length, width, adn height from there.
Answer:
The answer is: 245 yds cubed
Step-by-step explanation:
So first, you would cut the solid into 2 parts. One that is a big rectangular prism and the other is the smaller one. Next, we would solve the volume of the smaller rectangular prism. The measurements for that is:
Height: 2 Length: 5 Width: 2. There is a side of that small prism that is 2x2 so we will solve that first. 2*2=4. 4*5=20. The volume of the smaller rectangular prism is 20 yd^3.
Next, we solve the volume for the 2nd rectangular prism. The measurements for that are: Height: 5 Length: 9 Width: 5.
So we would first solve for one of the sides. 5*5=25. Then we would multiply it by 9. 25*9= 225. So the volume for the bigger rectangular prism is 225 yds^3.
Lastly, we will add the volumes of the two prisms together. 225+20=245.
The final answer is: 245 yds cubed