Answers
The trajectory of a projectile is proven to be parabolic by eliminating time from the horizontal and vertical motion equations to receive the form y = ax + bx², thus describing the projectile's path.
Explanation:To prove the trajectory of a projectile is parabolic, we start with the motion equations given for horizontal and vertical positions, which are x = V0x t and y = V0y t - (1/2)gt2, respectively.
First, we solve the horizontal motion equation for t to find t = x/V0x.
We then substitute this expression for t into the vertical position equation to eliminate t.
After substitution, we get an equation of the form y = ax + bx2, where a is V0y/V0x and b is -g/(2V0x2).
These constants a and b represent the initial velocity components and the acceleration due to gravity, which together describe the parabolic path of a projectile motion.
The equation of the parabola is: y = 0(x - (-2.5))^2 + 2
To determine the equation of the parabola, we can use the general form of the equation for a parabola:
y = a(x-h)^2 + k
where (h, k) represents the vertex of the parabola.
Given two points on the graph, (-2,2) and (-3,4), we can use these points to find the values of h and k.
Let's start by finding the x-coordinate of the vertex, h. Since the parabola is symmetric, the x-coordinate of the vertex is the average of the x-values of the two given points:
h = (-2 - 3)/2 = -5/2 = -2.5
Next, let's find the y-coordinate of the vertex, k. We substitute the x-coordinate of the vertex into the equation and solve for y:
2 = a(-2.5 - (-2.5))^2 + k
Simplifying:
2 = a(0)^2 + k
2 = k
Therefore, the vertex of the parabola is (-2.5, 2).
Now that we have the values of h and k, we can substitute them into the equation to find the value of a. Using one of the given points, (-2,2), we have:
2 = a(-2 - (-2.5))^2 + 2
2 = a(-2 + 2.5)^2 + 2
2 = a(0.5)^2 + 2
2 = 0.25a + 2
0.25a = 0
a = 0
Therefore, the equation of the parabola is:
y = 0(x - (-2.5))^2 + 2
Simplifying:
y = 2
In this case, the parabola is a horizontal line passing through the vertex at y = 2.
Related Questions
A girl skateboards with a kinetic energy of 2543.2 J. If the girl and skateboard have a total mass of 110kg , what is her speed ?
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Answer:
6.8 Miles
Write at least 20 characters to explain it well.
A model car travels 20 meters in 15 seconds. How many meters will it travel in 45 seconds?
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The model car will travel 60 meters in 45 seconds
erica takes a cab to meet her grandmother at a musuem. her grandmother wiill giive her a ride hime. she only has$25.05 to spend and a cab cost.$3 plus $0.35 per mile. what are rhe maximum number if miles that Erica may travel before she has to walk the rest of the way to the museum?
Answers
The maximum miles that she can travel 63 miles before she can walk.
Final answer:
By setting up an equation that accounts for the cab's base fare and the additional per mile charge, we can determine that Erica can afford to travel a maximum of 63 miles in the cab before exceeding her budget of $25.05.
Explanation:
To determine the maximum number of miles Erica can travel in a cab without exceeding her budget of $25.05, we can create an equation where the cost of the cab is equal to the base fare plus the per mile charge times the number of miles (mileage). We know the base fare is $3 and the per mile charge is $0.35. Let's denote the number of miles Erica can travel as 'm'.
The cost equation would be: Cost = Base Fare + (Per Mile Charge × Mileage)
This gives us: $25.05 = $3 + ($0.35 × m)
Subtracting the base fare from both sides gives us: $22.05 = $0.35 × m
Dividing by the per mile charge yields: m = $22.05 / $0.35
Calculating this, we get: m = 63 miles
Therefore, Erica can travel a maximum of 63 miles in the cab before she would need to walk the rest of the way to the museum to stay within her budget.
you are charged $16.05 after tax for a meal. Assume sales tax is 7%, what was the menu price for the meal?
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[tex]1.07x=16.05[/tex]
[tex]16.05/1.07=15[/tex]
[tex]15=x[/tex]
The menu price for the meal is $15.
I do t get number 4
Answers
4.2 feet = 50.4 inches
divide the total height by the height of each sheet: 50.4/0.6 = 84
it's 84 sheets of plywood.
Simplify 3m^2(10+m) PLEASE HELP
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3m^2 (10+m)
Use FOIL
3m^2*m=3m^3
3m^2*10= 30m^2
Answer: 3m^3 + 10m^2
Solution :
Given expression [tex]3m^{2}(10+m)[/tex]
To simplify this expression, first we need to know about the Distributive property.
Distributive Property: [tex]a\times(b+c)=(a\times b)+(a\times c)[/tex]
Given expression [tex]3m^{2}(10+m)[/tex]
Applying Distributive property on this expression -
[tex]\Rightarrow 3m^{2}(10+m)=(3m^{2}\times10)+(3m^{2}\times m)[/tex]
[tex]= 30m^{2}+3m^{3}[/tex]
Simplified form of [tex]3m^{2}(10+m)[/tex] is [tex]30m^{2}+3m^{3}[/tex]
please help me find h(6)
Answers
To find H(6) for the function H(x) = 5(x - 6), substitute 6 for x, resulting in H(6) = 5(6 - 6) = 5(0) = 0.
The question asks for the evaluation of H(6) when H(x) = 5(x - 6). To find H(6), we simply substitute 6 in place of x in the function and calculate the result.
H(6) = 5(6 - 6)
Calculating the expression within the parentheses:
6 - 6 = 0
Now multiply by 5:
5 times 0 = 0
Therefore, H(6) = 0.
What is equal to 6 - -5
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6-(-5) will equal to
6+5=11
What’s is 38 divided by 100
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38 divided by 100
what you could do is that 38 in decimal form will be 38.00
So,...
38.00 divided by 100
when you divided by 10 or 100 or 1,000 or etc.
all you have to do is move the decimal from 38.00 to the left 2 times
(because there are only 2 zeros in 100)
and your answer will be 0.38
38 divided by 100 = 0.38
hope that helps
f(x)=2^x evaluate f(5)
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Hey there!
To solve this, we will first replace x with 5 anytime we see it in the equation.
f(5) = 2^5
Now, we simplify 2^5.
The base is 2 and the exponent is 5 in this case.
The exponent is the number of times you multiply the base by itself. In oour case:
2 x 2 x 2 x 2 x 2 = 32
f(5) = 32
Hope this helps!
Hello can you help me please?)
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The "vertical line test" tells you the relation is not a function if any vertical line intersects the graph in 2 or more places.
15. not a function
The vertical line x=0 crosses the graph at y=-6 and at y=6.
16. a function
The number a times 10 to the power of negative 2 is about 8 times greater than b times 10 to the power of negative 3. Find the correct value of a and b.
A. a = 3.1 and b = 2.5
B. a = 2.5 and b = 3.1
C. a = 2 and b = 1.2
D. a = 1.2 and b = 2
Answers
Answer:
c
Step-by-step explanation:
The correct values of a and b are a = 3.1 and b = 2.5, which corresponds to option A.
To solve the question, we need to set up an equation using the information given. Here's a step-by-step explanation:
a * 10^-2 = 8 * b * 10^-3Divide both sides by 10^-3 to simplify the equation: a * 10 = 8 * bPlugging in the values for a and b from option A, we get 3.1 * 10 = 8 * 2.5, which is true.Therefore, a = 3.1 and b = 2.5, matching option A.Write w-24 in verbal expression
Answers
"w - 24" said verbally is:
w minus twenty-four
hope this helps
~Rise Above the Ordinary
I believe that the correct answer is The difference of w and 24
Hope this helps!!!
You play a game where you score -6 points on the first turn and on each of the next 3 turns what is your score after those 4 turns
Answers
-24 if you score -6 each round
The midpoint of AB is (3,7). The coordinate of one endpoint is A(5,1). Find the coordinate of endpoint B. Show or explain work.
Answers
The formula of a midpoint:
[tex]M_{AB}\left(\dfrac{x_A+x_B}{2},\ \dfrac{y_A+y_B}{2}\right)[/tex]
We have
[tex]M(3,\ 7)\to x_M=3,\ y_M=7\\\\A(5,\ 1)\to x_A=3,\ y_A=7[/tex]
Substitute:
[tex]\dfrac{5+x_B}{2}=3\qquad|\cdot2\\\\5+x_B=6\qquad|-5\\\\x_B=1\\\\\dfrac{1+y_B}{2}=7\qquad|\cdot2\\\\1+y_B=14\qquad|-1\\\\y_B=13[/tex]
Answer: B(1, 13)A(5,1) which becomes (x1,y1)
P(3,7) which becomes (x,y)
B(x,y) which becomes (x2,y2)
Since it is a midpoint, we can use the midpoint formula directly.
x = (x1+x2)/2
3 = (5+x)/2
x=1
Thus our x coordinate is 1
y = (y1+y2)/2
7 = (1+y)/2
y=13
Thus our y coordinate is 13
Our answer is B(1,13)
Write An equation in slope intercept form for the line passing through each pair of points (-1,3) and (2,-5)
Answers
Slope m = y2-y1/x2-x1
Points (-1,3) and (2,-5)
M= -5-3/2-(-1)
M= -8/3
M= -8/3
Slope is -8/3
Now fill in the formula equation of a line using one if the points and slope to find b .
(2,-5) and slope -8/3
Y=mx+b
-5=-8/3(2)+b
-5=-16/3+b
-5+16/3=b
1/3=b
Now put all together
Y= -8/3x+1/3
Slope intercept form of a line is y = mx + b, where m is the slope and b is the y coordinate of the y intercept.
The easiest way to solve this problem is by using another equation for a line, also known as point slope form. This equation is best to use for a line if you have a point and slope of the line, but do not have the y-intercept.
We need to find the slope of this line passing through the pair of points (-1, 3) and (2, -5). We can do this by using the slope formula: [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]. Substitute in the appropriate coordinates.
[tex]\frac{-5-3}{2-(-1)}[/tex] = [tex]\frac{-8}{3}[/tex], so the slope of the line is -8/3.
Point slope form of a line is [tex]y-y_1=m(x-x_1)[/tex]. Substitute -8/3 for m, and use the point coordinate (-1, 3) for y1 and x1. You could use either point coordinate but I chose to use this one.
[tex]y-3= -8/3[x-(-1)][/tex]
Distribute -8/3 inside the parentheses.
[tex]y-3= -8/3x - 8/3[/tex]
Add 3 to both sides.
y = -8/3x + 1/3 is your answer (slope intercept form).
0.86 divide 5 -0.3 multiply 0.5
Answers
0.68÷5-0.3×0.5? or
0.86÷5 and -0.3×0.5
0.172 , -0.15
Answer:
The solution is 0.022.
Step-by-step explanation:
Given that,
[tex]\dfrac{0.86}{5}-0.3\times0.5[/tex]
We need to solve the equation
Using PEMDAS rule
On dividing 0.86 by 5
[tex]0.172-0.3\times0.5[/tex]
On multiply 0.3 from 0.5
[tex]0.172-0.15[/tex]
On subtract 0.15 from 0.172
[tex]0.022[/tex]
Hence, The solution is 0.022.
1. If ΔMNO≅ΔGHI, then which of the following is NOT true? A. ΔMON≅ΔGIH B. OM=IG C. ΔHIG≅ΔNMO D. ΔIHG≅ΔONM E. ∠GHI≅∠ONM
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When 1480 is divided into 12equal parts, the remainder is 4. What is a correct way to write the quotient
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[tex]123 \frac{4}{12} [/tex]
=
[tex]123 \frac{1}{3} [/tex]
what is 9(m+4)=7m ?? 50 points and brainliest for anyone who can answer im short on time and need this done oof
Answers
The answer you are looking for is M = -18.
To find this answer, you first distribute 9 into the parenthesis (m + 4). Once you've distributed, you should be left with 9m + 36 = 7m. Next, you subtract 9m from both sides. This will give you 36 = -2m. Finally, divide both sides by 2. Thus giving you a final answer of M = -18.
I hope this helps!
Answer:
The answer you are looking for is M = -18.
Step-by-step explanation:
if prices increase at a monthly rate of 1.4% by what percentage do they increase in a year?
Answers
Prices increase by approximately 18.17% in a year if they rise at a monthly rate of 1.4%.
The given monthly rate of 1.4% can be represented as 1.014 in decimal form (1 + 0.014).
To calculate the total increase over a year, we need to compound this monthly rate for 12 months since there are 12 months in a year. We can use the formula for compound interest to find the overall increase:[tex]\[A = P(1 + r)^n\][/tex]
Where:
[tex]\(A\)[/tex] = the final amount after [tex]\(n\)[/tex] periods (in this case, a year),
[tex]\(P\)[/tex] = the initial price (100% or 1 in decimal form, as it's the starting point),
[tex]\(r\)[/tex] = the monthly rate in decimal form (1.4% or 0.014), and
[tex]\(n\)[/tex] = the number of periods (12 months).
Plugging in the values:
[tex]\[A = 1 \times (1 + 0.014)^{12}\][/tex]
[tex]\[A = 1 \times 1.1771\][/tex]
[tex]\[A \approx 1.1771\][/tex]
The final amount [tex](\(A\))[/tex] represents the price increase over the year. To express this as a percentage, we subtract 1 from [tex]\(A\)[/tex] and then multiply by 100:
[tex]\[Price \, Increase \, Percentage = (A - 1) \times 100\][/tex]
[tex]\[Price \, Increase \, Percentage = (1.1771 - 1) \times 100\][/tex]
[tex]\[Price \, Increase \, Percentage \approx 18.17\%\][/tex]
Therefore, prices increase by approximately 18.17% in a year if they rise at a monthly rate of 1.4%.
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HELP PLEASE!!!!!!!! I GIVE 21 POINTS!!!!!!!!! AND BRAINLEAST <3
Answers
6. domain=age
range= number of pets
it is not a function because an x value repeats
7. domain=1,2,3,4,5
range= 50, 100, 150, 150, 200
it is a function because the lines don't connect
Miguel baked 5 loaves of bread. Each loaf required 7/8 cup of flour. How much flour dis miquel use?
Answers
The scale says a patient weighs 70kg.this is the same as weight how many pounds
Answers
Answer:
154 LBS
Step-by-step explanation:
1 KG = 2.2 LBS
70 KG X 2.2 = 154
To convert kilograms to pounds, you divide the weight in kilograms by 0.4536. So, a person weighing 70 kg would weigh approximately 154.32 lbs.
Explanation:The subject you're asking about is conversion from kilograms to pounds. A weight of 1 lb is equivalent on Earth to a mass of 0.4536 kg. So, to convert kilograms to pounds, you would divide the weight in kilograms by the equivalent mass of 1 pound in kilograms.
For example, a person weighing 70 kg would weigh approximately 154.32 pounds. This was calculated by dividing 70 kg by 0.4536 kg per pound (70/0.4536 = 154.32 pounds). It's important to note that while weight can vary slightly depending on location due to differences in gravitational pull, this conversion factor still provides a good estimation for most common situations.
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A package weighs 2.6 pounds how much do 8 of the same sized packages weigh
Answers
you would multiply 2.6 x 8 and that equals 20.8
8 packages weigh 20.8 pounds.
Explanation: It's simple. 2.6 x 8 = 20.8
Rafael has been given a list of 4 bands and asked to place a vote . His vote must have the names of his favorite, second favorite and third favorite bands from the list. How many different votes are possible
Answers
There will be twelve votes possible because 3*4=12
[tex]4p3[/tex]
4 permutation ( because in this scenario order matters ) 3 meaning that there are 4 choices and you can pick 3 In any order
The low temperature for 5 days was -5 degrees, -7 degrees, -2 degrees, 2 degrees, and - 3 degrees. What was the average temperature for those days
Answers
What is the volume of a 14 in diameter pipe that’s 2156 long?
Answers
Answer:
Step-by-step explanation:
given that diameter of the pipe = 14 inches
radius = 7 inches
Length =2156 inches
Pipe is in the form of a cylinder
Volume of cylinder = pi r^2 h
where r = radius and h = l = 2156
We have to substitute the values of r and h.
Let us take pi as 22/7
= 22/7 (7)(7)(2156)
Cancel out 7 and multiply the remaining 22 ,7 and 2156
=332024 cubic inches
Which of the following functions is the inverse of f (x) = 3x? A. F (x) = -3x. B. F (x) = X3. C. F (x)=x/3 D. This function does not have an inverse.
Answers
[tex]f(x)=3x\to y=3x\\\\\text{Interchange the y and the x}\\\\x=3y\\\\\text{Solve for y}\\\\3y=x\qquad|:3\\\\y=\dfrac{x}{3}\\\\Answer:\ C.\ f^{-1}(x)=\dfrac{x}{3}[/tex]
The required inverse function would be f⁻¹(x) = x / 3, which is the correct answer would be option (C).
What is an inverse function?The inverse function is defined as a function obtained by reversing the given function.
To determine the inverse of a function, all you have to do is switch where x and y are and resolve for y.
We have to find the inverse of the function below :
f(x) = 3x
So after switching x and y,
Now, we solve for y regularly.
f(x) = x = 3y
Solve for y :
⇒ x = 3y
⇒ x / 3 = y
⇒ y = x / 3 = f⁻¹(x)
Therefore, the required inverse function would be f⁻¹(x) = x / 3.
Hence, the correct answer would be an option (C).
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Point A has coordinate A(3, 2). The point is rotated 180° clockwise around the origin. Find the coordinates of point A’. A’(2, 3) A’(–3, –2) A’(–2, –3) A’(–2, 3)
Answers
Answer:
A' (-3,-2)
Step-by-step explanation:
When rotating a figure 180 degrees, imagine that you are able to take the figure and turn it clockwise or counterclockwise around a center point. To rotate a figure 180 degrees, you apply the rule (x, y) → (-x, -y). Start by using a coordinate grid with coordinates for each vertex of the figure. The center point of the coordinate grid is located at (0, 0), which is what you will rotate the figure around. Write down the original coordinates of the shape you are going to rotate. Then, apply the rule. For example, coordinate (3, 2) becomes (-3, -2). Another example would be, coordinate (-4, -2) becoming (4, 2).
(-3,-2) this is your answer