The height of the rock as it is thrown upwards is in the shape of a parabola which is described as follows;
Part A: Please find attached the graph of the parabola that describes the height of the rock after being projected into the air, created with MS Excel.
Domain; [0, 4]
Range; [0, 256]
Part B: The function that models the scenario, obtained using the vertex form of a parabola is; h(x) = -16·(x - 2) + 256
What is a parabola?A parabola is a geometric shape defined as the set of points that are both equidistant from a fixed point, known as the focus and a fixed line, known as the directrix.
To create a graph to represent the scenario, we can use the vertex form of a quadratic function, which is; y = a·(x - h)² + h
Where; (h, k) is the vertex of the parabola. We know that the height of the edge of the cliff from which the rock is thrown is 192 feet, so the initial height of the rock is 192 feet
The maximum height = 256 feet
The time to reach the maximum height = 2 seconds
Therefore; The coordinate of the vertex = (2, 256)
The time the rock takes to reach the ocean from the max height = 4 seconds
Total time the rock is in the air = 6 seconds
Therefore, we get;
y = a·(x - h)² + k
192 = a·(0 - 2)² + 256 = 4·a + 256
192 = 4·a + 256
192 - 256 = -64 = 4·a
-64 = 4·a
a = -64/4 = -16
a = -16
The equation is therefore;
y = -16·(x - 2)² + 256
The above function can be used to create the graph of the motion of the rock as follows;
The x-intercept is the point where y = 0, therefore, the x-intercept is 6
y = 0 = -16·(x - 2)² + 256
16·(x - 2)² = 256
(x - 2)² = 256/16 = 16
x - 2 = √(16) = 4
x = 4 + 2 = 6
x = 6
The x-intercept is; (6, 0)
The y-intercept is the point where x = 0, therefore;
y = -16·(x - 2)² + 256
y = -16·(0 - 2)² + 256 = 192
The y-intercept is; (0, 192)
Please find attached the required graph of the function created with MS Excel
Part B; The function of the graph is; f(x) = -16·(x - 2)² + 256
The domain of the function for the motion of the rock is; [0, 6] since the rock is in the air for 6 seconds
The range of the function is; [0, 256], since the maximum height reach is 256 feet and the lowest height reached is the ocean level or zero feet.
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HELP Darius owns a business that manufactures and sells record players, now that vinyl records have resurged in popularity. The graph shows Darius's expected revenue and cost in relation to the price he sets for each record player.
Answer: 32 and 85
Step-by-step explanation:
Darius set the price between $32 and $85.
What is Graph?The graph is simply a structured representation of the data. It aids in our comprehension of the data. The numerical information gathered through observation is referred to as data.
Given:
We have the graph shows Darius's expected revenue and cost in relation to the price he sets for each record player.
For the expected revenue = 32 the cost is $5539.
and, For the expected revenue = 85 the cost is $4062.
and there is a peak at expected revenue 52.
Then, for profit Darius set the price between $32 and $85.
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what is 4 divided by 6
Testing more properties of the Cobb-Douglas utility function Check if the Cobb-Douglas utility function u(x
1
,x
2
)=x
i
α
x
2
β
, where α,β>0, satisfies the following properties: (a) local nonsatiation, (b) decreasing marginal utility for both goods 1 and 2, (c) quasi-concavity, and (d) homotheticity.
The Cobb-Douglas utility function satisfies the properties of local non-satiation, decreasing marginal utility for both goods, quasi-concavity, and homotheticity.
The Cobb-Douglas utility function u(x1, x2) = xi^(α) * x2^(β), where α and β are both greater than zero, satisfies the following properties:
(a) Local non-satiation:
This property states that at each point of the consumption set, there is always another bundle that is arbitrarily close and strictly preferred. Thus, the function has local non-satiation.
(b) Decreasing marginal utility for both goods 1 and 2: The marginal utility of a good measures the utility obtained by consuming one more unit of it. The marginal utility of x1 can be obtained as:
MU1 = α * xi^(α−1) * x2^(β)
The marginal utility of x2 can be obtained as:
MU2 = β * xi^(α) * x2^(β−1)
Therefore, both marginal utilities are decreasing in x1 and x2, satisfying this property.
(c) Quasi-concavity:
The Cobb-Douglas function is quasi-concave. This means that the upper contour set of any level set of the function is convex. This can be proved by taking the second partial derivative of the function and checking whether it is negative or not.
(d) Homotheticity:
The Cobb-Douglas function is homothetic. This means that its shape is independent of the total level of utility. The proof can be achieved by checking whether the function is homogeneous of degree one or not. This is true, since multiplying the inputs by any positive scalar λ leads to a proportional increase in the output.
In conclusion, the Cobb-Douglas utility function satisfies all four properties - local non-satiation, decreasing marginal utility for both goods 1 and 2, quasi-concavity, and homotheticity.
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Calculate the amount of interest Jim will earn if he puts the $5,000 he received for graduating high school into a savings account with a five percent annual interest rate paid quarterly and does not touch the money until he graduates college in four years.
To calculate the amount of interest Jim will earn, we can use the formula for compound interest:
A = P*(1 + r/n)^(n*t)
where:
A = the final amount
P = the principal (initial) amount
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the time period, in years
In this case, Jim has put $5,000 in a savings account with a 5% annual interest rate, paid quarterly (n = 4), and left it untouched for 4 years (t = 4).
So, we have:
P = $5,000
r = 0.05 (5% as a decimal)
n = 4
t = 4
Plugging these values into the formula, we get:
A = $5,000*(1 + 0.05/4)^(4*4) = $6,381.44
So, the final amount Jim will have after 4 years is $6,381.44. To find the amount of interest earned, we need to subtract the initial principal amount from the final amount:
Interest = $6,381.44 - $5,000 = $1,381.44
Therefore, Jim will earn $1,381.44 in interest over four years.
I hope I helped!~~~Harsha~~~
what is the largest integer that is a divisor of (n 1)(n 3)(n 5)(n 7)(n 9) (n 1)(n 3)(n 5)(n 7)(n 9) for all positive even integers nn?
The largest integer that is a divisor of (n+1)(n+3)(n+5)(n+7)(n+9) is 15
Divisor of a Number :
A Divisor is any number that divides a given number completely or with a reminder. Where a factor, is a divisor that divides the number entirely and leaves no remainder.
Here we have,
(n + 1)(n + 3)(n + 5)(n + 7)(n + 9)
And n is a positive even integer
For n = 2 ⇒ (2 + 1)(2 + 3)(2 + 5)(2 + 7)(2 + 9) = (3× 5 × 7 × 9 × 11 )
For n = 4 ⇒ (4 + 1)(4 + 3)(4 + 5)(4 + 7)(4 + 9) = (5× 7 × 9 × 11 × 13 )
and so on.
From the above calculations,
we can say that (n + 1); (n + 3); (n + 5); (n + 7); (n + 9) are 5 consecutive odd numbers
In every 5 consecutive odd positive integers,
One of them is always divisible by 3
And one of them is always divisible by 5.
Therefore,
(n + 1)(n + 3)(n + 5)(n + 7)(n + 9) will be divisible by both 3 and 5
As we know product of 3 and 5 = 15
then (n + 1)(n + 3)(n + 5)(n + 7)(n + 9) will also divisible by 15
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The complete question is
What is the largest integer that is a divisor of (n+1)(n+3)(n+5)(n+7)(n+9) for all positive even integers n?
(A) 3 (B) 5 (C) 11 (D) 15 (E) 165
Find the value of (a+b)²-2ab when a=3 and b=2
Answer:
(a+b)^2-2ab= a^2+b^2+2ab-2ab=a^2+b^2= 3^2+2^2= 9+4= 13
hope it helps
What is the area of a triangle with vertices at (-2, -1), (4, -1), (6,5)?
6 square units
9 square units
18 square units
36 square units
Answer: C
Step-by-step explanation:
The Halpert Group produces a single product selling for $20 per unit. Variable costs are $7 per unit and total fixed costs are$10,000. What is the contribution margin ratio?
A. 1.11
B. 0.63
C. 0.90
D. 0.10
The contribution margin ratio for The Halpert Group is approximately 0.63. Therefore, option B. is correct.
To find the contribution margin ratio for The Halpert Group, we'll use the formula:
Contribution Margin Ratio = (Selling Price - Variable Cost) / Selling Price.
Identify the selling price and variable cost per unit.
Selling Price = $20
Variable Cost = $7
Calculate the contribution margin per unit.
Contribution Margin = Selling Price - Variable Cost
Contribution Margin = $20 - $7
Contribution Margin = $13
Calculate the contribution margin ratio.
Contribution Margin Ratio = Contribution Margin / Selling Price
Contribution Margin Ratio = $13 / $20
Contribution Margin Ratio = 0.65
The closest answer to 0.65 is option B. 0.63. Therefore, the contribution margin ratio for The Halpert Group is approximately 0.63.
So, option B. is correct.
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what is the original price if a 10% discount makes the sale price 50
Answer:
here is th answer:::::$45 for a item with original price of $50 when discounted 10%.
Step-by-step explanation:
hope it helps! if not let me know!
due in 30 min! Order the Angles from LEAST TO GREATEST
B, C, A
A, C, B
A, B, C
B, A, C
C, B, A
C, A, B
Answer:
Pretty sure it's C, A, B
Step-by-step explanation:
What is the solution set to F(x)=x4+2? Using small values, form a list of ordered pairs.
Include all of your work in your final answer. Submit your solution.
Answer:
If you don't agree or there's an error, let me know so I can edit.
Step-by-step explanation:
f(x) = x⁴ + 2
differentiate
f(x) = 4x³ + 0 =0
x(4x²) = 0
at x= 0 f(x) = 0 points = (0,0)
at x= 1. f(x) = 3 points = (4,3)......
The ordered pair is (4,3).
What is ordered pair?An ordered pair is a composition of the x coordinate (abscissa) and the y coordinate (ordinate), having two values written in a fixed order within parentheses. It helps to locate a point on the Cartesian plane for better visual comprehension. The numeric values in an ordered pair can be integers or fractions.
Given:
f(x) = x⁴ + 2
Now, differentiate the above function for the small values
f(x) = 4x³ + 0 =0
x(4x²) = 0
When x= 0
f(x) = 0
So, the points = (0,0)
when x= 1
f(x) = 3
so, the points = (4,3).
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3. The graph below shows the number of points that Lebron scored in each of his first
four games of a season.
On average, how many more points per game did Lebron score in the last two games than the
first two games?
Using the mean concept, it is found that LeBron scored 10 more points per game on his last two games than on his first two.
What is the mean?The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations.
For his first two games, he scored 20 + 15 = 35 points, hence the mean is:
35/2 = 17.5 points per game.
For his last two games, he scored 25 + 30 = 55 points, hence the mean is:
55/2 = 27.5 points per game.
The difference is:
27.5 - 17.5 = 10.
On average, LeBron scored 10 more points per game on his last two games than on his first two.
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Please help fast! 25 points and brainliest!! Let f(x) = 36x5 − 44x4 − 28x3 and g(x) = 4x2. Find f of x over g of x
Answer:
fx/gx=10
Step-by-step explanation:
fx= (36x5)-(44x4)-(28x3)
fx=80
gx= 4x2
gx=8
To work out fx/gx:
fx/gx=80/8
fx/gx=10
Write the rational number 46/1000 as a decimal
Answer:
0.046
Step-by-step explanation:
Answer:
0.046
Step-by-step explanation:
Use the given scale factor and the side lengths of the scale drawing to determine the side lengths of the real object. 10 in Scale factor. 5:1 10 in 12 in Scale drawing адь C Real object pls assp
The side lengths of the real object will be 50 inches and 60 inches.
What is a scale factor?The scale factor is the ratio of the actual size of the image to the new size of the image. It is used to Map the objects like if you want to increase or decrease the size without changing the original shape of the image it is done by the scale factor.
The given scale factor is 5:1, which means that the dimensions of the scale drawing are 1/5 of the dimensions of the real object.
To find the side lengths of the real object, we can use the ratio of the dimensions in the scale drawing and the real object.
For example, the length of the real object can be found by multiplying the length of the scale drawing by the scale factor:
Real object length = Scale drawing length x Scale factor
Real object length = 10 in x 5
Real object length = 50 in
Similarly, the width of the real object can be found using the same method:
Real object width = Scale drawing width x Scale factor
Real object width = 12 in x 5
Real object width = 60 in
Therefore, the side lengths of the real object are 50 inches and 60 inches.
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A researcher wants to set up a regression equation where Y is a function X. Evaluate the researcher’s options given the following scenarios: (3)
i. Y is I(0); X is I(0)
ii. Y is I(2); X is I(0)
iii. Y is I(1); X is I(1); and the error term is I(0).
The appropriate regression model depends on the stationarity properties of both the dependent and independent variables, as well as the error term. The researcher can use a standard OLS regression model with first-order differencing of both Y and X.
In the first scenario, both Y and X are I(0), which means they are stationary time series. In this case, the researcher can perform a standard linear regression analysis, as the stationary series would lead to a stable long-run relationship. The answer from this model will be reliable and less likely to suffer from spurious regressions. In the second scenario, Y is I(2) and X is I(0). This implies that Y is integrated of order 2 and X is stationary. In this case, the researcher should first difference Y twice to make it stationary before performing a regression analysis. However, this approach might not be ideal as the integration orders differ, which can lead to biased results.
In the third scenario, Y and X are both I(1) and the error term is I(0). This indicates that both Y and X are non-stationary time series, but their combination might be stationary. The researcher should employ a co-integration analysis, such as the Engle-Granger method or Johansen test, to identify if there is a stable long-run relationship between Y and X. If co-integration is found, then an error correction model can be used for more accurate predictions.
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I need help on this
Answer:
The repetition is used to show how music was all she thought about.
Step-by-step explanation:
Find the quotient of 902÷27
(It has a remainder)
Answer:
The quotient of 902 divided by 27 equals 33 and the remainder is 11.
PLZ HELP I BEGG!! 100 POINTS AND BRANLIEST
Answer:
Vertical angles are opposite angles that are formed from two intersecting lines. From this, the vertical angle to 3 is 5
Answer:
Step-by-step explanation:
<3 is a right angle so its opposite angle is vertical to it. The answer is <5.
What is the distance between (8, -3) and
(4, -7)?
Answer:
10.770
Step-by-step explanation:
can anyone help pleaseeee?
C. 0 + 4y = 2
Explaination:x + y =7 .. (1)
x - 3y = 5 ..(2)
Subtracting equation (2) from (1) , we get,
•°•4y = 2
Seven subtracted from a number is -18
Answer:
-11
Step-by-step explanation:
Just add 7 to -18
-18 + 7 = -11
Hope this helped :)
(If you want to check, just do -11 - 7)
How many cm are in 26 in? (1 in = 2.54 cm)
Answer:
66.04
Step-by-step explanation:
26 x 2.54 =
= 66.04
Answer:
66.04 cm
Step-by-step explanation:
All you need to do is multiply 2.54 cm twenty-six times for your answer.
2 . 5 4
2║40║10 ║0.8 ║→ 50.8
6║ 12║ 3 ║0.24║→ 15.24
50.8 + 15.24 = 66.04
The sides of a right-angled triangle are in the ratio 8:15:17. If the perimeter of the triangle is 160 cm, find the area.
Not sure what it is help
1) The functional dependency A -> B for relation schema R(A,B,C,D) implies that:
a. No two tuples in R can have the same value for the attribute B
b. Any two tuples in R that have the same value for B must have the same value for A
c. No two tuples in R can have the same value for A
d. Any two tuples in R that have the same value for A must have the same value for B
The function dependency A -> B for relation schema R(A,B,C,D) implies that:
d. Any two tuples in R that have the same value for A must have the same value for B
The correct answer is option d. This is because the function dependency A -> B means that the value of B is functionally dependent on A. The productivity function X → Y is called trivial if Y is part of X. In other words, the FD:X → Y dependency means that the value of Y is determined by the value of X. Two bunches of X values that share the same thing must have the same Y value where Z = U - XY is the residue. In simple terms, if the values of the X attributes are known (assuming they are x), then the values of the Y attributes corresponding to x can be determined by looking at them in an R tuple containing x.
Therefore, any two tuples in R that have the same value for A must have the same value for B. This ensures that the relationship is functional and follows the rules of normalization. Tuples are individual rows in a relation and value refers to a specific entry in a tuple for a particular attribute.
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What is the slope of a line perpendicular to 3Y + 6X = 12?
Select one:
a. -2
b. 2
c. 1/2
d. -1/2
e. 1/6
Which function represents g(x), a reflection of f(x)
(10)' across the x-axis?
g(x) = -2 (10)
g(x) = - CE
g(x) = f (0)
g(x) = {(10)-x
The function that represent reflection of f(x) is given by g(x) = Negative two-fifths(10)x
Describe Reflection of a function:Similar to reflections regarding the y-axis, the x-axis reflections are fundamentally the same. The only distinction is that the points are mirrored from above the x-axis to below the x-axis, and vice versa, rather than along the y-axis.
Make sure you have studied how to perform basic vertical and horizontal translations before we move on to reflections across the y-axis.
The reflection across the co-ordinate axis which is x-axis is as follows;
Reflection about the x-axis
Pre-image point before reflection = (x, y)
Point of image after reflection = ((x, -y)
Therefore, the x coordinate remains the same while the y coordinate changes sign
For which given that f(x) = y = 2/5(10)x and g(x) = Reflection of f(x) across the x-axis, we have
Reflection about the x-axis
Pre-image point before reflection = (x, f(x))
cordinate of image after the reflection = (x, g(x))
Hence g(x) = -f(x) = -2/5(10)x.
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Complete question:
Which function represents g(x), a reflection of f(x) = Two-fifths (10)x across the x-axis? g(x) = Negative two-fifths(10)x g(x) = Negative two-fifths (one-tenth) Superscript x g(x) = Two-fifths (one-tenth) Superscript negative x g(x) = Two-fifths(10)-x
Rex contracts with Spicy Pizza to deliver its products. After the deal has been partially performed, both parties inform each other that they would like to cancel the contract. Rex and Spicy may rescind Group of answer choices none of their contract. their entire contract. their contract to the extent that it is executory. their contract to the extent that it has been executed.
Rex and Spicy Pizza, after partially performing the contract, may rescind their entire contract or their contract to the extent that it is executory.
Rescission refers to the cancellation or termination of a contract. In this scenario, Rex and Spicy Pizza have both expressed their desire to cancel the contract after partially performing it. The parties have two options for rescinding the contract. First, they can rescind their entire contract, which means they nullify the entire agreement and both parties are released from their obligations. Alternatively, they can rescind the contract to the extent that it is executory, meaning they cancel the remaining unperformed obligations while preserving the rights and duties that have already been fulfilled. The specific choice between these options would depend on the mutual agreement and circumstances of the contract between Rex and Spicy Pizza.
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Of all the closed right circular cylindrical cans of volume 128πcm
3, find the dimensions of the can which has minimum surface area.
The can's minimum surface area should have a height of 8 cm and a radius of 4 cm.
Given:
The volume of closed right circular cylindrical cans = 128π cm³
As we know the volume of a cylinder = πr²h
By equating;
πr²h = 128π
h = 128/r²
To get the dimensions of a can with minimum surface area;
S = 2πrh + 2πr
Put h = 128/r²;
Therefore, S(r) = 256π/r + 2πr²
S'(r) = -256π/r² + 4πr
S''(r) = -(2*256π)/r³ + 4π
Now, for S(r) = 0;
r = 4cm
for S''(4) > 0 at r = 4 is minimum point.
Hence,
h = 128π/(π*4*4)
h = 8cm
Therefore, the minimum surface area of the can should have a radius of 4 cm and a height of 8 cm.
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