The shape of a roller coaster is modeled by a polynomial function, R(x). Describe how to find the x-intercepts of R(x) and how to construct a rough graph of R(x) so that the engineer can predict when there will be no change in the direction of the coaster. You may create a sample polynomial of degree 3 or higher to use in your explanations.

Answers

Answer 1

Answer:

The 1st feature of the polynomial function is that its graph is continuous, it is, in the graph of the polynomial function has no breaks. The 2nd feature is that the graph of the polynomial function has only smooth, rounded turns.

From the problem establishes that we can create the sample polynomial to be used in our explanations, we can say that this polynomial function is:

$R(x) = -2x^(4) + 2x^(2)$

To find the x-intercepts of R(x) set R(x) equal to zero and solve for x, so:

Set R (x) = 0

$0 = -2x^(4) + 2x^(2)$

$-2x^(4) + 2x^(2) = 0$

Remove common monomial factor :

$-2x^(4) + 2x^(2) = 0$

Factor out:

$-2x^(2) (x-1)(x+1)=0$

So the real zero are:

x = 0

x = 1

x = -1

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Answer 2

Answer:

ou will need three roots for this, so we have

Let x = -30, -10 and +20

So the factors will be (x+30)(x+10)(x-20)

The divide it to 100, this will help bring the peak up and down

So the polynomial function R(x) will become

1/100 * (x+30)(x+10)(x-20)

R(x) = 1/100 * (x+30)(x+10)(x-20)

Finding the X-intercept:

Let R(x) = 0 and solve for x.

1/100 * (x+30)(x+10)(x-20) = 0

x = -30, -10, 20 are the x-intercepts.

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Mike is pouring a two foot cement sidewalk around the perimeter of his swimming pool. His swimming pool measures 6 feet by 14 feet. If he plans for the sidewalk to be 9 inches deep, what volume of cement is needed for the sidewalk?

Answers

9 inches * 1 foot / 12 inches
= 3/4 feet deep

Area of the sidewalk:
= the sides of the pool * the width of the sidewalk + the corners of the sidewalk (width * width)
= 2 sides * 6 (feet / side) * 2 feet + 2 sides * 14 (feet / side) * 2 feet + 4 corners * (2 feet * 2 feet / corner)
= 12 feet * 2 feet + 28 feet * 2 feet + 4 * 2 feet * 2 feet
= 24 feet^2 + 56 feet^2 + 16 feet^2
= 96 feet^2

Volume:
= 96 feet^2 * 3/4 feet
= (96 * 3 / 4) feet^3
= (19 * 3) feet^3
= 57 feet^3

Answer:

the correct answer is B) 72^ft 3

The vertices of a feasible region are (14, 2), (0, 9), (6, 8), and (10, 3). What is the maximum value of P if P = 180x + 250y?

Answers

For this problem, we must first plot of each point using the given points. Assume that each coordinate given is in the (x,y) form. To get the maximum value, we can plus in each coordinate set to the equation to see which P comes out to be the largest. For (14,2), P=3020. For (0,9), P=2250. For (6,8), P=3080. For (10,3), P=2550. The maximum value for P would be P=3080.

Answer:

It’s C

Step-by-step explanation:

The difference between x and half of y

Answers

X - (1/2y)
The difference means to subtract so you would just take half of Y from X.

What is the 2x2 identity matrix?

Answers

Answer:

a matrix with 1's in the main diagonal and zeros everywhere. The identity matrix of order 2×2 is: [1 0 0 1].

Final answer:

The 2x2 identity matrix is a square matrix with 1s on the main diagonal and 0s elsewhere. It serves as the multiplicative identity in matrix multiplication, leaving the original matrix unchanged when multiplied.

Explanation:

In mathematics, the 2x2 identity matrix, denoted by the symbol I or Id, is a square matrix containing elements that make it act as the multiplicative identity in matrix multiplication. Specifically, a 2x2 identity matrix is written as:

I = [1, 0; 0, 1]

Here, the numbers 1 are positioned on the main diagonal from the top-left to bottom-right (also termed as principal diagonal). The other elements, outside the main diagonal, are 0. This particular configuration results in special properties such as, when any matrix is multiplied by the identity matrix, the original matrix is unchanged. So, if we have a 2x2 matrix A, then multiplying by the identity gives AI = IA = A.

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Two lines, A and B, are represented by the following equations:Line A: 4x + 4y = 16
Line B: x + y = 4

Which statement is true about the solution to the set of equations?

It is (1, 2).
There are infinitely many solutions.
It is (1, 5).
There is no solution.

Answers

If you would like to know which statement is true about the solution to the set of equations, you can calculate this using the following steps:

4x + 4y = 16
x + y = 4 /*(-4)
___________________
4x + 4y = 16
-4x - 4y = - 16
___________________
0 = 0

The correct result would be: There are infinitely many solutions.

One milliliter of water weighs one gram. Explain the relationship between the conversion. Then draw a conversion chart to show the relationship between one milliliter of water and grams, milligrams, kilograms, and metric tons.

Answers

Well, one mililiter is one gram, 1000 miligrams, .001 kilograms and $10^(-6)$ metric tons.

Answer:

one square millimeter of water weighs one gram. That's the relationship

Step-by-step explanation:

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