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Stella [2.4K]
3 years ago
8

What is cubic spline?​

Mathematics
2 answers:
Mila [183]3 years ago
7 0

Answer:

A cubic spline is a spline constructed of piecewise third-order polynomials in which pass through a set of control points. __________________________________________________________

Hope this helps!!

If I am wrong, please tell me, I enjoy learning from my mistakes:)

lara [203]3 years ago
4 0

Answer:

Here is your answer

Step-by-step explanation:

A cubic spline is a spline constructed of piecewise third order polynomials which pass through a set of control points. The second derivative of each polynomial is commonly set to zero at the endpoints since this provides a boundary condition that completes the system of equations.

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Simplify (*x* +2x? - 5x)+(-3x + x +1)+(3+* + 2x).
Mama L [17]

Answer:

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Step-by-step explanation:

4x^4+3x^2-3x^3-3x+1

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Sam bought some toys. He bought a baseball for $5.88, and paid $8.41
myrzilka [38]

Answer:

$5.71

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20-5.88=14.12

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If you have a cubic polynomial of the form y = ax^3 + bx^2 + cx + d and lets say it passes through the points (2,28), (-1, -5),
nikklg [1K]

Step-by-step explanation:

<u>Step 1:  Solve using the first point</u>

<em>(2, 28)</em>

28 = a(2)^3 + b(2)^2 + c(2) + d

28 = 8a + 4b + 2c + d

<u>Step 2:  Solve using the second point</u>

<em>(-1, -5)</em>

-5 = a(-1)^3 + b(-1)^2 + c(-1) + d

-5 = -a + b - c + d

<u>Step 3:  Solve using the third point</u>

<em>(4, 220)</em>

220 = a(4)^3 + b(4)^2 + c(4) + d

220 = 64a + 16b + 4c + d

<u>Step 4:  Solve using the fourth point</u>

<em>(-2, -20)</em>

-20 = a(-2)^3 + b(-2)^2 + c(-2) + d

-20 = -8a + 4b - 2c + d

<u>Step 5:  Combine the first and fourth equations</u>

<u />28 - 20 = 8a - 8a + 4b + 4b + 2c - 2c + d + d

8 = 8b + 2d

8 - 8b = 8b - 8b + 2d

(8 -8b)/2 = 2d/2

4 - 4b = d

<u>Step 6:  Solve for c in the second equation</u>

-5 + 5 = -a + b - c + d + 5

0 + c = -a + b - c + c + d + 5

c = -a + b + d + 5

<u>Step 7:  Substitute d with the stuff we got in step 5</u>

c = -a + b + (4 - 4b) + 5

c = -a + b + 4 - 4b + 5

c = -a - 3b + 9

<u>Step 8:  Substitute d and c into the first equation</u>

<u />28 = 8a + 4b + 2(-a - 3b + 9) + (4 - 4b)

28 = 8a + 4b - 2a - 6b + 18 + 4 - 4b

28 - 22 = 6a - 6b + 22 - 22

6 / 6 = (6a - 6b) / 6

1 + b = a - b + b

1 + b = a

<u>Step 9:  Substitute a, b, and c into the third equation</u>

220 = 64(1 + b) + 16b + 4(-(1 + b) - 3b + 9) + (4 - 4b)

220 = 64 + 64b + 16b + 4(-1 - b - 3b + 9) + 4 - 4b

220 - 100 = 60b + 100 - 100

120 / 60 = 60b / 60

2 = b

<u>Step 10:  Find a using b = 2</u>

a = b + 1

a = (2) + 1

a = 3

<u>Step 11:  Find c using a = 3 and b = 2</u>

c = -a - 3b + 9

c = -(3) - 3(2) + 9

c = -3 - 6 + 9

c = 0

<u>Step 12:  Find d using b = 2</u>

d = 4 - 4b

d = 4 - 4(2)

d = 4 - 8

d = -4

Answer:  a = 3, b = 2, c = 0,d = -4

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(2y-at)(y+2at)


Answer: <span><span><span>−<span><span>2<span>a^2</span></span><span>t^2</span></span></span>+<span><span><span>3a</span>t</span>y</span></span>+<span>2<span>y^<span>2

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weeeeeb [17]

The equation of the quadratic function is f(x) = x²+ 2/3x - 1/9

<h3>How to determine the quadratic equation?</h3>

From the question, the given parameters are:

Roots = (-1 - √2)/3 and (-1 + √2)/3

The quadratic equation is then calculated as

f(x) = The products of (x - roots)

Substitute the known values in the above equation

So, we have the following equation

f(x) = (x - \frac{-1-\sqrt{2}}{3})(x - \frac{-1+\sqrt{2}}{3})

This gives

f(x) = (x + \frac{1+\sqrt{2}}{3})(x + \frac{1-\sqrt{2}}{3})

Evaluate the products

f(x) = (x^2 + \frac{1+\sqrt{2}}{3}x + \frac{1-\sqrt{2}}{3}x + (\frac{1-\sqrt{2}}{3})(\frac{1+\sqrt{2}}{3})

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f(x) = x^2 + \frac{2}{3}x - \frac{1}{9}

So, we have

f(x) = x²+ 2/3x - 1/9

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