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sineoko [7]
3 years ago
8

Use cubic regression to find a function that fits the following points.

Mathematics
2 answers:
8090 [49]3 years ago
8 0

Answer:

y = 2x³ + x² - 4x + 6

Step-by-step explanation:

General formula:

y = ax³ + bx² + cx + d

If you replace point (0, 6) in the general formula, you get:

6 = a(0)³ + b(0)² + c(0) + d

6 = d

If you replace points (-1, 9), (1, 5) and (2, 18) in the general formula, you get the following system of equations:

9 = a(-1)³ + b(-1)² + c(-1) + 6

9 = -a + b - c + 6     (eq. 1)

5 = a(1)³ + b(1)² + c(1) + 6

5 = a + b + c + 6     (eq. 2)

18 = a(2)³ + b(2)² + c(2) + d

18 = 8a + 4b + 2c + 6     (eq. 3)

Adding equation 1 to equation 2:

14 = 2b + 12

(14 - 12)/2 = b

b = 1

Multiplying equation 1 by 2:

18 = -2a + 2b - 2c + 12     (eq. 4)

Adding equation 4 to equation 3, and replacing with b value:

36 = 6a + 6b + 18

36 = 6a + 6 + 18

(36 - 6 - 18)/6 = a

a = 2

Replacing a and b values in equation 1:

9 = -2 + 1 - c + 6

c = -2 + 1 + 6  - 9

c = -4

Fynjy0 [20]3 years ago
7 0

Answer:

y = ax³ + bx² +cx +d (Main eq.)

Solve for a, b, c and d.

Solution:

y = 2x³ + x² -4x +6

Step-by-step explanation:

i) Solving for d:

Given point (0,6), at this point your x value is 0 and your y value is 6. Substitute the values on the Main Eq. above and you will find the d value to be 6.

ii) Solving for a, b & c.

Using points (-1,9),(1,5) and (2,18)

Substitute the given points on the Main Eq. above and you will have 3 equations with 3 unknown variables and solve the equations simultaneously to find your a, b & c.

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3 years ago
Let z be the product of any 5 consecutive three digit odd natural numbers. When you multiply
Charra [1.4K]

Answer:

  5

Step-by-step explanation:

If x is the middle number of the 5 consecutive odd numbers, their product is ...

  x(x -2)(x +2)(x -4)(x +4) = x(x² -4)(x² -16)  = x⁵ -20x³ +64x

The first 3-digit prime is 101, so the product of that with this is ...

  101(x⁵ -20x³ +64x) = 101x⁵ -2020x³ +6464x

Since we're only interested in the units digit, we can find the mod 10 value of this to be ...

  (x⁵ +4x) mod 10

Possible units digits of x are 1, 3, 5, 7, 9, so possible units digits of this product are ...

  x(x⁴ +4) = 1(1⁴ +4) = 5

  3(3⁴ +4) = 3(1 +4) = 5 . . . . mod 10

  5(5⁴ +4) = 5(5 +4) = 5 . . . . mod 10

  7(7⁴ +4) = 7(1 +4) = 5 . . . . mod 10

  9(9⁴ +4) = 9(1 +4) = 5 . . . . mod 10

In every case, the units digit of 101z will be 5.

4 0
2 years ago
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Answer:

A

Step-by-step explanation:

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