If the shape of an arrow's path is f(x)=-0.3(x-8)^2+15, how can the equation be changed for the arrow to fly farther?

musickatia [10]

Let us model this problem with a polynomial function.

Let x = day number (1,2,3,4, ...)
Let y = number of creatures colled on day x.

Because we have 5 data points, we shall use a 4th order polynomial of the form
y = a₁x⁴ + a₂x³ + a₃x² + a₄x + a₅

Substitute x=1,2, ..., 5 into y(x) to obtain the matrix equation
| 1 1 1 1 1 | | a₁ | | 42 |
| 2⁴ 2³ 2² 2¹ 2⁰ | | a₂ | | 26 |
| 3⁴ 3³ 3² 3¹ 3⁰ | | a₃ | = | 61 |
| 4⁴ 4³ 4² 4¹ 4⁰ | | a₄ | | 65 |
| 5⁴ 5³ 5² 5¹ 5⁰ | | a₅ | | 56 |

When this matrix equation is solved in the calculator, we obtain
a₁ = 4.1667
a₂ = -55.3333
a₃ = 253.3333
a₄ = -451.1667
a₅ = 291.0000

Test the solution.
y(1) = 42
y(2) = 26
y(3) = 61
y(4) = 65
y(5) = 56

The average for 5 days is (42+26+61+65+56)/5 = 50.
If Kathy collected 53 creatures instead of 56 on day 5, the average becomes
(42+26+61+65+53)/5 = 49.4.

Now predict values for days 5,7,8.
y(6) = 152
y(7) = 571
y(8) = 1631

3 0

3 years ago

Read 2 more answers

Find the sum of (x + 5),(-4x - 2) and (2x - 1)

Elina [12.6K]

Answer:

-x + 2

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Algebra I

Combining Like Terms

Step-by-step explanation:

Step 1: Define

(x + 5) + (-4x - 2) + (2x - 1)

Step 2: Simplify

Combine like terms (x): -x + 5 - 2 - 1
Combine like terms (Z): -x + 2

7 0

3 years ago

Read 2 more answers

Solve. Check your answer. -3/z + 7/4z = 5/z-25

Anastaziya [24]

[~Answer~] (3.):

Hello there! I'm Avery, and I'm here to help you! I mostly believe the answer Could be: (the answer is in the screenshot. I couldn't write it, so I typed it.)

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[~Answer Explanation~]:

1:

Combine multiplied terms into a single fraction

2:

Find common denominator

3:

Combine fractions with common denominator

4:

Multiply the numbers

5:

Re-order terms so constants are on the left

6:

Combine exponents

7:

Rearrange terms

8:

Find common denominator

9:

Combine fractions with common denominator

10:

Re-order terms so constants are on the left

11:

Rearrange terms

12:

Multiply all terms by the same value to eliminate fraction denominators

13:

Cancel multiplied terms that are in the denominator

14:

Distribute

15:

Move terms to the left side

16:

Distribute

17:

Subtract the numbers

18:

Rearrange terms

19:

Use the quadratic formula

20:

Simplify

21:

Separate the equations

22:

Solve

Answer: z = $\frac{-50 + 2\sqrt{681} }{7}$

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[~Last Messages~]:

Okay, I really hope my answer is correct.