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viktelen [127]
3 years ago
5

Select ALL the correct answers.

Mathematics
2 answers:
Orlov [11]3 years ago
4 0

Answer:

r(n)=3n-1

Step-by-step explanation:

sammy [17]3 years ago
4 0

Answer:

The function r(n) = 3n-1 and r(1) = 2; r(n) = r(n-1)+3 can be used to find the number of rings she design in n hours

Explanation:

If Martha design 2 rings in the first hour and every additional hour, she designs 3 new rings, this will form an arithmetic sequence of the nature

2, (2+3), 2+(3×2), 2+(3×3)...

2, 5, 8, 11... (since she designs 3 new rings every three hours), the succeeding term keep increasing by factor of 3.

To get the functions that can be used to find the number of rings, r(n), she designs in n hours, we will use the formula for finding the nth term of an arithmetic sequence which is given as;

r(n) = a+(n-1)d where;

a is the first term of the sequence = 2

n is the number of terms

d is the common difference = 5-2 = 8-3 = 11-8 = 3

Substituting this values in the formula, we will have;

r(n) = 2+(n-1)3

r(n) = 2+3n-3

r(n) = 3n-1

The model of if r(1) = 2;

r(n) = r(n-1)+3 is also valid

To check if this is true for subsequent terms

When n = 2,

r(2) = r(2-1) +3

r(2) = r(1) + 3

r(2) = 2+3 = 5

When n = 3,

r(3) = r(3-1) +3

r(3) = r(2) + 3

r(3) = 5+3 = 8

This shows that the function r(n) = 3n-1 and r(1) = 2; r(n) = r(n-1)+3 can be used to find the number of rings she design in n hours

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ikadub [295]

Use the sum of cubes factoring rule

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\frac { \sin^{3} \theta + \cos^{3} \theta } { \sin \theta + \cos \theta } = 1 - \sin \theta \cdot \cos \theta\\\\\frac { (\sin \theta + \cos \theta)(\sin^2 \theta - \sin \theta \cdot \cos\theta + \cos^2 \theta) } { \sin \theta + \cos \theta } = 1 - \sin \theta \cdot \cos \theta\\\\

\sin^2 \theta - \sin \theta \cdot \cos\theta + \cos^2 \theta = 1 - \sin \theta \cdot \cos \theta\\\\(\sin^2 \theta + \cos^2\theta)- \sin \theta \cdot \cos\theta = 1 - \sin \theta \cdot \cos \theta\\\\1- \sin \theta \cdot \cos\theta = 1 - \sin \theta \cdot \cos \theta \ \ \checkmark\\\\

Throughout the entire process, the right hand side stayed the same.

On the last step, I used the pythagorean identity.

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2 years ago
a restaurant owner bought 4 boxes of disposable cups for $145 , with each box containing 1,656 cups. if he wanted to divvy up th
snow_lady [41]
1104 cups per 1 restaurant

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You divide this by 6, and TADA!

Hope this helps!
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3 years ago
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antiseptic1488 [7]

Answer:

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5 0
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kow [346]

Answer:

it is 1

Step-by-step explanation:

5 0
3 years ago
What is the fuction for the graph?
Andrews [41]

The <em>piecewise defined</em> function is formed by the following three functions: y = 40, for 0 ≤ x < 15, y = 0.0425 · x² - 3.8 · x + 87.438, for 15 ≤ x < 65 and y = 0.4 · x - 6, for x ≥ 65.

<h3>What is the piecewise defined function behind the graph?</h3>

In this problem we have a <em>piecewise defined</em> function formed by three functions: (i) <em>Linear</em> equation, (ii) <em>Quadratic</em> equation, (iii) <em>Linear</em> equation. The <em>first</em> function is y = 40, for 0 ≤ x < 15.

The <em>second</em> function can be found based on the knowledge of three points:

y = a · x² + b · x + c

(x₁, y₁) = (15, 40)

40 = 225 · a + 15 · b + c

(x₂, y₂) = (45, 2.5)

2.5 = 2025 · a + 45 · b + c

(x₃, y₃) = (65, 20)

20 = 4225 · a + 65 · b + c

And the <em>quadratic</em> equation is y = 0.0425 · x² - 3.8 · x + 87.438, for 15 ≤ x < 65.

And the <em>latter linear</em> equation is:

y = m · x + b

m = (30 - 20)/(90 - 65)

m = 0.4

And the x-intercept is:

b = y - m · x

b = 20 - 0.4 · 65

b = - 6

The <em>linear</em> equation is y = 0.4 · x - 6, for x ≥ 65.

The <em>piecewise defined</em> function is formed by the following three functions: y = 40, for 0 ≤ x < 15, y = 0.0425 · x² - 3.8 · x + 87.438, for 15 ≤ x < 65 and y = 0.4 · x - 6, for x ≥ 65.

To learn more on piecewise defined functions: brainly.com/question/12561612

#SPJ1

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