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jeka94
3 years ago
11

The average person American eats 49 pounds of french fries over 6 years. Which proportion could be used to determine how many po

unds of french fries a person eats in 18 years
Mathematics
1 answer:
Blababa [14]3 years ago
7 0
The average american eats 147 pounds of french fries in 18 years
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1. Derive the half-angle formulas from the double
lilavasa [31]

1) cos (θ / 2) = √[(1 + cos θ) / 2], sin (θ / 2) = √[(1 - cos θ) / 2], tan (θ / 2) = √[(1 - cos θ) / (1 + cos θ)]

2) (x, y) → (r · cos θ, r · sin θ), where r = √(x² + y²).

3) The point (x, y) = (2, 3) is equivalent to the point (r, θ) = (√13, 56.309°). The point (r, θ) = (4, 30°) is equivalent to the point (x, y) = (2√3, 2).

4) The <em>linear</em> function y = 5 · x - 8 is equivalent to the function r = - 8 / (sin θ - 5 · cos θ).

<h3>How to apply trigonometry on deriving formulas and transforming points</h3>

1) The following <em>trigonometric</em> formulae are used to derive the <em>half-angle</em> formulas:

sin² θ / 2 + cos² θ / 2 = 1                      (1)

cos θ = cos² (θ / 2) - sin² (θ / 2)           (2)

First, we derive the formula for the sine of a <em>half</em> angle:

cos θ = 2 · cos² (θ / 2) - 1

cos² (θ / 2) = (1 + cos θ) / 2

cos (θ / 2) = √[(1 + cos θ) / 2]

Second, we derive the formula for the cosine of a <em>half</em> angle:

cos θ = 1 - 2 · sin² (θ / 2)

2 · sin² (θ / 2) = 1 - cos θ

sin² (θ / 2) = (1 - cos θ) / 2

sin (θ / 2) = √[(1 - cos θ) / 2]

Third, we derive the formula for the tangent of a <em>half</em> angle:

tan (θ / 2) = sin (θ / 2) / cos (θ / 2)

tan (θ / 2) = √[(1 - cos θ) / (1 + cos θ)]

2) The formulae for the conversion of coordinates in <em>rectangular</em> form to <em>polar</em> form are obtained by <em>trigonometric</em> functions:

(x, y) → (r · cos θ, r · sin θ), where r = √(x² + y²).

3) Let be the point (x, y) = (2, 3), the coordinates in <em>polar</em> form are:

r = √(2² + 3²)

r = √13

θ = atan(3 / 2)

θ ≈ 56.309°

The point (x, y) = (2, 3) is equivalent to the point (r, θ) = (√13, 56.309°).

Let be the point (r, θ) = (4, 30°), the coordinates in <em>rectangular</em> form are:

(x, y) = (4 · cos 30°, 4 · sin 30°)

(x, y) = (2√3, 2)

The point (r, θ) = (4, 30°) is equivalent to the point (x, y) = (2√3, 2).

4) Let be the <em>linear</em> function y = 5 · x - 8, we proceed to use the following <em>substitution</em> formulas: x = r · cos θ, y = r · sin θ

r · sin θ = 5 · r · cos θ - 8

r · sin θ - 5 · r · cos θ = - 8

r · (sin θ - 5 · cos θ) = - 8

r = - 8 / (sin θ - 5 · cos θ)

The <em>linear</em> function y = 5 · x - 8 is equivalent to the function r = - 8 / (sin θ - 5 · cos θ).

To learn more on trigonometric expressions: brainly.com/question/14746686

#SPJ1

4 0
2 years ago
So, I'm completely lost on this. It's very easy to figure out as it's just writing a function, but I'm not entirely sure about t
Schach [20]
Width = w
length = w+2

f(w) =w(w+2) = w^2 + 2w.

Please, let me know whether the procedure is clear for you.

The answer is f(w)=w^2 + 2w.
8 0
3 years ago
Please help me with number 22 and if you can part b to please
m_a_m_a [10]
It's not a good picture.it's not possible to read it
6 0
3 years ago
PLEASE HELP ME!!!!!!! WILL GIVE THANKS AND RATING!!!!!! PLEASEEEEEEEEEEEEEE!!!!!!!
EastWind [94]
2 3/4 * 3.36 / (1 2/5) 
=11/4  *  3.36 / (7/5) 
= 9.24 /  (7/5) 
= 9.24 /  1.4
= 6.6
5 0
3 years ago
7TH GRADE MATH! PLEASE HELP BRAINLIEST ANSWER!
Harlamova29_29 [7]
<span>If y varies directly with x, the formula of the equation is y=ax, where a is a constant.
y=ax
(21)=a(7)
a=3
y=ax
y=(3)(-1.66)
y=-4.98, x=-1.66

If y varies inversely with x, the formula of the equation is y=a/x, where a is a constant
y=a/x
9=a/2.5
a=22.5
y=22.5/x
y=22.5/-0.6
y=-37.5

I hope this helped! =)
I hope you didn't mind but I got this from a website called: answers.yahoo.com but I got your answer.
</span>
3 0
3 years ago
Read 2 more answers
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