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3 years ago

How do the lengths of line segments define the golden ratio?

Mathematics

1 answer:

NISA [10]3 years ago

5 0

Answer:

$\frac{a+b}{a}=\frac{a}{b}$

Step-by-step explanation:

The golden ratio is a special number favored by the Greeks. Its ratio roughly equals 1.618. The ratio is formed by taking a line segment and dividing it into two parts labeled a and b. The golden ratio is formed when this proportion is true $\frac{a+b}{a}=\frac{a}{b}$ .

When you add a and b then divide by a, it will be the same as a divided by b. This will hold true only for specific lengths of a and b. This means you must divide the line segment in such a way that a and b meet this requirement.

Example:

If the line segment is 50 cm long. Split the segment into parts a and b where a = 30.9 and b = 19.1. Substitute the values into the proportion $\frac{a+b}{a}=\frac{a}{b}$ .

$\frac{30.9+19.1}{30.9}=\frac{30.9}{19.1}$

$\frac{50}{30.9}=\frac{30.9}{19.1}$

1.618 = 1.618

This is the golden ratio.

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Question 7 il pont) (2 +377)(2 – 377)

Elden [556K]

Answer:

142125

Step-by-step explanation:

Since we given two brackets to solve we will have to take the step by step procedure

So let's solve the question

(2+377)(2-377)

Let's start with the first bracket

(2+377)

It will give us 379

So let's solve the second bracket

(2-377)

It will give us -375

So back to the question

(379)(-375)

142125

So the final answer is 142125

3 0

3 years ago

Juan brought 4 Tshirts and leather jacket. The T shirts were all the same price, and the price of the leather jacket was 6 times

Alex

Let us say that:

x = the number of T shirts bought = 4

y = the number of leather jackets bought = 1

a = the price of the T shirts

b = the price of the leather jackets

With the given variables, we can say that the total cost is:

total cost = a x + b y

Since, b = 6 a, therefore:

total cost = a x + 6 a y

total cost = a (x + 6 y)

Since total cost is 209, therefore we can calculate for a since x and y are also given:

209 = a (4 + 6 * 1)

209 = a (10)

a = $20.9

Therefore each T shirt cost $20.9

7 0

3 years ago

A batting machine uses an automatic baseball feeder. During baseball

Inessa05 [86]

The feeders in battling machine are represented in proportions and fractions.

The equation that represents the problem is: $\mathbf{\frac 16x + 15 = \frac 23x}$
The feeder can hold 30 baseballs, when full

The given parameters are:

$\mathbf{Initial = \frac 16x}$ ------ 1/6 full

$\mathbf{Additional = 15}$ --- baseballs added

$\mathbf{Final = \frac 23x}$ ---- 2/3 full

So, the equation that represents the problem is:

$\mathbf{Initial + Additional = Final}$

So, we have:

$\mathbf{\frac 16x + 15 = \frac 23x}$

The number of baseballs it can hold is calculated as follows:

$\mathbf{\frac 16x + 15 = \frac 23x}$

Multiply through by 6

$\mathbf{x + 90 = 4x}$

Collect like terms

$\mathbf{4x - x = 90 }$

$\mathbf{3x = 90 }$

Divide through by 3

$\mathbf{x = 30 }$

Hence, the feeder can hold 30 baseballs, when full

Read more about proportions and fractions at:

brainly.com/question/20337104

5 0

2 years ago

Write the equation in slope intercept form y= 3 (x+ 1) + 5x

schepotkina [342]

Given:

$y=3(x+1)+5x$

Required:

To write the given equation in slope intercept form.

Explanation:

Consider

$\begin{gathered} y=3(x+1)+5x \\ \\ y=3x+3+5x \\ \\ y=8x+3 \end{gathered}$

Final Answer:

$y=8x+3$

5 0

1 year ago

It is impossible to create a square pyramid by rotating a shape about an axis because its base is not ________.

natta225 [31]

It is impossible because it's base is not circular. A solid of revolution is obtained by rotating a plane curve around some straight line, that is, the axis of revolution that lies on the same plane. The closest to a square pyramid applying this concept is by rotating a right triangle around the opposite or adjacent side (the axis), but the shape that you get is a straight circular cone.

7 0

3 years ago