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just olya
1 month ago
15

You have a fishing line spool with an end that has an area of 20.0 cm2. How much fishing line do you need to wind around the spo

ol 10 times?
Express your answer (in cm) to three significant figures.
Mathematics
1 answer:
PIT_PIT [12.4K]1 month ago
3 0

Solution Procedure

Considering the spool as a cylindrical shape, and calculating the circumference based on the area cited, we establish the connection between circumference and area as follows:

... C = 2√(πA)

To find ten times this circumference, we calculate:

... 10C = 20√(π·20 cm²) = 40√(5π) cm ≈ 159 cm

Derivation of Formulas

The standard formulas for circumference and area are:

... C = 2πr

... A = πr²

Multiplying the area formula by π and extracting the square root yields:

... πA = (πr)²

... √(πA) = πr

Doubling this value results in the circumference formula:

... C = 2√(πA) = 2πr

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Which function increases at a faster rate on 0 to infinity, f(x) = x2 or g(x) = 2x? Explain your reasoning.
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Based on a table of values, the outputs of f(x) for whole numbers are 0, 1, 4, 9, 16, 25, 36, and further. Meanwhile, for the same inputs, g(x) generates outputs of 1, 2, 4, 8, 16, 32, and 64. It is evident that g(x) consistently doubles its outputs, leading to numbers that surpass those produced by f(x). The exponential function, g(x), experiences a constant multiplicative change rate, allowing it to accelerate more quickly compared to the quadratic function.

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1 month ago
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How many possible values for y are there where y = cos^-1 0?
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The potential values for y areinfinite

Further clarification

Trigonometry is a branch of math focused on the connections between the sides and angles of triangles.

Considering special angles of trigonometric functions, for instance

\displaystyle sin~0=0\\\\cos~30=\frac{1}{2}\sqrt{3}\\\\tan~45=1\\\\sec~45=\sqrt{2}\\\\etc.

In the equation y = cos⁻¹ 0, the value of y can be derived as follows:

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y = arc cos 0

cos y = 0

Thus, the resulting value of y:

\displaystyle \frac{\pi }{2},\frac{3}{2}\pi,\frac{5}{2}\pi, etc

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trigonometric identities

Keywords: trigonometric, infinite values,arithmetic sequence

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1 month ago
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A rectangular garden is 6 feet long and 4 feet wide. A second rectangular garden has dimensions that are double the dimensions o
Svet_ta [12734]

Response:

100 percent increase

Detailed explanation:

1st garden

Length = 6 ft

Width = 4 ft

Perimeter = 2 (l+w)

                 = 2 (6+4) = 2(10) = 20

2nd garden

The length and width of this garden are double those of the first

Length = 2 *6 = 12

Width = 2 *4 = 8

Perimeter = 2 (l+w)

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Percent change = (new - old )/old * 100 percent

The first garden represents the old garden = 20  and the second refers to the new garden = 40

Substituting values in

Percent change = (40-20)/20 = 20/20 =100 *100 percent

                            = 100 percent increase

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18 days ago
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Answer:

The sequence decreases by 5

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Answer:

Step-by-step explanation:

34+23F=175

23F=175-34=141

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therefore, he will purchase an additional 7 bags

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2 months ago
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