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AlekseyPX
3 years ago
10

Jami is trying to model the movement of a tire. In order to properly model the movement, she is going to focus on the movement o

f the tire's air nozzle. The nozzle is on the right side of the tire and she is going to treat that position as the equilibrium position. She then slowly rotates the tire so that the nozzle goes up at the beginning of the rotation, and follows its change in height.
The distance of the nozzle from the center of rotation is nine inches. She finds that it takes eight seconds for the tire to make a single revolution.




Which of the following functions best models the position of the nozzle?




A. s(t)=9sin(4pi t)



B.s(t)=9sin(pi/4 t)



C.s(t)=9cos(4pi t)



D. s(t)=9cos(pi/4 t)
Mathematics
1 answer:
USPshnik [31]3 years ago
5 0

From the given data it is clear that the amplitude of the wave will be 9 inches.

It is also clear that the speed of rotation, ω, will be: \omega=\frac{2\pi}{T}=\frac{2\pi}{8}=\frac{\pi}{4}

Now, it is given that the nozzle is on the right side of the tire and that position is going to be treated as the equilibrium position, the tire is then rotated such that the nozzle goes up at the beginning of the rotation. This condition is possible only when we have a Sine (Sin) function.

Thus, our final answer can be arrived as:

Amplitude\times Sin(\omega t)

9\times sin(\frac{\pi}{4}t) =9sin(\frac{\pi}{4}t)

Thus, out of the given options, option B is the correct answer.


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Mercury is a naturally occurring metal that can be harmful to humans. The current recommendation is for humans to take in no mor
kirill [66]

Answer:

A.) A person weights 80 kg can consume Haddock fish = 149 grams

B.) A person weights 80 kg can consume Swordfish fish = 8 grams

C.) A person weights 80 kg can consume Tuna fish = 23 grams

D.) A person weights 80 kg can consume Snapper fish = 50 grams

Step-by-step explanation:

Given - Mercury is a naturally occurring metal that can be harmful to humans. The current recommendation is for humans to take in no more than 0.1 microgram for every kilogram of their weight per day. Fish generally carry high levels of mercury, although certain fish have higher mercury content than others. Fish, however, are healthy sources of many other nutrients, so nutritionists recommend keeping them in the human diet. The figure below shows the average mercury content of several types of fish.

To find - If a person weighs 82 kg, how much of each fish can they safely consume? round to the nearest gram.

A.Haddock

B.Swordfish

C.Tuna

D.Snapper​

Proof -

Firstly, determine how many micro grams of mercury a person can consume who weighs 82 kilograms.

⇒82 × 0.1 =  8.2 micro grams.

Now,

a.)

For Haddock fish-

It consumes 0.055 micro grams of mercury

So,

A person can consume fish = 8.2 ÷ 0.055

                                              = 149.09 ≈ 149 grams

So,

A person weights 80 kg can consume Haddock fish = 149 grams

b.)

For Swordfish fish-

It consumes 0.995 micro grams of mercury

So,

A person can consume fish = 8.2 ÷ 0.995

                                              = 8.24 ≈ 8 grams

So,

A person weights 80 kg can consume Swordfish fish = 8 grams

c.)

For Tuna fish-

It consumes 0.350 micro grams of mercury

So,

A person can consume fish = 8.2 ÷ 0.350

                                              = 23.43 ≈ 23 grams

So,

A person weights 80 kg can consume Tuna fish = 23 grams

d.)

For Snapper fish-

It consumes 0.165 micro grams of mercury

So,

A person can consume fish = 8.2 ÷ 0.165

                                              = 49.697 ≈ 50 grams

So,

A person weights 80 kg can consume Snapper fish = 50 grams

6 0
3 years ago
The volleyball team has 41 members. There are 3 more boys than girls how many girls are there?
Pie
19 members are girls
4 0
3 years ago
25% of 68000 is how much
hjlf
1 \% =\frac{1}{100} \\ \\25 \% =\frac{25}{100}=0,25\\ \\25 \% \cdot 68000 = 0,25 \cdot 68000 =17 000


6 0
2 years ago
Read 2 more answers
Directions: Drag each operation and expression to the correct location on the equation. Not all operations or expressions will b
butalik [34]
5.0 x 10^6 X 473 = 2.4 x 10^9

There are 5 x 10^6 blood cells in a ml, and 473 ml in a pint. simply multiply both numbers together and put the answer in scientific notation (one digit before the decimal)
6 0
3 years ago
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Corbin is selling cheese at the farmers’ market. One wheel of cheese has a diameter of 11 inches.
sveticcg [70]

Answer:

I. 94.99 in²

II. $0.23

Step-by-step explanation:

<u>Given the following data;</u>

Diameter of wheel = 11 inches

\pi = 3.14

Cost of wheel = $21.35

Radius, r = \frac {diameter}{2}

Radius, r = \frac {11}{2} = 5.5 \; inches

<em><u>Part A</u></em>

To find the area;

We know that a wheel is circular in nature. Thus, the area of a circle is given by the formula;

Area, A = \pi r^{2}

Substituting into the equation, we have;

Area, A = 3.14 * 5.5^{2}

Area, A = 3.14*30.25

<em>Area, A = 94.99 in²</em>

<em><u>Part B</u></em>

To find cost per square inch;

Cost \; per \; square \; inch = \frac {Cost \; per \; wheel}{Area \; of \; wheel}

Cost \; per \; square \; inch = \frac {21.35}{94.99}

<u>Cost per square inch = $0.23</u>

6 0
2 years ago
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