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2 years ago

a pulley rotates through 97 degrees in one minute. how many rotations does the pulley make in an hour?

Mathematics

1 answer:

zhuklara [117]2 years ago

6 0

The number of rotations made by the pulley in hour is 16 rotations

<h3>Data obtained from the question</h3>

Front the question given above, the following data were obtained:

97 degree rotation = 1 mimute
Number of rotation in 1 hour =?

<h3>How to determine the time to rotate 360 degrees</h3>

We'll begin by calculating the time to rotate 360 degrees since a complete rotation has an angle of 360 degrees. This can be obtained as illustrated below:

97 degree rotation = 1 mimute

Therefore,

360 degrees = 360 / 97

360 degrees = 3.71 minutes

<h3>How to determine the number of rotations in 1 hour</h3>

1 rotation = 360 degrees = 3.71 minutes
Number of rotation in 1 hour (60 minutes) =?

The number of rotation made in 1 hour (i.e 60 minutes), can be obtained as follow:

3.71 mins = 1 rotaion

Therefore,

60 mins = 60 / 3.71

60 mins = 16 rotations

Thus, the pulley will made an approximate of 16 rotations in 1 hour

Learn more about rotation of pulley:

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Place these numbers in order from greatest to least. 19/5, 1.62, –14/3, –0.5

max2010maxim [7]

Answer:

See below:

Step-by-step explanation:

Hello my name is Galaxy and I'll be helping you today. I hope you are having a nice day!

Simplification

To figure out how we can order them, we can first simplify the problems so that we can easily determine its place. We can put the fractions into decimal form so that they are are in one form and will be easy for us to comprehend.

$\frac{19}{5}=3\frac{4}{5}=3.80$

We know that $\frac{1}{5}$ is equal to 0.20 because we know that 1.00 will be equal to 100 in this case and we can divide that by five to get 20 which will be divided back to get to 0.20.

As I've explained how I've simplified the first one, simplifying the others should be a quite similar process, feel free to comment below if you need any assistance with this.

$\frac{19}{5}=3.80\\1.62=1.62\\\frac{-14}{3}=-4.6667\\ -0.5=-0.5$

(Everything simplified to decimal form.)

We can now proceed to ordering them.

Ordering

Ordering decimals doesn't have to be as hard as it looks, we know that as per the number line a number that is more negative (e.g. -37) will be less than (e.g. -5) as it is closer to the number 0.

Now that we know how to order the negative numbers, we can order them into order, and for ordering the positive numbers, we should already know how to do that.

So, now, in order from Greatest to Least. We can order them by what I said above.

$3.80>1.62>-0.5>-4.666$

We can convert the numbers back into their original form by looking at how we converted them in the Simplification section.

Final Answer

After converting them into a way that we can comprehend, we get our final answer in terms of greatest to least as:

$\frac{19}{5}>1.62>-0.5>\frac{-14}{3}$

Cheers!

6 0

2 years ago

Cos sec² a - cot²a=1

alex41 [277]

Answer:

We want to prove the relation:

cosec(a)^2 - cot(a)^2 = 1

where:

cosec(a) = 1/sin(a)

cot(a) = 1/tg(a) = cos(a)/sin(a)

We can start with the relationship:

cos(a)^2 + sin(a)^2 = 1

Now, let's divide by sin(a)^2 in both sides:

(cos(a)^2 + sin(a)^2)/sin(a)^2 = 1/sin(a)^2

cos(a)^2/sin(a)^2 + sin(a)^2/sin(a)^2 = (1/sin(a))^2

(cos(a)/sin(a))^2 + 1 = (1/sin(a))^2

and remember that:

cosec(a) = 1/sin(a)

cot(a) = 1/tg(a) = cos(a)/sin(a)

Then we can write:

(cos(a)/sin(a))^2 + 1 = (1/sin(a))^2

as:

cot(a)^2 + 1 = cosec(a)^2

1 = cosec(a)^2 - cot(a)^2

And this is the relation we wanted to prove.

3 0

3 years ago

Simplify (q and (-q or p)) or (p and -(q and p))

Vesnalui [34]

Step-by-step explanation:

(q and (not q or p)) = (q and not q) or (q and p) = false or q and p = q and p

(p and not (q and p)) = (p and (not q or not p)) =

= (p and not q) or (p and not p) = (p and not q) or false =

= p and not q

so, we have in total

(q and p) or (p and not q) = (p and q) or (p and not q).

this is p, because if p=false both brackets are false and therefore the whole expression is false. and if p=true, then one of the 2 brackets must be true, which makes the whole expression true.

5 0

4 years ago

The mathematics department of a college has 15 male professors, 14 female professors, 6 male teaching assistants, and 11 fema

dolphi86 [110]

Answer:

77%

Step-by-step explanation:

6 0

4 years ago

help me... the angle pairs.. for example linear pair, vertical angles... that stuff.... I said that because last time I asked th

Cerrena [4.2K]

<h3>Answers: </h3>

Angle 1 and 3: Vertical Angles

Angle 4 and 8: Corresponding Angles

Angles 4 and 6: Alternate Interior Angles

Angles 3 and 5: Alternate Interior Angles

Angles 7 and 8: Linear Pair

Angles 1 and 7: Alternate Exterior Angles

=================================================

Explanation:

Vertical angles are formed when you cross two lines to form an X shape. The vertical angles are opposite one another in this configuration.

Corresponding angles are ones that show up in the same corner of each four-corner crossing. In the case of angles 4 and 8, both are in the southwest corner of each four-corner crossing.

Alternate interior angles are angles in between parallel lines and on opposite sides of a transversal. Alternate exterior angles are similar, but they are outside the parallel lines.

A linear pair of angles are adjacent and supplementary (meaning they add to 180).

8 0

3 years ago