MATHEMATICS HIGH SCHOOL






A pulley with a radius of 8 inches rotates three times every five seconds. Find the
angular velocity of the pulley in radians/sec (round to the nearest hundredth). Find the
linear velocity to the nearst ft/hr. 

Answers

Answer 1
Answer: If the pulley rotates at a rate of 3 revolutions per second, then the period T of movement is  (1)/(3)s

a) calculate the angular velocity:

\omega=(2 \pi)/(T)\n \n \omega=(2 \pi)/((1)/(3))=6 \pi \ rad/s

b) calculate the linear velocity:

v=(2 \pi R)/(T)=(2 \pi.8)/((1)/(3))=24 \pi \ in/s \approx 75,36 \ in/s

Remember: 1 in/s = 300 ft/h

So, 75,36 in/s = 22,608 ft/h

Related Questions

In Russel Elementary School there are 50 students. At the beginning of the year, each student planted three flowers in the school yard. During the year, eight flowers withered. Which of the following expressions represents the number of flowers that remained in the school yard? A. (3 × 50) – 8 B. (50 + 3) – 8 C. (50 × 8) – 3 D. (50 × 3) ÷ 8
Can someone please help?
A garden is in the shape of a rectangle and has a perimeter of 58 yards. The length of the garden is 5 more than twice the width. Find the dimensions of the garden.
A data set contains an independent and dependent variable which must be true or the data set of a linear function can be used to represent the data
a company manufactures and sells novelty Mugs. the manufacturing cost consist of a fixed cost of R8000 and a variable cost of R15 rand per mug. the mugs are sold at R35 each. assume a linear profit function. determine the profit function

Jose wants to find the perimeter of triangle ABC. He uses the distance formula to determine the length of AC. Finish Jose’s calculations to find the length of AC.What is the perimeter of triangle ABC? Round the answer to the nearest tenth, if necessary.

12.0 units
12.4 units
15.0 units
15.4 units

Answers

AC = √ (-5)² + (4)²
AC = √ 25 + 16
AC = √41
AC = 6.40  This is the measure of the hypotenuse.

long leg = 5      distance from -2 to +3 (x - axis)
short leg = 4     distance from 2 to 6 (y - axis)

perimeter = 6.4 + 5 + 4 = 15.4 units

How many hours between 8:15 to 12:45 ?

Answers

4.5
an hour to 9:15
one to 10
one to 11
one to 12
and .5 to 1215 to 1245
Subtract:

12h   45' -
08h   15'
-----------
04h   30'

!50 POINTS! (1 SIMPLE GEOMETRY QUESTION)

QUESTION BELOW
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Answers

Answer:

x= 40.33

Step-by-step explanation:

In geometry, alternate exterior angles are a pair of angles that are on the outer side of two parallel lines but on opposite sides of the transversal. In other words, they are the angles that are not on the same line as the parallel lines.

The alternate exterior angles are always equal in measure. This is because when a transversal intersects two parallel lines, it creates two pairs of alternate exterior angles, and each pair of angles is supplementary to each other (meaning that their measures add up to 180 degrees).

In this case:

a° = b°

Since,, the alternate exterior angles are always equal in measure.

3x+17 = 138

subtracting 17 on both sides

3x + 17-17 = 138-17

3x = 121

dividing both sides by 3.

(3x)/(3) = (121)/(3)

\sf x \approx 40.33

The value of x is 40.33 which  proves that r is parallel to s.

Answer:

c)  40.3

\hrulefill

Step-by-step explanation:

According to the Alternate Exterior Angles Theorem, when two parallel lines are intersected by a transversal, the angles that are exterior to the parallel lines and on the alternate sides of the transversal are congruent.

Therefore, if lines r and s are parallel, then a° = b°.

To find the value of x that proves line r is parallel to line s, solve a° = b° for x.

\begin{aligned}a^(\circ)&=b^(\circ)\n\n3x+17&=138\n\n3x+17-17&=138-17\n\n3x&=121\n\n(3x)/(3)&=(121)/(3)\n\nx&=40.33333....\n\nx&=40.3\; \sf (nearest\;tenth)\end{aligned}

Therefore, the value x that proves line r is parallel to line s is:

\Large\boxed{x=40.3}

The rectangular coordinates of a point are given. Find polar coordinates (r,θ) of this point with expressed in radians. Let r>0 and -2π (-2√3,2)

Answers

Answer:

To find the polar coordinates (r, θ) of the point (-2√3, 2), you can use the following formulas:

r = √(x^2 + y^2)

θ = arctan(y / x)

In this case:

x = -2√3

y = 2

Let's calculate r and θ:

r = √((-2√3)^2 + 2^2)

r = √(12 + 4)

r = √16

r = 4

Now, calculate θ:

θ = arctan(2 / (-2√3))

First, find the angle in radians from the arctan:

θ = arctan(-√3)

θ ≈ -π/3 (in radians)

So, the polar coordinates of the point (-2√3, 2) are approximately (4, -π/3) in radians.

Step-by-step explanation:

Will 3/5 x 2/7 be less than, greater than or equal to 3/5

Answers

3/5 times 2/7=6/35
compare 3/5 to 6/35

5 times 7=35

3/5 times 7/7=21/35

21/35 ? 6/35
21 ? 6
21> 6


an easy way is if we do

3/5=x, a random number
rememberig that taking a fraction of something makes it smaller

x times fraction is smaller than x
so
3/5 times 2/7 is less than 3/5
3/5×2/7=6/35
3/5=3/5×7/7=15/35
3/5 ×2/7  is less than 3/5

If the variance of the data values in a population is 324, what is the standard deviation of the data values?A. 14
B. 12
C. 16
D. 18

Answers

Simply the standard deviation of the data values is the square root of the variance:S= √(V)= √(324)=18
Answer: D)18
  

Answer:

18

Step-by-step explanation:
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