MATHEMATICS HIGH SCHOOL

A belt runs a pulley of radius 8 inches at 60 revolutions per minute. a) Find the angular speed in radians per minute. b) Find the linear speed in inches per minute.

Answers

Answer 1

Answer:

Answer:

Part a) $120\pi\ (rad)/(min)$

Part b) $960\pi\ (in)/(min)$

Step-by-step explanation:

we have

60 rev/min

Part a) Find the angular speed in radians per minute

we know that

One revolution represent 2π radians (complete circle)

$1\ rev=2\pi \ rad$

To convert rev to rad, multiply by 2π

$60\ (rev)/(min)=60(2\pi)=120\pi\ (rad)/(min)$

Part b) Find the linear speed in inches per minute

we know that

The circumference of a circle is equal to

$C=2\pi r$

we have

$r=8\ in$ ----> given problem

substitute

$C=2\pi(8)$

$C=16\pi\ in$

Remember that

One revolution subtends a length equal to the circumference of the circle

$1\ rev=16\pi\ in$

To convert rev to in, multiply by 16π

$60\ (rev)/(min)=60(16\pi)=960\pi\ (in)/(min)$

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The sum of two consecutive even integers is −234. what are the two integers

Answers

Does this help answer you question?

2x+(2x+2)=234

4x=232

x=58

So, 2x=2(58)=116

116+118=234

The answer is -118 and -116

The inequality x2 + 12x + 35 ≥ 0 has two critical points and three possible intervals for solutions. Choose each set of possible test points for the three intervals.–8, –6, –4

–10, –6, 0

–6, 0, 6

–6, 0, 10

Answers

The answers are...

-8, -6, -4
-10, -6, 0

Answer:

–8, –6, –4

-10, –6, 0

Step-by-step explanation:

a & b are the correct answers

The solution of the equation 2d - 6 = 5 is _____.

Answers

If you would like to solve the equation 2 * d - 6 = 5, you can do this using the following steps:

2 * d - 6 = 5
2 * d = 5 + 6
2 * d = 11 /2
d = 11/2
d = 5 1/2

The correct result would be 5 1/2.

$2d-6=5\n\nAdd\ 6\ on\ both\ sides.\n\n2d=11\n\nDivide\ by\ 2\ on\ both\ sides.\n\nd= (11)/(2)\n\nd=5(1)/(2)$

$\sf\ Answer:\ {\boxed{d=5(1)/(2)}}$

What is the aswer ??????

Answers

Answer:

A prime numbers are numbers which have only two factor

The answer is prime number because it’s only two factor

4. The shortest distance from a point to a straight line is A. a parallel through the point to the line.

B. the perpendicular bisector of the line.

C. a vertical line through the point.

D. the perpendicular from the line to the point.