A spin balancer rotates the wheel of a car at 500 revolutions per minute. If the diameter of the wheel is 26 inches, what road speed is being tested?a. 26 rad/s
b. 3.2 rad/s
c. 52 rad/s
d. 81 rad/s

Answers

Answer 1

Answer:

Answer:

c. 52 rad/s

Step-by-step explanation:

Final question does not correspond with available option. The real question is: What is the angular speed in radians per second?

At first we assume that spin balance rotates at constant rate and convert given angular speed, measured in revolutions per minute, into radians per second:

$\omega = \left(500\,(rev)/(min) \right)\cdot \left(2\pi\,(rad)/(rev) \right)\cdot \left((1)/(60)\,(min)/(sec) \right)$

$\omega \approx 52.360\,(rad)/(s)$

Which corresponds to option C.

Answer 2

Answer:

The wheel rotates at an angular speed of 52 rad/s and the equivalent road speed is about 39 mph.

To solve this, we need to consider the given spin speed which is 500 revolutions per minute and convert this to rev per second by dividing by 60.

This is because a minute has 60 seconds.

Hence, the wheel rotates at 500/60 = 8.33 rev/s.

Furthermore, we need to know that in physics, one full revolution equals 2π radians (this is the equivalent of going around a circle once).

So, to convert from revolution to radian, we multiply by 2π, so the wheels is spinning at 8.33 * 2π ≈ 52.36 rad/s, which most closely matches option c. 52 rad/s.

Lastly, the linear (or road) speed can be calculated by multiplying the Angular momentum by the radius of the wheel (which is half the diameter), so v = (52.36 rad/s) * (13 in) = 680.68 in/s.

To convert it to mph, note that 1 inch/s = 0.057 mph, hence the wheel is spinning at about 39 mph.

Learn more about Angular momentum here:

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NEED HELP ASAP WILL MARK BRAINLIEST!!!!!!!!!What is the solution to the system of equations

-4x - 5y - z = 18
-2x - 5y -2z=12
-2x + 5y +2z=4

A) (4,0,2)
B) (-4,0,-2)
C) (-4,2,0)
D) (-4,0,2)

Answers

Answer:

Step-by-step explanation:

When we have multiple answers, we can check each to find the solution. Each ordered pair is written as (x,y,z). We substitute each into the equations to find which satisfy all equations and which do not.

A) (4,0,2)

-4(4)-5(0)-(2)=18

-16-0-2=18

$-18\neq18$

Not a solution

B) (-4,0,-2)

-4(-4)-5(0)-(-2)=18

16-0+2=18

18=18 is true. We now try the other equations.

-2(-4)-5(0)-2(-2)=12

8-0+4=12

12=12

We try the last equation.

-2(-4)+5(0)+2(-2)=4

8+0+-4=4

4=4

We no longer need to try C or D because a system of equations only has one solution. B is the solution.

A model rocket is launched straight into the air from platform 3 feet above the ground with an intial velocity of 192 feet per second

Answers

Answer:

Step-by-step explanation:

the function -16t^2 + 64t + 192 give the height S, in ft, of a model water rocket launched with a velocity of 64 ft/second from a hill that is 192 ft high. a) determine how long it will take the rocket to reach the ground, b) find the interval on which the height of the rocket is greater than 240 ft.

In a rectangle CALM, LD =15cm. Find the length of diagonal CL. A. 15cm C. 25cm B. 20cm D. 30cm

Answers

In a rectangle, opposite sides are equal in length. Therefore, in rectangle CALM, CL is equal to AD, the diagonal of the rectangle.

Since LD is given as 15 cm, and LD is the same as AD, the length of diagonal CL is also 15 cm.

So, the correct answer is:

A. 15 cm

Final answer:

The length of diagonal CL in rectangle CALM, with LD=15cm, was calculated on the assumption that CALM is a square. Using the Pythagorean theorem, we derived approximately 21.21cm for the diagonal length, although none of the provided alternatives matched this result.

Explanation:

In rectangle CALM, if LD is 15 cm, we can solve for the length of diagonal CL using the Pythagorean theorem. The theorem relates the lengths of the sides and diagonal (hypotenuse) of a right triangle, which is formed by the diagonal and two sides of the rectangle. In this case, if LD is 15 cm and assuming that the rectangle is a square (both sides equal), we would have a right triangle with two sides of 15 cm.

Using the Pythagorean theorem, we can calculate the diagonal: a² + a² = d², where a represent the length of the sides and d stands for the diagonal. Using the equation, we get 15^2 + 15^2 = d^2, after solving it we get d=approximately 21.21.

However, none of the provided alternatives (15cm, 20cm, 25cm, 30cm) match this result, indicating that the rectangle may not be a square or that a different side (not LD) might define the diagonal length. It is crucial to have all required measurements to accurately solve the problem.

Learn more about Pythagorean theorem here:

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What is the greatest integer that is less than √6+√7?It would make me happy if someone answered this question :)