Circular gears p and q start rotating at the same time at constant speeds. gear p makes 10 revolutions per minute, and gear q makes 40 revolutions per minute. how many seconds after the gears start rotating will gear q have made exactly 6 more revolutions than gear p ?

  12 seconds

Step-by-step explanation:

The difference in rotation rate is 40 - 10 = 30 rev/min. That means the faster gear makes one more revolution in 1/30 minute = 2 seconds. For 6 more revolutions, it will take 6×(2 seconds) = 12 seconds.

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In 12 seconds = 1/5 minute, P makes 10/5 = 2 revolutions; Q makes 40/5 = 8 revolutions. 8 is 6 more than 2.

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below:

£56

step-by-step explanation:

u divide 24 by 3 and u get 8 so if u do 8 time 7 or 8+8+8+8+8+8+8 u get 56 and 56 divided by 7 is 8.