A79-tooth gear drives a smaller gear which has 42 teeth. if the larger gear rotates at 316 rpm, what is the speed of the smaller gear, to the nearest rpm?

594 rpm

Step-by-step explanation:

Two gears will have the same linear speed, so:

v₁ = v₂

ω₁ r₁ = ω₂ r₂

(316 rpm) (79) = ω (42)

ω ≈ 594 rpm

what is

step-by-step explanation:

5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = = -

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, - 8 ), then

- 8 = - + c ⇒ c = -

y = - x - ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form