The force f (in newtons) of the hydraulic cylinder in a press is proportional to the square of sec x where x is the distance (in meters) that the cylinder is extended in its cycle. the domain of f is [0, pi/3], and f(0) = 500.a) find f as a function of x. f(x)=) find the average force exerted by the press over the interval [0, pi/3] (round your answer to 1 decimal place)f= n

Part A) F(x) =500 sec(x)

Part B) Average force exerted by the press = 750 N

Step-by-step explanation:

Given:

F(x) ∝ sec(x)

Range of x = [0,Pi/3] or x = [0 , 60°]

F(0) = 500 N i.e. F is 500 N at x = 0.

As we now that:

Force is proportional to sec(x) therefore we may write an equation by introducing Proportionality Constant (k) as under:

F(x) = k * sec(x) - Say it Equation 1

Then using given information of F=500 N at x = 0 we have:

500 = k * sec(0)

As sec(0) = 1, therefore we get:

k = 500

By putting value of k in equation 1 we have:

F(x) = 500 * sec(x)

Now by putting max value of x from the given range that is Pi/3 in the above equation we get:

F(Pi/3) = 500 * sec(Pi/3)

As Pi = 180 there we simplify the above equation as:

F(60°) = 500 * sec(60°)

F(60°) = 500 * 2 ; By putting sec(60°) = 2

F(60°) = 1000 N

Now the avg. of force exerted by the hydraulic press is given by:

Avg. Force = Minimum Force + [(Maximum Force - Minimum Force) / 2] - Say it equation 2

Considering sec(x) is minimum at x = 0 and maximum at x = 60° within the given range [0 , 60°] therefore we have:

The minimum force being put at x = 0 i.e. F = 500 N and max. force at x = 60° which is F = 1000 N.

Finally we get the average force using equation 2 as under:

Average force = 500 +  [(1000 - 500) / 2]

Average Force = 500 + 250

Average Force = 750 N

associative property hopes this ! : )

step-by-step explanation:

option a is correct.

step-by-step explanation:

scale factor: it is used to find proportional measurements.

proportions means having the same ratio.

scale factor is the ratio of the model measurement to the actual measurement in a simplest form.

or we can say that the ratio of any two corresponding lengths in two similar geometric figures

if the scale factor is more than 1, then it is an enlargement,

if the scale factor less than 1, then it is a reduction.

given the two geometric figure:

by definition of proportions, we have