( 50 POINTS )In order to host track and field competitions, a 400-meter track needs to be created. A typical Olympic track looks like the one on the picture.

a) Show that the runner who runs in the inside lane runs 400 meters.
b) All other runners in a 400 meters race start a little further ahead since their lane is a little longer. If the radius of lane 2 (the one beside the inside lane) is 37.92 meters, find how much of a stagger (head start) the lane 2 runner should be given. Round your answer to the nearest hundredth.

Step-by-step explanation:

The answer is b because the racer run a equivalent amount

c. 27 units.

step-by-step explanation:

we are told that in circle a, ∠bae ≅ ∠dae.

we can see from our given diagram that in and ;

, as these are radii of our given circle.

therefore, by sas congruence postulate.

hence, side be will be equal to side de as corresponding parts of congruent triangles are congruent. so we can set an equation to find the value of x as:

now let us substitute x=17 in the expression for the length of be.

therefore, length of be will be 27 units and option c is the correct choice.

$3720

step-by-step explanation:

taxable income = $31000

as per the 2018-2019 us tax bracket, the tax rate is 12% for an individual whose taxable income is between $9,526 to $38,700.

so, the tax to be paid by him = 12% of 31000

= 0.12 * 31000     [12% converted to decimal as 0.12]

= $3720