In the electric current flow, it is found that the resistance (measured in the units called ohms) offered by a fixed length of wire of a given material varies inversely as the square of the diameter of the wire. if a wire 0.01 in. in diameter has a resistance of 0.306 ohm, what is the resistance of a wire of the same length and material with diameter 0.0299 in. to the nearest ten-thousandth?

Here's your explanation:
R = k / d^2 (k is a constant, unknown)
d1 = 0.01 and R1 = 0.306
d2 = 0.0299 R2 = ?

Use the equation in line 1 for both case and divide and k will go away and you can find R2

Since you have not included the experiment situation and the data, of course, i can not give you specific details about it. but i can you with this question.1) i will assume that the motion is projectile (parabolic) motion.2) yes, the horizontal distance depends on the horizontal velocity as, naming vx the horizontal velocity and t the time, it is: x = vx × t3) now, observe that the flight time depends on the vertical velocity as, naming voy the initial vertical velocity, t the time and y the vertical distance before reaching the ground: y = yo + voy×t - gt² / 2.the higher the initial vertical velocity (voy) the longer the object will be flying and so t will be higher in the equation for the horizontal distance.that explains the relationship between the horizontal distance and the horizontal velocity.