The force needed to overcome friction and drag a person across the floor depends on the person's weight. Manuel Dexterity can drag Gil O' Teen across the floor by pulling with a force of 51 pounds. Gil's brother, Nick who weighs twice as much can be dragged across the floor by pulling with a force of 102 pounds.

A.) How does force cary with the person's weight?

How do I come up with the equation? I don't know how to do this... it's something link

Y=kX or something of the sort...

This stupid math class expects us to use pounds for force instead of newtons

A.) To find the equation that relates the force needed to drag a person across the floor and their weight, you can use the data given about Manuel pulling Gil and his brother.

Let F be the force needed to drag a person and W be their weight. As you mentioned, the relationship is of the form:

F = k * W

Now, plug in the data from the problem into the equation. For Gil:

51 pounds = k * (weight of Gil)

For Nick:

102 pounds = k * (2 * (weight of Gil)) [since Nick weighs twice as much as Gil]

Now you have a system of two equations:

1) 51 = k * W_Gil
2) 102 = k * (2 * W_Gil)

You can use these equations to solve for k and the weight of Gil.

First, divide equation (2) by 2:

(2) 51 = k * W_Gil

Now, both equation (1) and (2) are essentially the same:

51 = k * W_Gil

So, the force needed to drag a person across the floor is directly proportional to their weight, with a constant factor of 1 (k=1). In other words, the force needed is equal to the person's weight. The equation is:

F = W

In this math class, the force is measured in pounds instead of Newtons, but the relationship still holds. The force needed to drag a person across the floor is equal to their weight, regardless of the units used for force and weight.

To determine how force varies with a person's weight, we can use a proportionality equation. Let's represent the force needed to drag a person as F and the person's weight as W. We know that Manuel Dexterity can drag Gil O' Teen with a force of 51 pounds, and Nick with a force of 102 pounds.

Based on this information, we can set up the following equation:

F = kW

where k is the constant of proportionality. To find the value of k, we can use any of the given scenarios. Let's use the scenario where Manuel is dragging Gil O' Teen:

51 = k × (Gil O' Teen's weight)

Since we don't know the weight of Gil O' Teen, let's represent it as W1. The equation becomes:

51 = k × W1

Next, let's use the scenario where Manuel is dragging Nick, who weighs twice as much as Gil O' Teen:

102 = k × (Nick's weight)

Since Nick's weight is twice that of Gil O' Teen, we can write it as 2W1 (where W1 is Gil O' Teen's weight). The equation now becomes:

102 = k × 2W1

Simplifying further:

102 = 2k × W1

Now, divide this equation by the first equation we obtained:

(102 ÷ 2) = (2k × W1) ÷ (k × W1)

51 = 2k

Solving for k:

k = 51 ÷ 2

k = 25.5

Hence, the equation relating force and weight is:

F = 25.5W

This equation shows that force is directly proportional to weight, with the constant of proportionality being 25.5.

To determine how force varies with the person's weight, we can analyze the given information and establish a relationship between the force and weight. Let's start by examining the two scenarios provided:

Scenario 1: Manuel Dexterity pulls with a force of 51 pounds to drag Gil O' Teen.
Scenario 2: The same person, Manuel Dexterity, pulls with a force of 102 pounds to drag Gil O' Teen's brother, Nick, who weighs twice as much.

Based on these scenarios, we can observe that as the weight of the person being dragged doubles, the force required to overcome friction and drag that person also doubles. This suggests a linear relationship between force and weight, as one quantity is directly proportional to the other.

In mathematical terms, we can represent this linear relationship as:

Force (F) = k * Weight (W)

Here, F represents the force required, W represents the weight of the person, and k is the constant of proportionality. We need to solve for k.

In the first scenario, Manuel Dexterity exerts a force of 51 pounds (F) to drag Gil O' Teen (W). Using these values:

51 = k * W (Eq. 1)

In the second scenario, Manuel Dexterity exerts a force of 102 pounds (F) to drag Nick, who weighs twice as much as Gil O' Teen:

102 = k * 2W (Eq. 2)

From Eq. 1, we can isolate k:

k = 51 / W

Substituting k into Eq. 2:

102 = (51 / W) * 2W

Simplifying:

102 = 102W / W

102 = 102

This equation is true, indicating that our assumption of a linear relationship between force and weight is correct. The constant of proportionality, k, is therefore equal to 51 / W.

In conclusion, the force required to overcome friction and drag a person across the floor is directly proportional to the person's weight. The equation that represents this relationship is:

Force (F) = (51 / W) * Weight (W)

Although pounds are used in this particular problem, it is true that Newtons are the standard unit for force in the International System of Units (SI). Feel free to convert the measurements into Newtons if desired for consistency with the SI unit system.