1. Jeffs builds model train layouts. He has $75 to spend on packages of miniature landscape items. He receives 6 free packages with each order. The number of packages y that Jeff can buy is given by y = 75/x + 6, where x represents the cost of each package in dollars. Describe the reasonable domain values and graph the functions.

A: Both the number of packages and the cost of each package in dollars will be nonnegative, so the nonnegative vlaues are reasonable for the domain and range.

Graph: ?

2. Suppose a cone and a cylinder have the same radius and that the slant height l of the cone is the same as the height h of the cylinder. Find the ratio of the cone's surface area to the cylinder's surface area.

Area of cone: S = πrl + πr^2

Area of cylinder: S = 2πrh + 2πr^2

2.

conearea/cylinder area= (rl+r^2)/(rh+r^2)=

(l+r)/(h+r)

1. For the equation y = 75/x + 6, the domain represents the possible values for x (the cost of each package). Since both the number of packages and the cost of each package cannot be negative, the reasonable domain values for x would be x ≥ 0.

To graph the function, you can create a table of values by choosing different values for x and calculating the corresponding y values. For example, you can choose x = 5, 10, 15, 20, etc., and then substitute these values into the equation to find the corresponding y values. Plot these points on a graph and connect them to get a smooth curve.

2. To find the ratio of the cone's surface area to the cylinder's surface area, we need to substitute the given conditions into the formulas for the surface area of a cone and a cylinder.

Let's consider the cone first. The formula for the surface area of a cone is S = πrl + πr^2, where r is the radius and l is the slant height of the cone. In this case, the slant height l is the same as the height h of the cylinder.

Next, let's consider the cylinder. The formula for the surface area of a cylinder is S = 2πrh + 2πr^2, where r is the radius and h is the height of the cylinder. In this case, the height h of the cylinder is the same as the slant height l of the cone.

Since the radius and height are the same for both the cone and the cylinder, we can simplify the ratios of their surface areas by canceling out some terms.

For the cone's surface area, the term πr^2 appears in both the πrl and πr^2 terms. We can factor out πr^2 to get S_cone = πr(r + l).

For the cylinder's surface area, the term 2πr^2 appears in both the 2πrh and 2πr^2 terms. We can factor out 2πr^2 to get S_cylinder = 2πr(r + h).

Now, we can find the ratio of the cone's surface area to the cylinder's surface area by dividing S_cone by S_cylinder:

Ratio = (S_cone / S_cylinder) = (πr(r + l)) / (2πr(r + h))

Canceling out the common terms, we get:

Ratio = (r + l) / (2(r + h))

Therefore, the ratio of the cone's surface area to the cylinder's surface area is (r + l) / (2(r + h)).