Answer:
The base of the triangle is decreasing at a rate of 1.4167 inch/hour.
Step-by-step explanation:
Area of a triangle:
The area of a triangle of base b and height h is given by:

In this question:
We have to derivate the equation of the area implicitly in function of time. So

The altitude of a triangle is increasing at a rate 2 inch/hour while the area of the triangle is decreasing at a rate of 0.5 square inch per hour.
This means that:

At what rate is the base of the triangle is changing when the altitude is 6 inch and the area is 24 square inch?
This is
when 
Area is 24, so the base is:



Then





The base of the triangle is decreasing at a rate of 1.4167 inch/hour.
This expression is in the form of a quadratic
Answer:
169.5 yd²
Step-by-step explanation:
See attachment.
In situations like this, ALWAYS (!) make as sketch.
Divide the areas by adding dotted lines on sensible places, and write in the missing numbers for the correct distances.
The only possible difficult one is the triangle, which is the half of a rectangle. So you are dealing with a series of areas of rectangles. That is really easy if you understand what you are doing.
Total area =
area 1 + area 2 + area 3 + area 4
10*4 + 4*7 + 3*13 + (0.5 * 7*17)
40 + 28 + 42 + 59.5
Total area = 169.5 yd²
I wrote answers in picture and I use Desmos app to solve this equations