Answer:
25
Step-by-step explanation:
When we write expressions for the total cost of each field visit and set them equal, we find the solution to be the ratio of the difference in fixed cost to the difference in variable cost.
y = 75 +7x . . . . . cost for x students to visit the science center
y = 50 +8x . . . . cost for x students to visit the natural history museum
__
Subtracting the first equation from the second, we get ...
0 = -25 +x
25 = x . . . . . add 25; the number of students such that costs are equal
The cost will be the same either place for 25 students.
__
<em>Additional comment</em>
Here, the fixed cost difference is 75-50=25, and the variable cost difference is 8-7=1. The ratio of these costs is ...
$25/($1 /student) = 25 students.
This relationship only holds when the higher fixed cost is associated with the lower variable cost. Charges are such that one place caters to larger numbers of students (science center), and one prefers fewer students (natural history museum).
and 
use the second expression to calculate the left-hand side of the first equation:

Add 10 to both sides if this equation to get

and divide both sides by 2

this proves that x = 17, give the two initial equations
The volume of the trough is V(w) = w³ + 20w² - 429w and the rate of change of the volume over a width of 38 inches to 53 inches is 4695 in³/in
<h3>What is an
equation?</h3>
An equation is an expression that shows the relationship between two or more variables and numbers.
Let w represent the width, hence:
length = w + 33, height = w - 13
Volume (V) = w(w + 33)(w - 13) = w³ + 20w² - 429w
V(w) = w³ + 20w² - 429w
Rate of change = dV/dw = 3w² + 40w - 429
When w = 38, dV/dw = 3(38)² + 40(38) - 429 = 5423
When w = 53, dV/dw = 3(53)² + 40(53) - 429 = 10118
Rate = 10118 - 5423 = 4695 in³/in
The volume of the trough is V(w) = w³ + 20w² - 429w and the rate of change of the volume over a width of 38 inches to 53 inches is 4695 in³/in
Find out more on equation at: brainly.com/question/2972832
#SPJ1
Answer:
35
Step-by-step explanation:
You have 17 either side to make 18 the middle e.g if 2 was the middle then you have 1 either side.