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
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Answer:
The linear function is: p(x) = 3x+65The linear function is: p(x) = 3x+65
Step-by-step explanation:
Let x be the number of t-shirts and y be the total pay
As we can clearly see in the table that there is a linear relationship between x and y
A linear function is given as:
Here m is the gradient of the function then
Taking any two pairs of x and y
(1,68) and (2,71)
Putting in equation
Putting a pair (1,68) in the equation to find the value of b
Putting the value of b
Let p(x) be the linear function
Hence,
The linear function is: p(x) = 3x+65
The amount of passwords possible is:
Since he only tries once for the first try we get:
Thus there is a:
Chance he will guess the password on his first try.
Assuming gravity is constant and ignoring wind resistance...
h(t)=hi+vit-16t^2....vi=0 and hi=256 so
h(t)=256-16t^2
When it hits the ground, h=0 so
256-16t^2=0
16t^2=256
t^2=16, and since t>0
t=4 seconds