Answer:
y = - x - 1
Step-by-step explanation:
Assuming you require the equation of the line
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = - , then
y = - x + c ← is the partial equation
To find c substitute (12, - 4) into the partial equation
- 4 = - 3 + c ⇒ c = - 4 + 3 = - 1
y = - x - 1 ← equation of line
Answer:
The dimension of the open rectangular box is .
The volume of the box is 8.217 cubic inches.
Step-by-step explanation:
Given : The open rectangular box of maximum volume that can be made from a sheet of cardboard 11 in. by 7 in. by cutting congruent squares from the corners and folding up the sides.
To find : The dimensions and the volume of the open rectangular box ?
Solution :
Let the height be 'x'.
The length of the box is '11-2x'.
The breadth of the box is '7-2x'.
The volume of the box is
Derivate w.r.t x,
The critical point when V'(x)=0
Solve by quadratic formula,
Derivate again w.r.t x,
Now, (+ve)
(-ve)
So, there is maximum at x=1.392.
The length of the box is
The breadth of the box is
The height of the box is h=1.392.
The dimension of the open rectangular box is .
The volume of the box is
The volume of the box is 8.217 cubic inches.
We need to graph the given piecewise function.
To graph any piecewise function we do that into parts
Let's graph upper part first which is
restriction for that is
that means we are free to pick any number for x that is between -5 and 3, including 3.
So we will find few points by plugging random numbers between -5 and 3.
Let's use x=-5, we get:
so first point is (-5,27).
similarly we can find other points like (0,2), (2,6), (-1,3) etc.
Now we join those points by a curved line.
means we use a close circle at -5
x<3 means use open circle at 3
------------
Repeat same process for 2nd part f(x)=x-4
choose any number between 3 and 7 like x=3, 4 etc
so we get points (3,-1), (4,0) etc
Now graph them
So the final graph will look like:
