Answer:
The function is negative for all real values of x where
x < –3 and where x > 1.
Step-by-step explanation:
This quadratic function is downward parabola.
It's root are -3 and 1.
Quadratic is positive between -3 and 1.
And negative on R-(-3,1).
Answer:
θ is decreasing at the rate of
units/sec
or
(θ) = 
Step-by-step explanation:
Given :
Length of side opposite to angle θ is y
Length of side adjacent to angle θ is x
θ is part of a right angle triangle
At this instant,
x = 8 ,
= 7
(
denotes the rate of change of x with respect to time)
y = 8 ,
= -14
( The negative sign denotes the decreasing rate of change )
Here because it is a right angle triangle,
tanθ =
-------------------------------------------------------------------1
At this instant,
tanθ =
= 1
Therefore θ = π/4
We differentiate equation (1) with respect to time in order to obtain the rate of change of θ or
(θ)
(tanθ) =
(y/x)
( Applying chain rule of differentiation for R.H.S as y*1/x)
θ
(θ) = 
- 
-----------------------2
Substituting the values of x , y ,
,
, θ at that instant in equation (2)
2
(θ) =
*(-14)-
*7
(θ) = 
Therefore θ is decreasing at the rate of
units/sec
or
(θ) = 
Answer:
Length = 2 ft
Width = 2 ft
Height = 5 ft
Step-by-step explanation:
Let the square base of the box has one side = x ft
Therefore, area of the base = x² ft²
Cost of the material to prepare the base = $0.35 per square feet
Cost to prepare the base = $0.35x²
Let the height of the box = y ft
Then the volume of the box = x²y ft³ = 20
-----(1)
Cost of the material for the sides = $0.10 per square feet
Area of the sides = 4xy
Cost to prepare the sides of the box = $0.10 × 4xy
= $0.40xy
Cost of the material to prepare the top = $0.15 per square feet
Cost to prepare the top = $0.15x²
Total cost of the box = 0.35x² + 0.40xy + 0.15x²
From equation (1),
Total cost 


Now we take the derivative of C with respect to x and equate it to zero,
= 0



x = 2 ft.
From equation (1),

4y = 20
y = 5 ft
Therefore, Length and width of the box should be 2 ft and height of the box should be 5 ft for the minimum cost to construct the rectangular box.
Answer:
0.3
Step-by-step explanation:
answer and step by step in the attachment