Answer:
The dimension of the cardboard is 34 cm by 34 cm by 17 cm.
Step-by-step explanation:
Let the dimension of the cardboard box be x cm by y cm by z cm.
The surface area of the cardboard box without lid is
f(x,y,z)= xy+2xz+2yz.....(1)
Given that the volume of the cardboard is 19,652 cm³.
Therefore xyz =19,652
......(2)
putting the value of z in the equation (1)


The partial derivatives are


To find the dimension of the box set the partial derivatives
and
.Therefore 
.......(3)
and 
.......(4)
Now putting the x in equation (3)



⇒y=34 cm
Then
=34 cm.
Putting the value of x and y in the equation (2)

=17 cm.
The dimension of the cardboard is 34 cm by 34 cm by 17 cm.
It would likely just be written as "two point four five", or "two and forty-five hundredths".
Answer:
(a) Circle Q is 9.4 units to the center of circle P
(b) Circle Q has a smaller radius
Step-by-step explanation:
Given


Solving (a): The distance between both
The equation of a circle is:

Where


P and Q can be rewritten as:


So, for P:


For Q:


The distance between them is:

Where:
--- 
--- 
So:





Solving (b): The radius;
In (a), we have:
--- circle P
--- circle Q
By comparison

<em>Hence, circle Q has a smaller radius</em>