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 costs the zoo 0.86 per day to feed each bat a variety of soft fruits, therefore the cost of 17 egyptian fruit bats would be $14.62
<h3>What is an
equation?</h3>
An equation is an expression that shows the relationship between two or more numbers and variables.
A quadratic equation is in the form:
y = ax² + bx + c
it costs the zoo 0.86 per day to feed each bat a variety of soft fruits. Hence:
Cost of 17 egyptian fruit bats = $0.86 per day * 17 = $14.62
It costs the zoo 0.86 per day to feed each bat a variety of soft fruits, therefore the cost of 17 egyptian fruit bats would be $14.62
Find out more on equation at: brainly.com/question/2972832
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We can solve this by first finding the diameter of the two semicircles. We know that the width of the rectangle is 27 inches, which also happens to be the diameter of the circle.
The circumference of a circle is 2πr or πd. The problem says that it is a semicircle, however, it says that there are two of them. Since the two semicircles are the same size, we know that they can combine to form one circle, so we can just find the circumference of one circle to account for both of the semicircles:
C=27π inches
We also know that the length of the rectangle is 60 inches. We only want to find the perimeter of the frame, so we don't have to account for the widths of the rectangle because it is inside the frame. Therefore, the two sides of the rectangle together are 120 inches. Now we can add this to the circumference we found:
120+27π inches or 204.78 inches (depends on what your teacher is asking for)
