Domain – All of the values that go into a relation or a function are called the domain. Range – All of the entities (output) which emerge from a relation or a function are called the range. All input values that are used (independent values) forms the Domain set.
we are given
where
F is the number of board feet
d is the diameter (in inches) of the log
Since, we have to minimize F
so, firstly we will find it's derivative
now, we can set it to 0
and then we can solve for d
so, we get diameter as
..............Answer
Answer:
perimeter is 4 sqrt(29) + 4pi cm
area is 40 + 8pi cm^2
Step-by-step explanation:
We have a semicircle and a triangle
First the semicircle with diameter 8
A = 1/2 pi r^2 for a semicircle
r = d/2 = 8/2 =4
A = 1/2 pi ( 4)^2
=1/2 pi *16
= 8pi
Now the triangle with base 8 and height 10
A = 1/2 bh
=1/2 8*10
= 40
Add the areas together
A = 40 + 8pi cm^2
Now the perimeter
We have 1/2 of the circumference
1/2 C =1/2 pi *d
= 1/2 pi 8
= 4pi
Now we need to find the length of the hypotenuse of the right triangles
using the pythagorean theorem
a^2+b^2 = c^2
The base is 4 ( 1/2 of the diameter) and the height is 10
4^2 + 10 ^2 = c^2
16 + 100 = c^2
116 = c^2
sqrt(116) = c
2 sqrt(29) = c
Each hypotenuse is the same so we have
hypotenuse + hypotenuse + 1/2 circumference
2 sqrt(29) + 2 sqrt(29) + 4 pi
4 sqrt(29) + 4pi cm
Answer:
312cm2
Step-by-step explanation:
Area of the triangles:
A =1/2bh
A=1/2(10*12) = 1/2*120=60.
There are two triangles. 60*2=120. 120 is the area of both triangles.
Area of the rectangle:
16*12=192.
120+192=312cm2
Answer:
a) 0.1535
b) 0.4866
c) 0.8111
Step-by-step explanation:
The probability that the next call come within the next t minutes is:
According to this model,
a) the probability that a call in comes within 1/2 minutes is 
=0.1535
b) the probability that a call in comes within 2 minutes is 
=0.4866
c) the probability that a call in comes within 5 minutes is 
=0.8111
