Answer:
The rate is 1 ÷ 2 yards per hour
Step-by-step explanation:
The computation of the rate does the amount of yarn changes is given below:
= 3 3 ÷ 4 - 1 1 ÷8
= 15 ÷ 4 - 9 ÷ 8
= 21 ÷ 8 yards
Now divide the above fraction by the number of hours
= 21 ÷ 8 yards ÷ 5 1 ÷ 4
= 21 ÷ 8 × 4 ÷ 21
= 1 ÷ 2 yards per hour
Hence, the rate is 1 ÷ 2 yards per hour
The same would be relevant
Answer:
The explicit form is 
Step-by-step explanation:
The explicit form of a geometric sequence is given by:
where an is the nth term, a is the first term of the sequence and r is the common ratio.
In this case:
a=162
The value of the common ratio is obtained by dividing one term by the previous term.
For the first and second terms:
108/162=2/3
For the second and third terms (In order to prove that 2/3 is the common ratio)
72/108=2/3
Therefore:
r=2/3
Replacing a and r in the formula:
Answer:
Step-by-step explanation:
The volume of a rectanguiar shape like this one is V = L * W * H, where the letters represent Length, Width and Height. Here L is the longest dimension and is 28 - 2x; W is the width and is 22-2x; and finally, x is the height. Thus, the volume of this box must be
V(x) = (28 - 2x)*(22 - 2x)*x
and we want to maximize V(x).
One way of doing that is to graph V(x) and look for any local maximum of the graph. We'd want to determine the value of x for which V(x) is a maximum.
Another way, for those who know some calculus, is to use the first and second derivatives to identify the value of x at which V is at a maximum.
I have provided the function that you requested. If you'd like for us to go all the way to a solution, please repost your question.
