Answer:
Step-by-step explanation:
GIVEN: A farmer has of fencing to construct a rectangular pen up against the straight side of a barn, using the barn for one side of the pen. The length of the barn is .
TO FIND: Determine the dimensions of the rectangle of maximum area that can be enclosed under these conditions.
SOLUTION:
Let the length of rectangle be and
perimeter of rectangular pen
area of rectangular pen
putting value of
to maximize
but the dimensions must be lesser or equal to than that of barn.
therefore maximum length rectangular pen
width of rectangular pen
Maximum area of rectangular pen
Hence maximum area of rectangular pen is and dimensions are
Answer:
The rate of change for the given function is 6.
Step-by-step explanation:
Given function is:
The interval on which we have to find the rate of change is:
1≤x≤2
Here
a = 1
b = 2
We have to find the values of function on both points
Putting 1 in place of input (x)
Putting x = 2
The rate of change is calculated by using the following formula
Hence,
The rate of change for the given function is 6.
Answer:
Step-by-step explanation:
Answer:
a. 2
b. 4
c. 13
Step-by-step explanation:
The general term of an arithmetic progression is ...
an = a1+d(n-1)
where a1 is the first term, and d is the common difference.
The sum of n terms is ...
Sn = n(2a1 +d(n -1))/2
__
The given relations tell us ...
S10 = 10(2a1 +9d)/2 = 10a1 +45d = 130
and
a5 = 3a1
a1 +4d = 3a1
4d = 2a1
2d = a1
Using this in the equation for S10 above, we have ...
10(2d) +45d = 130
d = 130/65 = 2
___
(a) The common difference is 2.
d = 2
__
(b) The first term is a1 = 2d = 2(2)
a1 = 4.
__
(c) an = 28 = 4 +2(n -1)
24 = 2(n -1)
12 = n -1
13 = n
The 13th term is 28.
The formula for distance problems is: distance = rate × time or d = r × t
Things to watch out for:
Make sure that you change the units when necessary. For example, if the rate is given in miles per hour and the time is given in minutes then change the units appropriately.
It would be helpful to use a table to organize the information for distance problems. A table helps you to think about one number at a time instead being confused by the question.
The following diagrams give the steps to solve Distance-Rate-Time Problems. Scroll down the page for examples and solutions. We will show you how to solve distance problems by the following examples:
Traveling At Different Rates
Traveling In Different Directions
Given Total Time
Wind and Current Problems.