Answer:
0.77 M
Step-by-step explanation:
I'm going to assume this is a half-circle
Formula:
A = (πr^2)/ 2
D = 1.4
r = 0.7
A = (π 0.7^2)/2
A = (0.49π)/2
A = 0.7693
A = 0.77
By the polynomial remainder theorem,
will be a factor of
if the remainder upon division is 0, and this remainder is given by
:
Since
, it follows that
. But notice that if
, then we have
and since
, the equation above requires that either
or
, which is impossible. So
.
So we have 8 cases to check:
(1) Notice that if
, we have
. This is only possible for
.
(2) If
, then
, and so we can have
.
(3) If
, then
, and so
.
(4) If
, then
.
(5) If
, then
.
(6) If
, then
.
(7) If
, then
.
(8) If
, then
.
At the same time, we have 8 cases to consider to find how many options there are for
.
(1)
. We have only one choice of
.
(2)
. This is the same as when
, which we found to be 2 choices.
(3) Same as
; 3 choices.
(4) Same as
; 4 choices.
(5) 5.
(6) 4.
(7) 3.
(8) 2.
In total, there are
ways to choose
such that
is a factor of
, so the answer is B.
Note the symmetry of the sum above. You can easily give a slightly briefer combinatorial argument for this answer, but I figured a more brute-force approach would be easier to follow.
Answer:
y=4/3 x -5/3
Step-by-step explanation:
Please see attached picture for full solution.
The baker make should make 5 trays of corn muffin and 2 trays of bran muffin to maximize his profit
<h3>How to determine how many trays of each type of muffin should the baker make to maximize his profit?</h3>
The given parameters can be represented in the following tabular form:
Corn Muffin (x) Bran Muffin (y) Total
Milk 8 4 48
Wheat flour 5 5 35
Profit 5 3
From the above table, we have the following:
Objective function:
Max P = 5x + 3y
Subject to:
8x + 4y <= 48
5x + 5y <= 35
x, y > 0
Express the constraints as equations
8x + 4y = 48
5x + 5y = 35
Divide 8x + 4y = 48 by 4 and divide 5x + 5y = 35 by 5
So, we have:
2x + y = 12
x + y = 7
Subtract the equations
2x - x + y - y = 12 - 7
Evaluate
x = 5
Substitute x = 5 in x + y = 7
5 + y = 7
This gives
y = 2
So, we have
x= 5 and y = 2
Hence, the baker make should make 5 trays of corn muffin and 2 trays of bran muffin to maximize his profit
Read more about maximizing profits at:
brainly.com/question/13799721
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You would do vide the numbers
Ex: a sloth travels 5 ft every 10 minutes. you would divide the numbers and the answer would be 2ft/min
which would be 2 feet per minute