Answer:
<h3>36 and 12</h3>
Step-by-step explanation:
Let the two positive integers be x and y.
If their product is 432, then
xy = 432 ......... 1
Also if the sum of the first plus three times the second is a minimum, then;
p(x) = x + 3y
From 1;
y = 432/x ..... 3
Substitute 3 into 2;
p(x) = x+3y
p(x)= x + 3(432/x)
p(x) = x + 1296/x
Since the expression is at minimum when dp(x)/dx = 0
dp/dx = 1 + (-1296)/x²
dp/dx = 1 -1296/x²
0 = 1 -1296/x²
0 = (x²-1296)/x²
cross multiply
0 = x²-1296
x² = 1296
x = √1296
x = 36
Since xy = 432
36y = 432
y = 432/36
y = 12
Hence the two positive numbers are 36 and 12
There are two servings size 4/3 cup in 8/3 cups of cereal

Answer: 2
ANSWER

EXPLANATION
The given function is,

This function has a period of

just as the parent function

A sample period of this parent function is
![[ 0 , 2\pi]](https://tex.z-dn.net/?f=%5B%200%20%2C%202%5Cpi%5D)
Which begins at zero.
For the transformed function,

There has been a horizontal shift of

to the left.
The transformed function will have a sample period,
![[ - \frac{\pi}{4} , \frac{7\pi}{4} ]](https://tex.z-dn.net/?f=%5B%20-%20%5Cfrac%7B%5Cpi%7D%7B4%7D%20%2C%20%5Cfrac%7B7%5Cpi%7D%7B4%7D%20%5D)
Therefore a sample period begins at
Answer:8
Step-by-step explanation:
The laundry one is C
The ladder one is B.