Answer:
see below
Step-by-step explanation:
5*72*32 is not a prime factorization to begin with because neither 72, nor 32 are primes. A prime factorization for this product would be:
2*2*2*2*2*2*2*2*3*3*5
and the number with this factorization is 11520.
There is a small chance that what you meant to write was this: 
in which case the number for this prime factorization is 2205.
Answer:
A = 54.8 - (1200/x) - 2x
Step-by-step explanation:
Given <em>x</em> the wide and <em>y</em> the height, we have
x*y = 50
⇒ y = 50/x
The area of the printed region is A = w*h
where
Wide: w = (x-2*1.2) = x-2.4
Height: h= (y-2*1) = y-2
then
A = (x-2.4)(y-2) = xy - 2.4y - 2x + 4.8 = 50 - 24*(50/x) - 2x + 4.8
⇒ A = 54.8 - (1200/x) - 2x
The minimum distance is the perpendicular distance. So establish the distance from the origin to the line using the distance formula.
The distance here is: <span><span>d2</span>=(x−0<span>)^2</span>+(y−0<span>)^2
</span> =<span>x^2</span>+<span>y^2
</span></span>
To minimize this function d^2 subject to the constraint, <span>2x+y−10=0
</span>If we substitute, the y-values the distance function can take will be related to the x-values by the line:<span>y=10−2x
</span>You can substitute this in for y in the distance function and take the derivative:
<span>d=sqrt [<span><span><span>x2</span>+(10−2x<span>)^2]
</span></span></span></span>
d′=1/2 (5x2−40x+100)^(−1/2) (10x−40)<span>
</span>Setting the derivative to zero to find optimal x,
<span><span>d′</span>=0→10x−40=0→x=4
</span>
This will be the x-value on the line such that the distance between the origin and line will be EITHER a maximum or minimum (technically, it should be checked afterward).
For x = 4, the corresponding y-value is found from the equation of the line (since we need the corresponding y-value on the line for this x-value).
Then y = 10 - 2(4) = 2.
So the point, P, is (4,2).
Answer:
Step-by-step explanation:
Split the polygon into 3 triangles as pictured below
<u>They have base and height:</u>
- 4 and 3, 1 and 1, 3 and 1
<u>Find the area of 3 triangles and add up:</u>
- A = 1/2*4*3 + 1/2*1*1 + 1/2*1*3 = 6 + 1/2 + 3/2 = 8 square units
