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
1.
1.
1.Let's solve for x.<span>y=<span><span>2x</span>−2</span></span>Step 1: Flip the equation.<span><span><span>2x</span>−2</span>=y</span>Step 2: Add 2 to both sides.<span><span><span><span>2x</span>−2</span>+2</span>=<span>y+2</span></span><span><span>2x</span>=<span>y+2</span></span>Step 3: Divide both sides by 2.<span><span><span>2x</span>2</span>=<span><span>y+2</span>2</span></span><span>x=<span><span><span>12</span>y</span>+1
</span></span>Answer:<span>x=<span><span><span>12</span>y</span>+<span>1</span></span></span>
There, I hope this helps... If you have any questions please feel free to ask me!!
Answer:
Step-by-step explanation:
The area of a circle is :A= π r² r : the radius
A= 8π square units
so : π r² = 8π
r² = 8
r = √8 = √(4 × 2) =√4×√2
r = 2√2 units