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
You should double the sugar as well, but first let us simplify the 2 2/3 to become 8/3, then double that to have 16/3,
Which is then can be simplified to 5 1/3
Answer:
The given sides does not form a triangle
Step-by-step explanation:
The given sides does not form a triangle
We know the triangle property which states that the sum of any two sides of the triangle should be greater than the third side.
Here given th esides of the triangle are 6x,7x,21x
6x+7x=13x < 21x
for any value of x the above equation does not satisfy.
Answer:
12(3√6)
Step-by-step explanation:
6(3√12)(3√2)
= 6(3√4√3)(3√2)
= 12(3√3)(3√2)
= 12(3√6)
Step-by-step explanation:
The distance formula between two points:
Substitute the coordinates of the points.
If a ≤ b < c are the sides of the right triangle, then
a² + b² = c²
used 
for a ≥ 0.
therefore ΔABC is a right triangle.
