Find two positive numbers such that the sum of the first and twice the second is 56 and whose product is a maximum
1 answer:
Let
x-------> the first number
y-------> the second number
P-----> product
we know that
x+2y=56----------> 2y=56-x-----> y=28-0.5x------> equation 1
P=x*y----> equation 2
substitute equation 1 in equation 2
P=x*[28-0.5x]-----> P=28x-0.5x²
using a graph tool
see the attached figure
the vertex is the point (28,392)
that means
for x=28
the product is 392 (maximum)
find the value of y
y=28-0.5x----> y=28-0.5*28----> y=14
the answer is
the numbers are 28 and 14
x-------> the first number
y-------> the second number
P-----> product
we know that
x+2y=56----------> 2y=56-x-----> y=28-0.5x------> equation 1
P=x*y----> equation 2
substitute equation 1 in equation 2
P=x*[28-0.5x]-----> P=28x-0.5x²
using a graph tool
see the attached figure
the vertex is the point (28,392)
that means
for x=28
the product is 392 (maximum)
find the value of y
y=28-0.5x----> y=28-0.5*28----> y=14
the answer is
the numbers are 28 and 14
You might be interested in
<h2>Greetings</h2>
<h2>Hope this helps!</h2>
Answer:
The other base is 8 feet.
Step-by-step explanation:
You need to recall the area of a trapezoid equation:
We need to work back, so we need to divide the area by 6:
60 ÷ 6 = = 10
Then we need to multiply this by two to find a + b value:
10 x 2 = a + b
20 = a + b
Beause we know the value of a, which is 12, we can factor this in:
20 = 12 + b
Move the +12 over to the other side, making it a negative:
20 - 12 = b
8 = b
<h3>So the other base is 8 feet!</h3><h2>Hope this helps!</h2>