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masya89 [10]
3 years ago
11

The sum of two positive numbers is 12. what two numbers will maximize the product g

Mathematics
1 answer:
son4ous [18]3 years ago
4 0

Given two numbers x and y such that:

x + y = 12   ...    (1)


<span>two numbers will maximize the product g</span>

from  equation (1) 

y = 12 - x  

Using this value of y, we represent xy as

xy = f(x)= x(12 - x)

 f(x) = 12x - x^2

Differentiating the above function:

f'(x) = 12 - 2x

Maximum value of f(x) occurs at point for which f'(x) = 0.

Equating f'(x) to 0 we get:

12 - 2x = 0

 2x =  12

> x = 12/2 = 6

Substituting this value of x in equation (2):

y = 12 - 6 = 6

Therefore, value of xy is maximum when:

x = 6 and y = 6

The maximum value of xy = 6*6 = 36

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Answer:

X=45

Step-by-step explanation:

45+3x=180

180-45=135

135/3=45

x has to be 45

x=45

4 0
3 years ago
Please help me thank you
S_A_V [24]
Question 1:

We have a 45-45-90 right triangle with the hypotenuse being the length from one corner to the opposite corner.

Multiply 30 ft with the square root of 2 and use a calculator to help give you numerical value to get your answer.

30 \sqrt{2} \approx 42

Your answer is the second choice.

Question 2:

The equilateral triangle can be divided into 2 30-60-90 triangles with the longer leg being the altitude. To get half of the side length of the right triangle, divide the altitude by the square root of 3.

\dfrac{15}{ \sqrt{3} }=\dfrac{15 \sqrt{3} }{3}=5 \sqrt{3}

The full side length is double of that, which is 10 \sqrt {3}.

Multiply that by 3 to get the full perimeter.
10 \sqrt{3}*3=30 \sqrt{3}

Your answer is the third choice. Hope this helps! :)
5 0
4 years ago
Read 2 more answers
Step by step, to find solution to -4(6n-4)+3n=
Dimas [21]

Answer:

-21n + 16

Step-by-step explanation:

Start with distributive property

-24n + 16 + 3n

Combine like terms

-21n + 16

There is a part of the equation missing so I can't solve completely

7 0
3 years ago
Read 2 more answers
A. The length of a rectangle is 3 meters less than twice its width.
Dmitriy789 [7]

Answer:

A: (x = length y = width) x = 2y-3

B: The width equals 7

Step-by-step explanation:

B explanation: using the formula from and the information from B x = 11, 11 = 2y - 3 we add 3 to both sides 14 = 2y and divide by two, 7 = y

8 0
3 years ago
Urgent please help..
zvonat [6]

Answer:

x = 12

Step-by-step explanation:

Here, we want to find the value of x

To do this, we use one of the circle tangent relationships

we have this as:

8^2= 4(4 +x)

8^2 = 16 + 4x

64 = 16 + 4x

64-16 = 4x

4x = 48

x = 48/4

x = 12

8 0
3 years ago
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