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aniked [119]
3 years ago
13

The product of two numbers is 192. what is the minimum value of the sum of the first value plus twice the second value

Mathematics
1 answer:
VARVARA [1.3K]3 years ago
4 0
Let x and y be the two positive numbers. -  Their product is 192: x *  y  =  192   equation 1

-  the sum of the first plus twice the second is a minimum:  x + 2y

<span>From the first equation, y =  192 / x. 
Substitute that into the second equation:
</span>
 x + 2y = x + 2(<span>192/x ) = x + 384/x

</span>f(x) is minimum when f'(x) = 0 and f"(x) > 0 

f(x)= <span>x + 384/x
</span>
f(x) = 1-384/x^2 

<span>1-384  / x^2 =  0 

x^2-384 = 0 

x^ 2= 354
 x = radical  354    = 18.8  here i'm confused why the number is decimal
???/ 
</span>

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Read 2 more answers
Find the total area for the regular pyramid.
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Answer:

  • Option B

Step-by-step explanation:

Given is the hexagonal pyramid.

We know the radius of the base is same as its side.

<u>Find the base area:</u>

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  • A = 3√3/2*6² = 54√3

<u>Given the height and radius, find the side of the lateral triangular faces:</u>

  • \sqrt{8^2+6^2} =\sqrt{100} =10

Each of 6 triangles have sides 10, 10 and 6 units.

<u>Find the area using heron's formula:</u>

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<u>Total surface area:</u>

  • S = 6*3\sqrt{91}+54\sqrt{3}  =18\sqrt{91}+54\sqrt{3}

Correct choice is B

3 0
2 years ago
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