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Evgen [1.6K]
2 years ago
7

Find two positive numbers whose product is 64 and whose sum is a minimum. (If both values are the same number, enter it into bot

h blanks.) slader
Mathematics
1 answer:
DedPeter [7]2 years ago
3 0

Answer:

X = 8, y = 8

Step-by-step explanation:

This question is an optimization problem. Two equations are going to be needed here

n = x+y

P = xy

Such that 64 = xy

When we divide through by x we get:

y = 64/x

So that n becomes:

n = x + 64/x

n = x+64x^-1

We take derivative

n' = 1-64x^-2

When n' = 0 then a min|max occurs

0 = 1-64x^-2

Such that:

64/x² = 1

Divide through by x²

64 = x²

x = √64

x = 8

Remember y = 64/x

So,

Y = 64/8

Y = 8.

X = 8, y = 8

Thank you!

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zimovet [89]
The area is 36 units squared.

You have three ways you can solve this question.

Method 1:

Split the rhombus into two equal triangles.
You will get triangle ACD and triangle ACB.

Count the base length and height length of each triangle using the diagram.
You will get base = 6 units and height = 6 units. Plug this into the area of a triangle and then multiply it by 2.

A = bh/2 * 2
A = 6(6) / 2 * 2
A = 36 / 2 * 2
A = 18 * 2
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Method 2:

Calculate the length of DP.
The length of line segment DP is √28.8

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Put into equation A = bh.

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A = 36

Method 3:

Calculate the length of each diagonal and put into formula A = 1/2(d1 * d2)

Diagonal DB = 12 units
Diagonal AC = 6 units

A = 1/2(d1 * d2)
A = 1/2(12 * 6)
A = 1/2(72)
A = 36

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6 0
3 years ago
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Answer:

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Step-by-step explanation:

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nasty-shy [4]

Answer:

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Step-by-step explanation:

Let's solve your inequality step-by-step.

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Step 2: Add 9 to both sides.

0.6x−9+9<6+9

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Step 3: Divide both sides by 0.6

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3 years ago
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RideAnS [48]

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Step-by-step explanation:

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pav-90 [236]

Answer:

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Step-by-step explanation:

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