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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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<span>f(x) = 2x – 5

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answer

</span><span>D39</span>
8 0
3 years ago
Holly spends 7 3/5 hours in school each day. Her lunch is 1/2 hour long, and she spends 7/10 of a hour switching classes. The re
Ira Lisetskai [31]
<span>
y = 7 + 3/5
y = 35/5 + 3/5
y = 38/5
y = 2*(38/5)
y = 76/10
---
lunch time:
z = 1/2
z = 5*(1/2)
z = 5/10
---
time switching classes:
w = 7/10
---
y - 6x - z - w = 0
6x = y - z - w
x = (y - z - w)/6
x = (76/10 - 5/10 - 7/10)/6
x = (76 - 5 - 7)/(10*6)
x = (64)/(10*6)
x = (2*2*2*2*2*2)/(2*5*2*3)
x = (2*2*2*2)/(5*3)
x = 16/15

x = 1.0666666666
---
check:
y = 7 + 3/5
y = 7.6
z = 1/2
z = 0.5
w = 7/10
w = 0.7
y - 6x - z - w = 0
6x = y - z - w
x = (y - z - w)/6
x = (7.6 - 0.5 - 0.7)/6
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answer:
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Determine if the two lines with the given slope are parallel, perpendicular, or neither. Circle your
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Answer:

As the lines are neither parallel nor perpendicular.

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Hence, option C is correct.

Step-by-step explanation:

Given

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We know that when two lines are parallel, they have equal slopes

But

m₁ ≠ m₂

3/2 ≠ -3/2

As the m₁ and m₂ are not equal.

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We know that when two lines are perpendicular, the product of their slopes is -1.

Let us check the product of two slopes m₁ and m₂

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As the lines are neither parallel nor perpendicular.

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