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gregori [183]
3 years ago
10

Find positive numbers x and y satisfying the equation xy=12 such that the sum 2x+y is as small as possible.

Mathematics
1 answer:
lbvjy [14]3 years ago
6 0

We are given equations as

xy=12

Firstly, we will solve for y

y=\frac{12}{x}

now, we are given sum as

S=2x+y

now, we can plug back y

S=2x+\frac{12}{x}

Since, we have to minimize it

so, we will find it's derivative

S'=2-\frac{12}{x^2}

now, we can set it to 0

and then we can solve for x

S'=2-\frac{12}{x^2}=0

x=\sqrt{6},\:x=-\sqrt{6}

Since , both numbers are positive

so, we will only consider positive value

x=\sqrt{6}

now, we can find y-value

y=\frac{12}{\sqrt{6}}

y=2\sqrt{6}

So, two positive numbers are

x=\sqrt{6}

y=2\sqrt{6}............Answer

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If ||| m, solve for x and y.
rosijanka [135]

Answer:

x = 11, y = 3

Step-by-step explanation:

(13x - 19) and (9x + 25) are corresponding angles and congruent, thus

13x - 19 = 9x + 25 ( subtract 9x from both sides )

4x - 19 = 25 ( add 19 to both sides )

4x = 44 ( divide both sides by 4 )

x = 11

Then

13x - 19 = 13(11) - 19 = 143 - 19 = 124

(17y + 5) and 124 are alternate angles and are supplementary, thus

17y + 5 + 124 = 180, that is

17y + 129 = 180 ( subtract 129 from both sides )

17y = 51 ( divide both sides by 17 )

y = 3

4 0
3 years ago
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A 12-foot ladder is leaning against a wall. The distance from the base of the wall to the base of the ladder is 6 StartRoot 2 En
Hoochie [10]

Answer:

a

b

d

e

Step-by-step explanation:

he triangle is isosceles.

The leg-to-hypotenuse ratio is 1:StartRoot 2 EndRoot.

The leg-to-hypotenuse ratio is 1:StartFraction StartRoot 2 EndRoot Over 2 EndRoot. The nonright angles are congruent. The ladder represents the longest length in the triangle.

3 0
3 years ago
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What value of B makes the expression. x² + Bx + 81 a perfect square trinomial?
Oxana [17]

Answer:

B.) 18

Step-by-step explanation:

To find the correct b value we use this formula

b² - 4ac = 0

b = What we are solving for

a = 1

c = 81

b² - 4(1)(81) = 0

b² - 324 = 0

b² = 324

b = \sqrt{324}

b = ±18

And 18 is one of the answer choices

So B.) 18 is the correct answer.

4 0
3 years ago
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Using Newton's Law of Cooling. You are a medical examiner called to an abandoned house in which a dead body has been discovered.
Artyom0805 [142]
A) The differential equation comes from the fact that the rate of temperature change is proportional to the difference in temperatures.
\frac{dT}{dt} = \alpha(T -52)

B) Find general solution by separating variables and integrating\int\frac{dT}{T-52} = \alpha \int dt   \\  ln (T-52) = \alpha t + C  \\  T = C e^{\alpha t} +52:


C) Initial condition is t=0, T = 87
87 = C +52 \\  C = 35

D) Total time elapsed is 10 minutes, new temperature is 84
84 = 35 e^{10\alpha} +52
solve for alpha
e^{10\alpha} =\frac{32}{35}  \\  \alpha = \frac{ln(32/35)}{10} \\  \alpha = -.00896

E) Temperature function is:
T = 35 e^{-.00896 t} +52
solving for t
t = \frac{ln (\frac{T-52}{35})}{-.00896}
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This is approximately 32 minutes before he arrived or about 1:20 AM
3 0
3 years ago
Someone please help.
frutty [35]

Answer:

a

Step-by-step explanation:

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