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3 years ago

Given this equation, what is the largest possible value for z?

Mathematics

1 answer:

Gre4nikov [31]3 years ago

7 0

Hello,
z=-2x²+15x-3y²+21y-6
=-2(x²-2*15/2*x+(15/2)²) -3(y²-2*7/2y+(7/2)²)-6+2*225/4+3*49/4
=-2(x-15/2)²-3(y-7/2)²+573/4

The max is for x-15/2=0 and y-7/2=0 thus 537/4

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By counting the combinations, we will see that there are 10 combinations such that the sum gives a Fibonacci number.

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2 years ago

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Hello Austint1414

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2 years ago

A tank can be filled by one pump in 3.2 hours and by another pump in 80 minutes. A third pump can drain the tank in 2 hours and

Mademuasel [1]

Answer:

Rounding to the nearest minute, it would take 95 minutes, or 1 hour and 35 minutes.

Step-by-step explanation:

Let's convert each time to minutes:

3.2 hours = 192 minutes

80 minutes = 80 minutes

2 hr 20 min = 140 minutes

Next, let's find the least common multiple:

LCM(192, 80, 140) = 6720

So let's say the volume of the tank is 6720 units. The speed of each pump is therefore:

Pump 1 = 6720 units / 192 minutes = 35 units/minute

Pump 2 = 6720 units / 80 minutes = 84 units/minute

Pump 3 = -6720 units / 140 minutes = -48 units/minute

Their combined speed is:

35 + 84 − 48 = 71 units/minute

So the time to fill the tank is:

6720 units / (71 units/minute) = 94.65 minutes

Rounding to the nearest minute, it would take 95 minutes, or 1 hour and 35 minutes.

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3 years ago

An envelope from the post office is 3 inches wide with a total area of 30 square inches.what is the height of the envelope

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3 years ago

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2 years ago