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3 years ago

A candle burns down at the rate of 0.5 inches per hour. The original height of the candle was 9 inches.

1 answer:

5 0

<span>You can get those ordered pairs subtracting 9-0.5, then that result minus 0.5 because from the rate the candle reduces its height 0.5inches per each hour.Part B: Is this relation a function? Yes, because each value of x has a single result or output in “y” (image)Part C: Yes, only difference is the time, the candle reduces its height 0.45 inches per each hour, examples of ordered pairs: (0,9) (1,8.55) (2,8.1)</span>

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Use Lagrange multipliers to find the maximum and minimum values of the function subject to the given constraint. f(x,y)= e^xy; X

kotykmax [81]

Answer:

f(x,y) = $e^{xy}$ is maximum at x = 2 and y = 2 and f(2,2) = $e^{4}$

Step-by-step explanation:

Since f(x,y) = $e^{xy}$ and x³ + y³ = 16, Ф(x,y) = x³ + y³ - 16

df/dx = y $e^{xy}$ , df/dy = x $e^{xy}$ , dФ/dx = 3x² and dФ/dy = 3y²

From the method of Lagrange multipliers,

df/dx = λdΦ/dx and df/dy = λdΦ/dy

y $e^{xy}$ = 3λx² (1) and x $e^{xy}$ = 3λy² (2)

multiplying (1) by x and (2) by y, we have

xy $e^{xy}$ = 3λx³ (4) and xy $e^{xy}$ = 3λy³ (5)

So, 3λx³ = 3λy³

⇒ x = y

Substituting x = y into the constraint equation, we have

x³ + y³ = 16

x³ + x³ = 16

2x³ = 16

x³ = 16/2

x³ = 8

x = ∛8

x = 2 ⇒ y = 2, since x = y

So, f(x,y) = f(2,2) = $e^{2 X2}$ = $e^{4}$

We need to determine if this is a maximum or minimum point by considering other points that fit into the constraint equation.

Since x³ + y³ = 16 when x = 0, y is maximum when y = 0, x = maximum

So, 0³ + y³ = 16

y³ = 16

y = ∛16

Also, when y = 0, x = maximum

So, x³ + 0³ = 16

x³ = 16

x = ∛16

and f(0,∛16) = $e^{0X\sqrt[3]{16} } = e^{0} = 1$ .

Also, f(∛16, 0) = $e^{\sqrt[3]{16}X0 } = e^{0} = 1$ .

Since f(0,∛16) = f(∛16, 0) = 1 < f(2,2) = $e^{4}$

f(2,2) is a maximum point

8 0

3 years ago

Chef Andy needed to adapt his recipes for his European kitchen staff in Paris. He was 1-pound portions of entrecote, 2 ounces

Ronch [10]

Answer:

1 pound = 0.454 kilograms

1 ounce = 0.0296 liters

1 ounce = 0.0283 kilograms

Step-by-step explanation:

You need to convert the quantities to their corresponding unit.

Convert pounds to kilograms (For the entrecote)

1 pound = 0.454 kilograms

Thus, 1 pound of entrecote = 0.454 kilograms

Ounces to liters (for the Béarnaise, since it is a liquid)

1 ounce = 0.0296 liters

2 ounces of Béarnaise = 0.0592 liters

Ounces to kilograms (for the asparagus)

1 ounce = 0.0283 kilograms

4 ounces of asparagus =0.1132 kilograms

8 0

3 years ago

The value of 3 x 10, when x = 2, can be

forsale [732]

Answer:

ujiuhgufxzfjzkgdlhckgfiyditdoydoydktdktdkydjgx

6 0

3 years ago

Mrs. Steward needs to save (4.2 X 10^6) dollars for her children's college education. If she can save (1.4 X 10^2) each month, h

qwelly [4]

Answer: 30,000 months or 2,500 years

She'd better start saving more haha.

Step-by-step explanation:

$Goal=4.2x10^6\\Savings/month=1.4x10^2$

$\frac{4.2x10^6}{1.4x10^2} =(\frac{4.2}{1.4})x10^(^6^-^2^)=(3)x10^4=3x10^4 =30000 months=\frac{30000}{12}=2500years$

3 0

3 years ago

Help plz 1o pionts all i have

stira [4]

Your answer is C

hope it helps

5 0

3 years ago

Read 2 more answers