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Wittaler [7]
2 years ago
14

If the graph of the second equation in the system passes through the points (-12, 20) and

Mathematics
1 answer:
Rasek [7]2 years ago
8 0

answer: the system had no solution

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Find positive numbers x and y satisfying the equation xyequals12 such that the sum 4xplusy is as small as possible. Let S be the
WITCHER [35]

Answer:

The objective function in terms of one​ number, x is

S(x) = 4x + (12/x)

The values of x and y that minimum the sum are √3 and 4√3 respectively.

Step-by-step explanation:

Two positive numbers, x and y

x × y = 12

xy = 12

S(x,y) = 4x + y

We plan to minimize the sum subject to the constraint (xy = 12)

We can make y the subject of formula in the constraint equation

y = (12/x)

Substituting into the objective function,

S(x,y) = 4x + y

S(x) = 4x + (12/x)

We can then find the minimum.

At minimum point, (dS/dx) = 0 and (d²S/dx²) > 0

(dS/dx) = 4 - (12/x²) = 0

4 - (12/x²) = 0

(12/x²) = 4

4x² = 12

x = √3

y = 12/√3 = 4√3

To just check if this point is truly a minimum

(d²S/dx²) = (24/x³) = (8/√3) > 0 (minimum point)

4 0
3 years ago
The fuel tank of a certain airplane can hold up to 300 gallons of fuel. Let W be the total weight of the airplane (in pounds). L
velikii [3]

Answer:

35

Step-by-step explanation:

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7 0
3 years ago
Anyone know what 422,391÷28=<br>​
saul85 [17]
15085.3929
Explanation
Use a calculator
5 0
2 years ago
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Suppose that the fixed costs for your clothing store are b = $10,000. Materials required to make each pair of jeans cost $24. Wh
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The FitnessGram Pacer Test is a multistage aerobic capacity test that progressively gets more difficult as it continues. The 20 meter pacer test will begin in 30 seconds. Line up at the start. The running speed starts slowly, but gets faster each minute after you hear this signal. [beep] A single lap should be completed each time you hear this sound. [ding] Remember to run in a straight line and run as long possible. The second time you fail to complete a lap before the sound. Your test will begin on the word start. On your mark, get ready, start<span>
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3 years ago
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If sinA+cosecA=3 find the value of sin2A+cosec2A​
Irina18 [472]

Answer:

\sin 2A + \csc 2A = 2.122

Step-by-step explanation:

Let f(A) = \sin A + \csc A, we proceed to transform the expression into an equivalent form of sines and cosines by means of the following trigonometrical identity:

\csc A = \frac{1}{\sin A} (1)

\sin^{2}A +\cos^{2}A = 1 (2)

Now we perform the operations: f(A) = 3

\sin A + \csc A = 3

\sin A + \frac{1}{\sin A} = 3

\sin ^{2}A + 1 = 3\cdot \sin A

\sin^{2}A -3\cdot \sin A +1 = 0 (3)

By the quadratic formula, we find the following solutions:

\sin A_{1} \approx 2.618 and \sin A_{2} \approx 0.382

Since sine is a bounded function between -1 and 1, the only solution that is mathematically reasonable is:

\sin A \approx 0.382

By means of inverse trigonometrical function, we get the value associate of the function in sexagesimal degrees:

A \approx 22.457^{\circ}

Then, the values of the cosine associated with that angle is:

\cos A \approx 0.924

Now, we have that f(A) = \sin 2A +\csc2A, we proceed to transform the expression into an equivalent form with sines and cosines. The following trignometrical identities are used:

\sin 2A = 2\cdot \sin A\cdot \cos A (4)

\csc 2A = \frac{1}{\sin 2A} (5)

f(A) = \sin 2A + \csc 2A

f(A) = \sin 2A +  \frac{1}{\sin 2A}

f(A) = \frac{\sin^{2} 2A+1}{\sin 2A}

f(A) = \frac{4\cdot \sin^{2}A\cdot \cos^{2}A+1}{2\cdot \sin A \cdot \cos A}

If we know that \sin A \approx 0.382 and \cos A \approx 0.924, then the value of the function is:

f(A) = \frac{4\cdot (0.382)^{2}\cdot (0.924)^{2}+1}{2\cdot (0.382)\cdot (0.924)}

f(A) = 2.122

8 0
3 years ago
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