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Amanda [17]
3 years ago
5

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

given sum. What is the objective function in terms of one​ number, x?
Mathematics
1 answer:
WITCHER [35]3 years ago
4 0

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)

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A 16 inch candle is lit and burns at a constant rate of 1.1 inches per hour. Let t represent the never of hours that have elapse
Alex17521 [72]

Answer:

(a) Number of inches that have burned from the candle since it was lit is (1.1t) inches

(b) The remaining length of the candle is (16 - 1.1t) inches

Step-by-step explanation:

(a). Length of candle before it was lit = 16 inches

Constant rate at which at which candle burns = 1.1 inches per hour

Let t represent the number of hours that have elapsed since the candle was lit

In 1 hour, 1.1 inches of the candle burned

Therefore, in t hours, (1.1t) inches of the candle would have burned since the candle was lit

(b) Remaining length of candle = length of candle before it was lit - length of candle that have burned = 16 inches - 1.1t inches = (16 - 1.1t) inches

6 0
3 years ago
Please someone help me with this word problem for my math class T.T
olga55 [171]

Answer:

<u>Perimeter</u>:

= 58 m (approximate)

= 58.2066 or 58.21 m (exact)

<u>Area:</u>

= 208 m² (approximate)

= 210.0006 or 210 m² (exact)

Step-by-step explanation:

Given the following dimensions of a rectangle:

length (L) = \sqrt{252} meters

width (W) = \sqrt{175} meters

The formula for solving the perimeter of a rectangle is:

P  = 2(L + W) or 2L + 2W

The formula for solving the area of a rectangle is:

A = L × W

<h2>Approximate Forms:</h2>

In order to determine the approximate perimeter, we must determine the perfect square that is close to the given dimensions.  

13² = 169

14² = 196

15² = 225

16² = 256

Among the perfect squares provided, 16² = 256 is close to 252 (inside the given radical for the length), and 13² = 169 (inside the given radical for the width).  We can use these values to approximate the perimeter and the area of the rectangle.

P  = 2(L + W)

P = 2(13 + 16)

P = 58 m (approximate)

A = L × W

A = 13 × 16

A = 208 m² (approximate)

<h2>Exact Forms:</h2>

L = \sqrt{252} meters = 15.8745 meters

W = \sqrt{175} meters = 13.2288 meters

P  = 2(L + W)

P = 2(15.8745 + 13.2288)

P = 2(29.1033)

P = 58.2066 or 58.21 m

A = L × W

A = 15.8745 × 13.2288

A = 210.0006 or 210 m²

8 0
2 years ago
What is the probability that a randomly selected person is on the swim team? Express the probability as a percent rounded to the
frez [133]
<span>What is the probability that a randomly selected person is on the swim team?
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so that's 28/67
</span><span>41.7910448% round to the nearest tenth 
41.8% is the answer. 

Hope this helps, Have a nice day!</span>
5 0
3 years ago
Which order pair is a solution of this equation. 5x+y=-25
crimeas [40]

Answer:

(-5,0) or (0,-25) is another solution

Step-by-step explanation:

Do you have a list of choices? If not, you could choose random choices for x and y to determine if they are solutions. Start by letting y = 0. We see that x = -5, so (-5, 0) is a solution to this equation. In fact, it represents the x-intercept of this line. Now, let x = 0. We now see that y = -25, so (0, -25) is another solution to the equation of this line. This coordinate pair is the y-intercept of the line. Try using other values of x and y to see if you can come up with other solutions to this equation. 

7 0
3 years ago
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Find the area (shaded) and round to the tenths place if necessary.
fomenos

Answer:

9π - 9

Step-by-step explanation:

Depends on what the question stated was pi (π). The area of the circle is 9(3 squared) * π. the shaded area is the area of the circle - the area of the triangle. The area of the triangle is base * high / 2. If the diameter of the circle (6) is what we use as the base, then 3 would be the high, making the area 9. This means the shaded area would be 9π - 9.

6 0
3 years ago
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