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3 years ago

Re-arrange this polynomial so its terms

Mathematics

1 answer:

Lera25 [3.4K]3 years ago

6 0

Answer:

It should be 2x3 - 7x2 +5x - 15

Step-by-step explanation:

You have to look at the variable with the greatest exponential value

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A piece of wire of length 5050 is cut, and the resulting two pieces are formed to make a circle and a square. Where should the

algol [13]

Answer:

x should be cut at 2221.5 to minimize the total combined area, and at 5050 to maximize it.

Step-by-step explanation:

Let x be the length of wire that is cut to form a circle within the 5050 wire, so 5050 - x would be the length to form a square.

A circle with perimeter of x would have a radius of x/(2π), and its area would be

$A_c = \pir^2 = \pi (\frac{x}{2pi})^2 = \frac{x^2}{4\pi}$

A square with perimeter of 5050 - x would have side length of (5050 - x)/4, and its area would be

$A_s = (\frac{5050 - x}{4})^2 = \frac{(5050 - x)^2}{16}$

The total combined area of the square and circles is

$\sum A = A_c + A_s = \frac{x^2}{4\pi} + \frac{(5050 - x)^2}{16}$

To find the maximum and minimum of this, we just take the 1st derivative, and set it to 0

$A' = \frac{2x}{4\pi} + \frac{-2(5050-x)}{16} = 0$

$\frac{x}{2\pi} - \frac{5050 - x}{8} = 0$

Multiple both sides by 8π and we have

$4x - 5050\pi + x\pi = 0$

$x(4 + \pi) = 5050\pi$

$x = \frac{5050\pi}{4 + \pi} = 2221.5$

At x = 2221.5:

$A = \frac{x^2}{4\pi} + \frac{(5050 - x)^2}{16}$ = 392720 + 500026 = 892746 [/tex]

At x = 0, $A = 5050^2/16 = 1593906$

At x = 5050, $A = \frac{5050^2}{4\pi} = 2029424$

As 892746 < 1593906 < 2029424, x should be cut at 2221.5 to minimize the total combined area, and at 5050 to maximize it.

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3 years ago

Solutions of inequalities

QveST [7]

Answer: Inverse operations

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2 years ago

What is the probability that the employee is less than 175 cm tall- chosen from those with brown hair

xxTIMURxx [149]

20% chance llllllllll

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3 years ago

Sierra used 4 pears and 12 apples to make a fruit salad. What is the

jolli1 [7]

Answer: 1:3

Step-by-step explanation: for every pear she uses 3 apples

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3 years ago

To find the height of a pole, a surveyor moves 120 feet away from the base of the pole and then, with a transit 8 feet tall, mea

Vikki [24]

Refer to the figure.
Let AB be the height of the pole; CD be the height of the transit; BC is the distance from the base of the pole to the transit.

Triangle ADE is a right triangle with angle D measuring 26 degrees. Using the tangent function, we have
$tan\:26^{\circ} =\frac{AE}{120}$
So,
$AE=120\:tan\:26^{\circ}$
$AE=58.53\:$

Therefore, the overall height of the pole is
$AB=58.53+8=66.53\:feet$

The height of the pole is 66.53 feet.

6 0

3 years ago