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Andrew [12]
3 years ago
8

Given the function

alt="g(x)=m(-2x+2)^5-n" align="absmiddle" class="latex-formula"> where m ≠ 0 and n ≠ 0 are constants.
A. Prove that g is monotonic (this means that either g always increases or g always decreases)

B. Show that the x-coordinate(s) of the location(s) of any critical points are independent of m and n
Mathematics
1 answer:
Alekssandra [29.7K]3 years ago
4 0

Answer:

<h2>See the explanation.</h2>

Step-by-step explanation:

The given function g(x) is a continuous function, since, for any x we can find a real value of the function.

A. \frac{d g(x)}{dx} = 5m(-2x + 2)^{4} \times (-2).

Since, m is a constant, which is not equals to 0, the above value of the differentiation of the function, will be negative.

For x = 1, the above value is 0, that is at x =  1, the function has either maximum value, or a minimum value.

B. As per the above information, we have get that for x = 1, \frac{d g(x)}{dx} = 0.

Hence, the function's critical point's x coordinate is x = 1.

The x- coordinate of the given point is not dependent on m or n.

Hence, proved.

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Answer:

y = 36

Step-by-step explanation:

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5 0
3 years ago
Please answer and show steps please show steps please show steps 10 points
natali 33 [55]

Answer:

it is C 10

Step-by-step explanation:

 If the positions are distinct, as in executive offices, then P(9, 5). 

P(9, 5) = 9!/(9 - 5)! = 15120 

If the positions are equivalent, such as seats in a legislative body, then C(9, 5). 

C(9, 5) = 9!/[(9 - 5)!(5!)] = 126

Assuming the five positions are unique in their duties and responsibilities (i.e. order matters): position 1 has 9 candidates to choose from, position 2 has 8, position 3 has 7, and so on. Otherwise, if you're talking about 5 distinct but duplicate positions - meaning their responsibilities are the same but 5 people are required to carry them out - you need to divide the previous total number of possibilities by the number of ways those possibilities could have been reordered.

8 0
3 years ago
Use synthetic division to divide x^3+5x^2−9x−7 by x−2 1 5 -9 -7 The quotient is: _____ The remainder is: ______
RoseWind [281]

Answer:

 The quotient is x² + 6x +3

       Remainder  = -1      

 Step-by-step explanation:

<u><em>Explanation:-</em></u>

Given Polynomial equation

   f(x) = x³+5x²−9x−7

By using synthetic division

 

 <em> x = 2  </em>         1       5       -9      -7

   <u>                   0       1       12     6</u>

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I need help on this:
marishachu [46]

The given number sentence is simplified as 1 3/5

<u>Step-by-step explanation:</u>

The given number sentence is 2-4/5 x 1/2

  • In order to solve this, the operations must be performed based on the BODMAS rule.
  • This means that, the operations should be performed in the order of Bracket, Of, Division, Multiplication, Addition and Subtraction.

Here, based on that above rule, the multiplication must be done in the first step and then subtraction should be done in the next step.

⇒ 2 - 4/5 × 1/2

⇒ 2 - 4/10

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Therefore, the given expression is reduced to 2- 2/5

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⇒ (10-2) / 5

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To further reduce the term, divide 8 by 5.

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The answer is written in the form of Quotient(Remainder/ divisor)

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3 years ago
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8 0
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