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3 years ago

What is the maximum number of relative extrema a polynomial function can have?

1 answer:

4 0

Relative extrema occur where the derivative is zero (at least for your polynomial function). So taking the derivative we get

20x3−3x2+6=0

 This is a 3rd degree equation, now if we are working with complex numbers this equation is guaranteed to have 3 solutions by the fundamental theorem of algebra. But the number of real roots are 1 which can be found out by using Descartes' rule of signs. So the maximum number of relative extrema are 1.

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One of the same-side exterior angles formed by two lines and a transversal is equal to 1/6 of the right angle and is 11 times sm

sergey [27]

One of the same-side exterior angles formed by two lines and a transversal is equal to 1/6 of the right angle and is 11 times smaller than the other angle. Then the lines are parallel

<h3>Solution:</h3>

Given that, One of the same-side exterior angles formed by two lines and a transversal is equal to 1/6 of the right angle and is 11 times smaller than the other angle.

We have to prove that the lines are parallel.

If they are parallel, sum of the described angles should be equal to 180 as they are same side exterior angles.

Now, the 1st angle will be 1/6 of right angle is given as:

$\begin{array}{l}{\rightarrow 1^{\text {st }} \text { angle }=\frac{1}{6} \times 90} \\\\ {\rightarrow 1^{\text {st }} \text { angle }=15 \text { degrees }}\end{array}$

And now, 15 degrees is 11 times smaller than the other

Then other angle = 11 times of 15 degrees

$\text {Other angle }=11 \times 15=165 \text { degrees }$

Now, sum of angles = 15 + 165 = 180 degrees.

As we expected their sum is 180 degrees. So the lines are parallel.

Hence, the given lines are parallel

5 0

3 years ago

How many hours he worked

Bogdan [553]

8.50x+100=308.25
subtract 100 from both sides
8.5x = 208.25
divide 8.5 from both sides
x= 24.5 hours worked

4 0

3 years ago

PLEASE HELP Which line has an x-intercept of -5 and a y-intercept of 3?

anygoal [31]

Answer:

the first answer or a

Step-by-step explanation:

just believe meeeee

5 0

3 years ago

A farmer has 90 feet of fence with which to make a corral. If he arranges it into a rectangle that is twice as long as it is wid

Leya [2.2K]

Answer:

W = 15 ft. and L = 30 ft.

Step-by-step explanation:

Perimeter = 90 ft.

Twice as long as it is wide: L=2W

P = 2(L + W) = 2(2W + W) = 6W

90 = 6W

W = 15 ft. and L = 30 ft.

6 0

3 years ago

Read 2 more answers

I will mark you as brainlis if you andwer this all.

dimaraw [331]

Answer: See below

Step-by-step explanation:

27. -(a-3)

28. (b-1)(b+3)

29. (c+4)(c+5)

30. d(d+5)

31. -(3/4)(2e-5)

Sorry - I don't have time to enter the details. Look for areas where the expressions can be factored in a manner that forms as many equivalent expressions in both the numerator and denominator.

For example: In problem 30:

(5d-20)/(d^2+d-20) * [??]/20d = 1/4

Factor:

(5(d-4)) d(d+5) = 1/4

(d-4)(d+5) 20d

The (d-4), d+5, and d terms cancel, leaving

5/20 = 1/4

7 0

2 years ago