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Over [174]
3 years ago
8

Given the function g(x) = x^3 − (8+1)x^2-4(9+2)x+(5x2-1) determine where the function is quickly(slowly) increasing (decreasing)

Mathematics
1 answer:
Elenna [48]3 years ago
3 0

Answer:

hence g(x) is increasing at point x= 3+14i,3-14i

Step-by-step explanation:

given, g(x)=x^3-(8+1)x^2-4(9+2)x+5x2-1

         g(x)=x^3-9x^2-44x+10x-1

         g(x)=x^3-9x^2-34x-1

   \frac{\partial g(x)}{\partial x}=3x^2-18x-34

for increasing and decreasing function,

3x^2-18x-34=0

x=3+14i \geq0

x=3-14i \geq0

hence g(x) is increasing at point x= 3+14i,3-14i answer

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I need to know the answer
MissTica

If Sachiko lets x represent the length of the side of the square and she wants to find the length of the perimeter of the square, it is appropriate for her to ...

... B. Set the area equal to x², solve for x, and then multiply the value of x by 4.

_____

The area of a square of side length x is x·x = x². The perimeter of a square of side length x is x+x+x+x = 4·x.

3 0
3 years ago
Determine whether the relationship between the circumfrance of a circle and its diameter is a direct variation. If so, identify
kipiarov [429]

Answer:

The relationship between the circumference of a circle and its diameter represent  a direct variation and the constant of proportionality is equal to the constant \pi

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form y=kx

where K is the constant of proportionality

In this problem we know that

The circumference of a circle is equal to

C=\pi D

therefore

the relationship between the circumference of a circle and its diameter is a direct variation and the constant of proportionality is equal to the constant \pi

3 0
3 years ago
PLZ HELP, AND PLZ EXPLAIN
shutvik [7]

Answer:

C

Step-by-step explanation:

To make it easy let's start by organizing our information :

  • AC=12 AND BD=8
  • ABCD is a rhombus
  • K and L are the midpoints of sides AD and CD
  • we notice that the rhombus ABCD is divided into four right triangles

What do you think of when you hear a right triangle ?

  • The pythagorian theorem !

AC and BD  are khown so let's focus on them .

If we concentrated we can notice that AB and BD are cossing each other in the midpoints . why ?

Simply because they are the diagonals of a rhombus .

ow let's apply the pythagorian theorem :

  • (AC/2)² + (BD/2)² = BC²
  • 6²+4²=52
  • BC²= 52⇒\sqrt{52}=BC

Now we khow that : AB=BC=CD=AD=\sqrt{52}

This isn't enough . Let's try to figure out a way to calculate the length of KL  wich is the base of the triangle

  • KL is parallel to AC
  • k is the midpoint of AD and L of DC

I smell something . yes! Thales theorem

  • KL/AC=DL/DC=DK/AD WE4LL TAKE OLY ONE
  • KL/12=\sqrt{52}/2*\sqrt{52}  
  • KL/12=1/2⇒ KL=6

Now we have the length of the base kl

Now the big boss the height :

  • notice that you khow the length of KL
  • BD crosses kl from its midpoint and DL = \sqrt{52} /2

What I want to do is to apply the pythgorian thaorem to khow the lenght of that small part that is not a part of the height of the triangle . I will call it D

  • DL²=(KL/2)²+D²
  • 52/4= 9+ D²
  • D² = 52/4-9 +4 SO D=2

now the height of the trigle is H= BD-D= 8-2=6

NOw the area of the triangle is :

  • A=(KL*H)/2 ⇒ A= (6*6)/2=18

THE ANSWER IS 18 SQ.UN

5 0
3 years ago
What is the letter v​
Nimfa-mama [501]

Answer:

Step-by-step explanation:

-81=-5(v+5)-2v                         Original equation

-81=-5v-25-2v                          Distributive property

-81=-7v-25                                Subtract like terms

-56=-7v                                     Simplify

8=v                                           Simplify

4 0
3 years ago
West high schools population is 250 students fewer then twice the population of East High school the two schools have a total of
gizmo_the_mogwai [7]

Answer:

1036 students

Step-by-step explanation:

Let the number of students at West High be "w" and the number of students at East High be "e"

West High population is 250 FEWER than TWICE of East High, we can write:

w = 2e - 250

Total students in both schools is 2858, so we can write 2nd equation as:

e + w = 2858

We can replace 1st equation in 2nd to get an equation in e, and find "e":

e + w = 2858

e + (2e - 250) = 2858

3e - 250 = 2858

3e = 2858 + 250

3e = 3108

e = 3108/3

e = 1036

Hence,

number of students attending East High School = 1036 students

3 0
3 years ago
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