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Free_Kalibri [48]

3 years ago

9

Find the absolute maximum and absolute minimum for f (x )equals x cubed minus 2 x squared minus 4 x plus 2 on the interval 0 les

s or equal than x less or equal than 3.

1 answer:

sineoko [7]3 years ago

8 0

9514 1404 393

Answer:

maximum: 2
minimum: -6

Step-by-step explanation:

The extrema will be at the ends of the interval or at a critical point within the interval.

The derivative of the function is ...

f'(x) = 3x² -4x -4 = (x -2)(3x +2)

It is zero at x=-2/3 and at x=2. Only the latter critical point is in the interval. Since the leading coefficient of this cubic is positive, the right-most critical point is a local minimum. The coordinates of interest in this interval are ...

f(0) = 2

f(2) = ((2 -2)(2) -4)(2) +2 = -8 +2 = -6

f(3) = ((3 -2)(3) -4)(3) +2 = -3 +2 = -1

The absolute maximum on the interval is f(0) = 2.

The absolute minimum on the interval is f(2) = -6.

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Will someone please help me

Rufina [12.5K]

Answer:

The filled table for each equation by using the exact values in the table is

10x+2y=56

x y

______________________

0 28

$\frac{56}{10}$ 0

________________________

8x+3y=49

x y

_________________________

0 $\frac{49}{3}$

$\frac{49}{8}$ 0

_________________________

Step-by-step explanation:

Given equations are 10x+2y=56 and 8x+3y=49

To fill the table for each equation by using the exact values in the table :

10x+2y=56

put x=0 in above equation we get

10(0)+2y=56

2y=56

$y=\frac{56}{2}$

$y=28$

Therefore (0,28)

put y=0 in the given equation 10x+2y=56 we get

10x+2(0)=56

10x=56

$x=\frac{56}{10}$

Therefore ( $\frac{56}{10}$ ,0)

10x+2y=56

x y

_________________________

0 28

$\frac{56}{10}$ 0

__________________________

For

8x+3y=49

put x=0 in above equation we get

8(0)+3y=49

3y=49

$y=\frac{49}{3}$

Therefore (0, $\frac{49}{3}$ )

put y=0 in the given equation 8x+3y=49 we get

8x+3(0)=49

8x=49

$x=\frac{49}{8}$

Therefore ( $\frac{49}{8}$ ,0)

8x+3y=49

x y

_________________________

0 $\frac{49}{3}$

$\frac{49}{8}$ 0

________________________

7 0

4 years ago

the numbers 1,2,3,4, and 5 are written on slips of paper, and 2 slips are drawn at random one at a time without replacet. find t

Tresset [83]

Consider such events:

A - slip with number 3 is chosen;

B - the sum of numbers is 4.

You have to count $Pr(A|B).$

Use formula for conditional probability:

$Pr(A|B)=\dfrac{Pr(A\cap B)}{Pr(B)}.$

1. The event $A\cap B$ consists in selecting two slips, first is 3 and second should be 1, because the sum is 4. The number of favorable outcomes is exactly 1 and the number of all possible outcomes is 5·4=20 (you have 5 ways to select 1st slip and 4 ways to select 2nd slip). Then the probability of event $A\cap B$ is

$Pr(A\cap B)=\dfrac{1}{20}.$

2. The event $B$ consists in selecting two slips with the sum 4. The number of favorable outcomes is exactly 2 (1st slip 3 and 2nd slip 1 or 1st slip 1 and 2nd slip 3) and the number of all possible outcomes is 5·4=20 (you have 5 ways to select 1st slip and 4 ways to select 2nd slip). Then the probability of event $B$ is

$Pr(B)=\dfrac{2}{20}=\dfrac{1}{10}.$

3. Then

$Pr(A|B)=\dfrac{\frac{1}{20} }{\frac{1}{10} }=\dfrac{1}{2}.$

Answer: $\dfrac{1}{2}.$

5 0

3 years ago

Find a value for k such that the following trinomial can be factored x^2-8x+k

mr_godi [17]

Answer:

16

Step-by-step explanation:

x^2-8x+k is a quadratic expression of the form ax^2 + bx + c. Here a = 1, b = -8 and c = k. Focus on x^2-8x and complete the square as follows: Take half of the coefficient of x (that is, take half of -8) and square the result:

(-4)^2 = 16; if we now write x^2-8x+ 16, we'll have the square of (x - 4): (x -4)^2.

Thus, k = 16 turns x^2-8x+k into a perfect square.

6 0

4 years ago

Calculate the missing angles and give a reason for your answer

Anon25 [30]

Answer:

a = 72°

Step-by-step explanation:

Alternate angles are angles that occur on opposite sides of the transversal line and have the same size. Alternate angles are equal: We can often spot interior alternate angles by drawing a Z shape. There are two different types of alternate angles, alternate interior angles, and alternate exterior angles.

In this situation a and 72 are alternate interior angles

5 0

3 years ago

A company's profits can be modeled by a quadratic function. In the past, it broke even (made zero profit) when it fulfilled 240

Alex73 [517]

Answer:

$f(x)=-2(x-560)^2+204,800$

or

$f(x)=-2x^2+2,240x-422,400$

Step-by-step explanation:

Let

f(x) ----> the profit earned

x ---> is the number of orders fulfilled

we know that

The equation of a quadratic equation in vertex form is equal to

$f(x)=a(x-h)^2+k$

where

a is the leading coefficient of the quadratic equation

(h,k) is the vertex

Remember that

The x-intercepts or roots are the values of x when the value of the function is equal to zero

In this problem

The x-intercepts are

x=240 and x=880

The x-coordinate of the vertex (h) is the midpoint of the roots

so

$h=(240+880)/2=560$

The y-coordinate of the vertex (k) is the maximum profit earned

$k=204,800$ ----> is given

so

The vertex is the point (560,204,800)

substitute in the quadratic equation

$f(x)=a(x-560)^2+204,800$

Find the value of a

we have the ordered pairs (240,0) and (880,0) (the x-intercepts)

take the point (240,0) and substitute the value of x and the value of y in the quadratic equation

$0=a(240-560)^2+204,800$

solve for a

$0=a(102,400)+204,800\\a=-2$

therefore

The function that models the profits of the company is given by

$f(x)=-2(x-560)^2+204,800$ ----> equation in vertex form

Convert to standard form

$f(x)=-2(x^2-1,120x+313,600)+204,800$

$f(x)=-2x^2+2,240x-627,200+204,800$

$f(x)=-2x^2+2,240x-422,400$

6 0

3 years ago