Hellpppppppppppppp ASAP

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Find the absolute maximum and absolute minimum values of f on the given interval.

[tex]f(x)=xe^{-\frac{x^{2}}{32} }[/tex] , [ -2,8]

Answer: Absolute maximum: f(4) = 2.42;

              Absolute minimum: f(-2) = -1.76;

Step-by-step explanation: Some functions have absolute extrema: maxima and/or minima.

Absolute maximum is a point where the function has its greatest possible value.

Absolute minimum is a point where the function has its least possible value.

The method for finding absolute extrema points is

1) Derivate the function;

2) Find the values of x that makes f'(x) = 0;

3) Using the interval boundary values and the x found above, determine the function value of each of those points;

4) The highest value is maximum, while the lowest value is minimum;

For the function given, absolute maximum and minimum points are:

[tex]f(x)=xe^{-\frac{x^{2}}{32} }[/tex]

Using the product rule, first derivative will be:

[tex]f'(x)=e^{-\frac{x^{2}}{32} }(1-\frac{x^{2}}{16} )[/tex]

[tex]f'(x)=e^{-\frac{x^{2}}{32} }(1-\frac{x^{2}}{16} )[/tex] = 0

[tex]1-\frac{x^{2}}{16}=0[/tex]

[tex]\frac{x^{2}}{16}=1[/tex]

[tex]x^{2}=16[/tex]

x = ±4

x can't be -4 because it is not in the interval [-2,8].

[tex]f(-2)=-2e^{-\frac{(-2)^{2}}{32} }=-1.76[/tex]

[tex]f(4)=4e^{-\frac{4^{2}}{32} }=2.42[/tex]

[tex]f(8)=8e^{-\frac{8^{2}}{32} }=1.08[/tex]

Analysing each f(x), we noted when x = -2, f(-2) is minimum and when x = 4, f(4) is maximum.

Therefore, absolute maximum is f(4) = 2.42 and

absolute minimum is f(-2) = -1.76

The absolute maximum and absolute minimum values of f(x) are 2.426 and -1.765, respectively.

The function is given as:

[tex]\mathbf{f(x) = xe^{-\frac{x^2}{32}}}[/tex]

Start by differentiating the function

[tex]\mathbf{f'(x) = e^{-\frac{x^2}{32}} - \frac{x^2}{16}e^{-\frac{x^2}{32}}}[/tex]

Set to 0

[tex]\mathbf{ e^{-\frac{x^2}{32}} - \frac{x^2}{16}e^{-\frac{x^2}{32}} = 0}[/tex]

Rewrite as:

[tex]\mathbf{ \frac{x^2}{16}e^{-\frac{x^2}{32}} = e^{-\frac{x^2}{32}}}[/tex]

Cancel out common factors

[tex]\mathbf{ \frac{x^2}{16}=1}[/tex]

Multiply both sides by 16

[tex]\mathbf{ x^2=16}[/tex]

Take square roots of both sides

[tex]\mathbf{ x=\pm 4}[/tex]

The interval is given as: [-2,8]

This means that the value of x = -4, is out of the interval.

So, we have the following critical points:

x = (-2, 4, 8)

Calculate f(x) at the these points

[tex]\mathbf{f(-2) = -2 \times e^{-\frac{(-2)^2}{32}}}[/tex]

[tex]\mathbf{f(-2) = -2 \times e^{-\frac{4}{32}}}[/tex]

[tex]\mathbf{f(-2) = -1.765}[/tex]

[tex]\mathbf{f(4) = 4 \times e^{-\frac{(4)^2}{32}}}[/tex]

[tex]\mathbf{f(4) = 4 \times e^{-\frac{16}{32}}}[/tex]

[tex]\mathbf{f(4) = 2.426}[/tex]

[tex]\mathbf{f(8) = 8 \times e^{-\frac{(8)^2}{32}}}[/tex]

[tex]\mathbf{f(8) = 8 \times e^{-\frac{64}{32}}}[/tex]

[tex]\mathbf{f(8) = 1.083}[/tex]

By comparison, the absolute maximum and absolute minimum values of f(x) are 2.426 and -1.765, respectively.

Read more about absolute maximum and absolute minimum values at:

https://brainly.com/question/12752779

Answer:

The 36-pack is a better buy by $0.50 per 36 bottles.

Step-by-step explanation:

24 bottles for $3 compared to 36 bottles for $4

Unit rates:

$3/24 = $0.125/bottle

$4/36 = $0.111/bottle

The 36-pack is a better buy since the unit price is lower.

$0.125 - $0.111 = $0.013888...

$0.01388888... * 36 = $0.50

Answer: The 36-pack is a better buy by $0.50 per 36 bottles.

Answer:

8 pies and 2 coffees must have been bought.

Step-by-step explanation:

Given that:

10 men bought either a pie or a cup of coffee.

Cost per pie = 60p

Cost per coffee = 50p

Total amount spent = £5.80 * 100 = 580p

Let,

x be the number of pies

y be the number of coffees

According to given statement;

x+y = 10     Eqn 1

60x+50y=580    Eqn 2

Multiplying Eqn 1 by 50

50(x+y=10)

50x+50y=500      Eqn 3

Subtracting Eqn 2 from Eqn 3

(60x+50y)-(50x+50y) = 580-500

60x+50y-50x-50y=80

10x=80

Dividing both sides by 10

[tex]\frac{10x}{10}=\frac{80}{10}\\x=8[/tex]

Putting x=8 in Eqn 1

8+y=10

y=10-8

y=2

Hence,

8 pies and 2 coffees must have been bought.

Answer:

Division and multiplication are inverse operations. This means they "undo" each other. You can check your answer by multiplying the quotient by the divisor. You should get the dividend.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Division and multiplication are inverse operations. This means they "undo" each other. You can check your answer by multiplying the quotient by the divisor. You should get the dividend.i hope this helps:)

Answer:

B)  divide a binomial by a trinomial

Step-by-step explanation:

We know that the polynomials are very nearest to the addition, subtraction and the multiplication part but the same cannot happen under the division part since the division of two polynomials could not become a polynomial it is not necessary  condition that it could become a polynomial

So if we divide the binomial by a trinomial therefore it would provides a rational expression and have a negative exponent and a negative exponent is not permitted under the polynomial

Therefore the option B is correct

Answer:

a=2

Step-by-step explanation:

Slope is found by (y2-y1)/(x2-x1)

Using the points, that is (5-a)/(4a-2) = 1/2

multiply both sides by the denominator 4a-2

5-a = (1/2)(4a-2)

5-a=2a-1

put like terms on opposite sides by adding a to both sides so a terms on the right, adding 1 on both sides so numbers are on the left

6=3a

divide both sides by 3

a=2

please give thanks :)

Answer:

-260

Step-by-step explanation:

Answer:

x = -260

Step-by-step explanation:

Answer:

The number of cars that go through the intersection each minute X has Poisson distribution with parameter λ = 11.5

and the PMF of X is;

P (X = x) = e^-λ ( λˣ / x! ); where x = 0, 1, 2, 3, , , , , ,

Step-by-step explanation:

Given that;

on average eleven and a half  cars go through the intersection each minute and It takes an average person ten seconds to walk across the intersection.

Therefore

The number of cars that go through the intersection each minute X has Poisson distribution with parameter λ = 11.5

and the PMF of X is;

P ( X = x ) = e^-λ ( λˣ / x! ) ;

where x = 0, 1, 2, 3, , , , , ,

Answer:

(-1,0) these two points have the same x-value

(x,y)

Step-by-step explanation:

Answer:

the highest common factor of the polynomial is (x + 2) (x - 3)

Step-by-step explanation:

The computation of the highest common factor of the polynomial is as follows:

According to the question, the following equation is given

'[tex]x^2 - x - 6[/tex]

Now do the factorization

[tex]x^2 -3x + 2x - 6[/tex]

x(x - 3) +2 (x - 3)

(x + 2) (x - 3)

hence, the highest common factor of the polynomial is (x + 2) (x - 3)

The same is to be considered

area

i took the test and got a 100                                          

Answer:

area, 244.4

Step-by-step explanation:

sorry it late

Answer:

the answer is d because it

Answer: Irrational

Step-by-step explanation:

Answer:

the answer is 70

Step-by-step explanation:

Answer:

b

24 ÷ 5 = x

X  ×  8 = 44

Answer:

9 cm2

Step-by-step explanation:

area=3×3=9cm2

.....

Answer:

9 cm^2

Step-by-step explanation:

inside the parallelogram, two right angled triangles form.

Use the formula, A = [tex]\frac{1}{2}[/tex] x base x height (Area of a triangle) and multiply by 2 as there are two triangles. So,

A = ([tex]\frac{1}{2}[/tex] x base x height) x 2

   = ([tex]\frac{1}{2}[/tex] x 3 x 3 ) x 2

   = 9 cm^2

Answer:

it is the answer A

Step-by-step explanation:

Answer:

-100

75

Step-by-step explanation:

Answer:

Put the dot on the 5 on the Y-axis

Step-by-step explanation:

Put the initial dot on the 5 on the y-axis (vertical), then it's rise over run if plotting a line. Since it's 3/4 you would go up 3 and over to the right four. You can get the rest of the line by going down 3 from the initial point on five, down left 3.  

Answer:

9

5

Step-by-step explanation:

Wyatt's class:

Each group of 3 students eats 1 1/2 pizzas.

There are 18 students.

18/3 = 6

There are 6 groups of 3 students.

Since each group of 3 students eats 1 1/2 pizzas, 6 groups eat

6 * 1 1/2 = 6 * 3/2 = 18/2 = 9

Answer: 9 pizzas

Jennifer's class:

There are 15 students. Each student eats 1/3 of a pizza.

15 * 1/3 = 15/3 = 5

Answer: 5 pizzas

Answer:

9

5

Answer: Though no choices of statements are shown, you can predict that x+2=-3, since both numbers are equal to y. (This isn't really an answer but I hope it'll at least help you in some way!)

-By subtracting 2 on both sides, you end up with x=-5. So in both equations, y is -3 and x is -5.

-The point where they intersect is (5,-3)

Answer:

each person would pay $11

Step-by-step explanation:

u have to do 55 divided by 5 and that would give you the $11

Answer: 11

Step-by-step explanation: 55/5=11

Answer: You earn 6% interest on that the next year.

Answer: 8 units

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

I hope this helps!

Answer: 13

Step-by-step explanation: