Consider the diagram below. Find the value of w.

The absolute maximum of the function is 184 and the minimum value of the function is -72.

If the graph of an absolute value function opens downward, the y-value of the vertex is the maximum value of the function.

Given the function f(x) = x⁴-18x²+9 at the interval [-5, 5], the absolute maximum and minimum values at this endpoints are as calculated;

At end point x = -5

f(-5) = (-5)⁴-18(-5)²+9

f(-5) = 625-450+9

f(-5) = 184

At end point x = 5

f(5) = (5)⁴-18(5)²+9

f(5) = 625-450+9

f(5) = 184

To get the critical point, this point occurs at the turning point i.e at

dy/dx = 0

if y = x⁴-18x²+9

dy/dx = 4x³-36x = 0

4x³-36x = 0

4x (x²-9) = 0

4x = 0

x = 0

x²-9 = 0

x² = 9

x = ±3

Using the critical points [0, ±3]

when x = 0, f(0) =  0⁴-18(0)+9

f(0) = 9

Similarly when x = 3, f(±3)=  (±3)⁴-18(±3)²+9

f(±3) = 81-162+9

f(±3) = -72

It can be seen that the absolute minimum occurs at x= ±5 and the absolute minimum occurs at x =±3

absolute maximum = 184

absolute minimum = -72

Hence, the absolute maximum of the function is 184 and the minimum value of the function is -72.

Learn more about absolute maximum value here;

https://brainly.com/question/17001091

#SPJ4

[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-5}~,~\stackrel{y_1}{-4})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{-7})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{[3 - (-5)]^2 + [-7 - (-4)]^2}\implies d=\sqrt{(3+5)^2 + (-7+4)^2} \\\\\\ d=\sqrt{8^2 + (-3)^2}\implies d=\sqrt{64+9}\implies d=\sqrt{73}[/tex]

Answer:

[tex]\frac{1}{81}[/tex]

Step-by-step explanation:

[tex](\frac{1}{3} )^{4}[/tex]

We know this is written as

[tex]\frac{1}{3}*\frac{1}{3}*\frac{1}{3}*\frac{1}{3}[/tex]

Let's solve:

[tex]\frac{1}{3} * \frac{1}{3} = \frac{1}{9}\\ \frac{1}{9} *\frac{1}{3} = \frac{1}{27} \\\frac{1}{27} * \frac{1}{3} = \frac{1}{81}[/tex]

Answer:

sin Ф.

Step-by-step explanation:

Cos (-270) = cos 90 = 0 and sin(-270) = sin 90 = 1.

So cos ( Ф - 270) =   cos Ф cos (-270) + sin Ф sin(-270)

=  cos Ф * 0 + sin Ф * 1

= sin Ф.

Answer:

[tex]5^{-8}[/tex]

Step-by-step explanation:

[tex]\sf \boxed{\dfrac{a^{m}}{a^n}=a^{m-n}}[/tex]

  [tex]\sf \dfrac{5^{-4}}{5^{4}}=5^{-4-4}[/tex]

         [tex]= 5^{-8}[/tex]

Answer:

28

Step-by-step explanation:

each question is worth 2 points and he missed 6,6 times 2 is 12.therefore you subtract 40 by 12 and get 28 :)

Answer:

[tex]196 m^{2}[/tex]

Step-by-step explanation:

A square is a  shape that which all sides are equal

14 is one side of the square and to find the area of a square/rectangle, you do  length*width

14*14=196

Answer:

C.8/27

Step-by-step explanation:

#1

Area

#2

Area

#3

Area

#4

Area

Answer:

Formula:    Area of a rectangle = width × length

Substitution:    Area = 2.5 mi × 5 mi

Answer:    Area = 12.5 mi²

Formula:   Area of a triangle = 1/2 × base × height

Substitution:   Area = 1/2 × (12 ft + 4 ft) × 5 ft

Answer:   Area = 40 ft²

Formula:  Area of a parallelogram = base × height

Substitution:   Area = 24 cm × 6 cm

Answer:   Area = 144 cm²

Formula:   Area of a parallelogram = base × height

Substitution:   Area = 7 m × 4 m

Answer:   Area = 28 m²

Answer:

looks like a triangle to me

Step-by-step explanation:

Answer:

C Hope this helps This may be wrong though

Step-by-step explanation:

Answer:

See below ~

Step-by-step explanation:

Finding the distance of each side length :

Perimeter :

Area :

Answer:

Step-by-step explanation:

Answer:

it would be 24 or 27

Step-by-step explanation:

because for a parralelogram you multiply the base and height and you gave 3 numbers so it is either 6 times 4 which is 24.or you multiply 6 times 4.5 and get 27.

Answer:

Step-by-step explanation:

ΔBOC is isosceles and M is the midpoint of BC

then

∠MOC = ∠BOM = 30°

then

∠BOC = 60°

……………………

OC // AB

then

∠ABO = ∠BOC = 60° (alternate-interior angles)

……………………………………………

In ΔOAB ,we have :

OA = OB and ∠ABO = 60°

Then ,

ΔOAB is an equilateral triangle.

then

∠AOB = 60°

……………………………

We get :

∠AOC = ∠AOB + ∠BOC = 60° + 60° = 120°

……………………………………………………

∠ADC = ∠AOC/2 = 120/2 = 60°

Answer:

10 bags

Step-by-step explanation:

Answer:2/12

Step-by-step explanation:

2/12 is the probability of rolling 2 4's in a row.

Answer:

The second and fourth choices.

Step-by-step explanation:

Probability of getting a blue marble = 0.25 = 1/4.

Therefore the number of blue bags will be 1/4 of the total of marbles.

The second choice has 10 blue marbles out of a total of 40, so this is one.

The 4th bag has 12 marbles of which 3 are blue. 3/12 = 1/4 so this is another answer which is correct.

Answer:

option 2 and 4

Step-by-step explanation:

add up all the values given then divide the number of blue given.

Answer:

[tex]144[/tex] [tex]inches^2[/tex]

Step-by-step explanation:

Hey there!

In order to find the area of a triangle, you need to:

Multplipy the base by the height

Then you take that product and multiply it by 1/2 (basically divide it by 2)

Then you get your area!

Base: 19

Height: 12

19 x 12

228

228 x 1/2

228/2

114

So the area of this triangle is [tex]144[/tex] [tex]inches^2[/tex]

Answer:

12

Step-by-step explanation:

If there are 5 orange beads, and 3 purple beads, that means there is 8 beads that aren't pink in the bag.

If the rest are pink, and it's 3/5, that means 8 is 2/5. Divide by 2, and 4 is 1/5.

We can conclude that there are 12 pink beads, which is 3/5 of the total beads, by adding 2/5 and 1/5 (8 and 4)

The remaining 2/5 are the orange and purple beads.

Answer:

1. 20.724 or 6.6π

2.3.14 or π

3. 15.7 or 5π

4. 9.42 or 3π

5. 25.12 or 8π

6. 18.84 or 6π

Step-by-step explanation:

just ask :)

The evaluation of the function [tex]f(x)=e^x[/tex] at a=0 and x=5 by the taylor series will have a value 65.37.

We know the fromula of taylor series is given as:

[tex]f(x)=f(a)+\dfrac{f'((a)}{1!}(x-a)+\dfrac{f''(a)}{2!}(x-a)^2+\dfrac{f'''(a)}{3!}(x-a)^3.................[/tex]

Now for the function [tex]f(x)=e^x[/tex] the taylor's series will become.

[tex]f(x)=e^a+e^ax+\dfrac{e^ax^2}{2!}+\dfrac{e^ax^3}{3!}+\dfrac{e^ax^4}{4!}[/tex]

[tex]f(x)=1+x+\dfrac{x^2}{2!}+\dfrac{x^3}{3!}+\dfrac{x^4}{4!}[/tex]

So at x=5 the values will become

[tex]f(x)=1+5+12.5+20.83+26.04=65.37[/tex]

hence the evaluation of the function [tex]f(x)=e^x[/tex] at a=0 and x=5 by the taylor series will have a value 65.37.

To know more about Taylor series follow

https://brainly.com/question/24188700

#SPj4

Answer:

Possible base lengths are 1, 2, 3, 4, 5

Step-by-step explanation:

Area = base x height / 2

Let base be b

b x 8 / 2 < 24 (Area < 24)

4b < 24

b < 6

Answer:

Step-by-step explanation:

area=s*s

       =3*4

        =12cm squared

Perimeter=S+S+S+S

                = 4+4+3+3

                 =14cm

HOPE I HELPED

Answer:

5,400.00

Step-by-step explanation:

hope this helps

Answer:

13%

Step-by-step explanation:

Total is 100 tickets sold as 13+87=100, 13/100 is 13%

Answer:

3/8 gallons

Step-by-step explanation:

Let T be the total amount of water which can fill the bin.

The equation formed will be :

Now, multiply each side by 3 :

Divide each side by 2 :

Let the total gallons be x

Multiply 3 to complete whole bin

Step-by-step explanation:

The option "StartFraction 1 Over 3 Superscript 8" is correct

That is 138 is correct answer

Therefore [(2−2)(34)]−3×[(2−3)(32)]2=138

Step-by-step explanation:

Given expression is ((2 Superscript negative 2 Baseline) (3 Superscript 4 Baseline)) Superscript negative 3 Baseline times ((2 Superscript negative 3 Baseline)

The function for the total cost will be given as h(x)  =  5.94x  +  2.25.

A function is defined as the expression that set up the relationship between the dependent variable and independent variable.

Given that:-

The function h(x) for total cost will be calculated as:-

h ( x )  =  4.95x   +   0.99x  +   2.25

h ( x )  =  5.94x   +   2.25

Therefore the function for the total cost will be given as h(x)  =  5.94x  +  2.25.

To know more about function follow

https://brainly.com/question/25638609

#SPJ1

The function for the total cost will be given as h(x)  =  5.94x  +  2.25.

What is a function?

A function is defined as the expression that set up the relationship between the dependent variable and independent variable.

Given that:-

The function f(x) = 4.95x represents the cost to purchase x pounds of chocolate from a candy company

The function g(x) = 0.99x + 2.25 models the cost to ship x pounds of chocolate from the company.

The function h(x) for total cost will be calculated as:-

h ( x )  =  4.95x   +   0.99x  +   2.25

h ( x )  =  5.94x   +   2.25

Therefore the function for the total cost will be given as h(x)  =  5.94x  +  2.25.

To know more about function follow

brainly.com/question/25638609

#SPJ1