Find the exact location of all the relative and absolute extrema of the function.] (Order your answers from smallest to largest x.)
f(x) = x4 − 8x3 with domain [−1, +[infinity])
f has (select)(a relative minimum, a relative maximum, an absolute minimum, an absolute maximum, no extremum,) at (x, y) = ____________
f has (select)(a relative minimum, a relative maximum, an absolute minimum, an absolute maximum, no extremum,) at (x, y) = ____________

By using the formula for the distance between the two points, it is found that S could lie on the perpendicular bisector QR.

Distance between points:

The distance between two points, (x1,y1) and (x2,y2) is calculated as,

D = √(x2 - x1)² + (y2 - y1)²

Given,

Here we have the coordinates: Q(-5, 4), R(8, -3), S(-2,-5)

Now, we have to determine if S could lie on the perpendicular bisector of QR with the given coordinates.

Here we have the endpoints are: Q(-5, -1), R(3, 7)

Point S is (4,-2).

The distance of S to Q is calculated as,

D = √(4 - (-5))² + (-2 - (-1))²

D = √82

Now, the distance of S to R is calculated as,

D = √(4 - 3)² + (-2 - 7)²

D = √82

Both have the Same distance, thus states the S could lie on the perpendicular bisector QR.

To know more about Distance between points here.

https://brainly.com/question/15958176

#SPJ1

The explicit formula to represent the given  situation is

Explicit: pn = 14 + 9*n

Here we want to express the number of pizza delivered. Lets try to understand the case.

If we buy one pizza (p1) the cost is 14 because of the delivery plus 9 for the cost of the pizza. So:

p1 = 14 + 9 = 23

If we buy 2 pizzas (p2) we have to pay 14 for the delivery and 9 for each pizza:

p2 = 14 + 9 + 9 = 14 + 2*9 = 32

If 3 pizzas are bought (p3) the reasoning is the same, 14 for the delivery and 9 for each pizza:

p3 = 14 + 9 + 9 + 9 = 14 + 3*9 = 41

Here we can see a pattern: for any amount of pizzas n the cost will be 14 plus n-times 9, the price of a pizza. It is:

pn = 14 + 9*n

But we can separate the last equation in such a way:

pn = 14 + 9*(n-1) + 9 , as 9*(n-1) + 9 = 9*n

But if our general formula it true, the first to terms on the right are the vost of buying n-1 pizzas, so:

pn = pn-1 + 9

We can keep on separating terms as we did to arrive to this form, this is, separating the 9n in  9*(n-2) + 9*2,  9*(n-3) + 9*3, ...,  9*(n-m) + 9*m for any m < n . Here I will keep pn = pn-1 + 9 as the Recursive Formula, but you could use other formulation with, e.g., pn-2, pn-3, etc, using the above recursion.

Now, the explicit formula is such that gives as the value of any amount, finding all the terms of the sequence with those not depending on previous terms (contrary to the recursive). This formula was showed above and is: pn = 14 + 9*n. This is, given any number of pizzas we can find the cost without knowing the cost of previous values.

So, we have:

Recursive: pn = pn-1 + 9

Explicit: pn = 14 + 9*n

Learn more about Explicit formula at

https://brainly.com/question/24198356

#SPJ4

Any two triangles must meet a number of requirements in order for congruence to be established. In order for two triangles to be similar:

Investigation is required to determine whether the triangles in the preceding diagram, ABC and CDA, are congruent. Considering the diagram

The two triangles share side AC.

Side BC equals Side AD (given)

Angle DAC equals angle ACD (alternate angles as depicted in the diagram)

Therefore, ABC and CDA are congruent because both triangles' two sides and an included angle (SAS) are equivalent.

Learn more about congruent triangles here;

https://brainly.com/question/27983958

#SPJ4

The question is incomplete. Completed question is given below;

Based on the given information in the figure at the right, how can you justify that triangle ABC is congruent to triangle CDA?ASA, SSS, AAS, SAS

Figure is attached

Answer:

Step-by-step explanation:

a

2/2 x^2 = 24/2

x^2 = 12

x = √12

x = 3.464102 = 3.46

x = -√12 = -3.46

b

x^2 = 14 + 4

x^2 = 18

x = √18

x = 4.242641 = 4.24

x = -√18 = -4.24

The volume of a pyramid with a square base, where the area of the base is 8. 3m² and the height of the pyramid is 9. 8 m is 222.7m³

Given,

Each length (l) of the base of the pyramid = 8.3 m

Height(h) of the pyramid = 9.8m

We need to find the volume of the pyramid.

Formula

Volume of the pyramid = 1/3 ×area of the base×height

Area of the base =  l²

Now,

The volume of the pyramid = 1/3 ×l²×h

= 1/3 ×8.3²×9.8 cube inch = 222.7 cube meter(approx)

Therefore, the volume of a pyramid with a square base, where the area of the base is 8. 3m² and the height of the pyramid is 9. 8 m is 222.7m³

To learn more about volume refer here

https://brainly.com/question/23963432

#SPJ4

The problem is saying there are two distinct zeros, and both are strictly lie between 0 and 1. The least positive integer value of "a" is 5 for which such a polynomial exists.

Let f(x) = ax² - bx + c , be our polynomial.

where a,b are integers coefficient and c constant. It has two distinct real roots lying between 0 and 1. f(x) can be written as, f(x) = a(x−α)(x−β)

where α and β are the roots of the equation.

we can be observed that f(0)f(1) > 0

As a,b and c are integers f(0)f(1) > 1

f(0) = aαβ , f(1)=a(1−α)(1−β)

=> a²(α)(1−α)(β)(1−β) > 0 -------(1)

Using A.M ≥ G.M, we get

(α+1−α+β+1−β)/4 > (αβ(1−α)(1−β))¹/⁴

Arithmetic Mean and Geometric Mean cannot be equal because the equation has distinct roots.

a²/16 > a²(αβ(1−α)(1−β)).

=> a²/16 > 1

=> a > 4

Therefore, the minimum value of 'a' is 5

The discriminant of the equation,

Δ = b²−4ac ≥ 0

=> b² >20c

consider the minimum value of c = 1,

we get b² >20

=> Minimum Value of b = 5.

Hence, the least positive integer of 'a' is 5.

To learn more about quadratic equation roots, refer:

https://brainly.com/question/25841119

#SPJ4

The quotient of of x³ + 1 divided by x² - x + 1 is x + 1

Given,

The polynomial function; x³ + 1 and x² - x + 1

We have to find the quotient of x³ + 1 divided by x² - x + 1

Polynomial function;-

In an equation such as the quadratic equation, cubic equation, etc., a polynomial function is a function that only uses non-negative integer powers or only positive integer exponents of a variable. For instance, the polynomial 2x+5 has an exponent of 1.

Here,

Divide x³ + 1  by x² - x + 1

x² - x + 1 ) x³ + 1        (x + 1 ⇒ Quotient

               x³ - x² + x

             0 + 1 + x² - x

            0 + 1 + x² - x

                          0   ⇒ Remainder

That is,

The quotient of of x³ + 1 divided by x² - x + 1 is x + 1

Learn more about polynomial division here;

https://brainly.com/question/22346047

#SPJ4

The percent of men are between 64 and 66. 5 inches tall is 13.59%

The distribution of heights of adult american men is approximately normal with mean 69 inches

Standard deviation 2. 5 inches.

13.59%.  66.5 inches is 1 standard deviation shorter than the mean, while 64 inches is 2 standard deviations from the mean.  looking at a graph of the normal distribution, 13.59% of samples will fall between 1 and 2 standard deviations below the mean.

Therefore, the percent of men are between 64 and 66. 5 inches tall is 13.59%

To learn more about standard deviation refer here

https://brainly.com/question/24298037

#SPJ4

By using x0 = 0.49 the value goes to more than 1.

Given function f(x) = x³- sinx

By newton's method x₀ = 0.49

Formula for the newton's method is

Xₙ₊₁ = Xₙ - f( Xₙ)/ f'( Xₙ)

X₀ =  0.49,f(x) = x³- sinx and  f'(x) = 3x²- cosx

X₁ = X₀ - f( X)/ f'( X)

X₁ = 0.49 - x³- sinx/3x²- cosx

X₁ = 0.49-(0.49)³-sin(0.49)/3(0.49)²-cos(0.49)

X₁ = 0.658

X2 = X1 - f(X₁)/ f'(X₁)

By substituting the values we get,

X2 = 1.012

So, Using x0 = 0.49 the value goes to more than 1.

To learn more about Newton's method click here:

brainly.com/question/14865059

#SPJ4

The decay rate for the resale price of laser cutting tool will be -121000[tex]e^{-0.22t}[/tex]

Let R is the resale value of a particular type of laser cutting tool after years

Where, R(t) = 550000[tex]e^{-0.22t}[/tex]

Rate at which the resale value is changing will be dR/dt = 550000[tex]e^{-0.22t}[/tex](-0.22)= -121000[tex]e^{-0.22t}[/tex]

Initial value of the laser cutting tool, at time ‘t’ =0 will be 550000[tex]e^{-0.22t}[/tex]x0 = 550000

At time ‘t’ resale value is 550000 [tex]e^{-0.22t}[/tex]

Therefore, the decay in resale price = 550000 - 550000 [tex]e^{-0.22t}[/tex]

Therefore, the decay rate = (550000 - 550000 [tex]e^{-0.22t}[/tex])/t = 550000(1-[tex]e^{-0.22t}[/tex])/t

As we have dR/dt = R’ = -121000[tex]e^{-0.22t}[/tex]

Therefore, R’(10) = -121000[tex]e^{-2.2}[/tex] = -13407.18

Therefore, after 10 years the resale price will be -13407.18

R’(20) = -121000[tex]e^{-4.4}[/tex]= -1485.55

Therefore, after 20 years the resale price will be -1485.55

To know more about the decay rate, visit here:

https://brainly.com/question/28461852

#SPJ4

The closest object that she is going to be able to see clearly is going to be situated at a distance of 20 cm from her eyes.

Here, it has been given that the lens-to-retina distance of her eye is = 2.00 cm (i)

The normal power for distant vision is 50.00 Dioptres. This woman has the ability to increase lens strength by 10%. The new power for this is going to be -

= P1 = 50.00 + 10% of 50

= P1 = 55.00 D (ii)

Now, the power of a lens, P = 1/f = 1/u + 1/v where f = focal length of the lens, u = object distance from eye lens, and v = image distance from eye lens.

We are aware of the formula = P1 = 1/u + 1/v

Using the values of (i) and (ii) and the formula, we get -

= 1/u = P'- 1/v

= 1/u = 55.0 D - 1/0.02 m

= 1/u = 5.0 m⁻¹

= u = 1/5.0 m⁻¹

= u = 20 cm

Hence, we have found out that the woman can see objects at a distance of 20 cm.

Learn to know more eyesight on

https://brainly.com/question/28790942?referrer=searchResults

#SPJ4

The density function for the distance between the ambulance and the accident is  equal to  2(l-a) / l².

As given in the question,

Let 'x' and 'y' represents the position of the ambulance and location of the accident on the road.

Both variables are independent .

f(x, y)=  [tex]F_{x} (x) F_{y} (y)[/tex]

        = ( 1/l² ) for ( x, y ) ∈ 9 0, l²

Distance between the ambulance and the accident is

Z : ( x- y)

P ( z≤ a) = 1 -P ( z >a)

            = 1 - ( l - a)² / l²

Density function is given  y :

[tex]f_{z}(a)[/tex] = d/da [ 1 - ( l - a)² / l² ]

        = -2( l - a) / l² ( -1)

        = 2( l - a) / l²

Therefore, for the given condition the distance between the  ambulance and the accident is given by [tex]F_{z}(a)[/tex] = 2(l-a) / l².

Learn more about distance here

brainly.com/question/15172156

#SPJ4

Yes, you can be confident that your portfolio will not lose more than 30% in value over the next year.

the reason is

For this question, the portfolio has an average return of 12.5% ​​with a standard deviation of 19.5%. It is estimated that next year will be a 30% loss. Confidence intervals are 95%.

Range = Average return ± 2 x Standard deviation Low aid = 12.5% - (2 x19.5%) =12.5% -39% = -26.5%

High end = 12.5% +(2 x19.5%) =12.5%+39% = 51.5%

Thus, the low end is 26.5%

Returns range from -26.5% to 51.5% with 95% confidence intervals

learn more about confidence intervals at

https://brainly.com/question/17156191

#SPJ4

The value of x is 128, for equations x/2=y² and x/4=4y

Two or more expressions with an Equal sign is called as Equation.

Given,

x/2=y²...(1) and

x/4=4y ...(2)

We need to find value of x and  x not equal to zero

x=2y²

Substitute in equation 2

2y²/4=4y

y²/2=4y

y/2=4

y=8

Now substitute in equation 2

x/4=4(8)

x/4=32

x=128

Hence the value of x is 128, for equations x/2=y² and

x/4=4y

To learn more on Equation:

https://brainly.com/question/10413253

#SPJ1

The four ways to care for our nervous system are exercise, meditation, proper sleep and healthy food.

There are many ways to care and protect our nervous system. But some of the basics and the most important ways to care for our nervous system are to follow a basic routine which includes regular exercise, practicing meditation daily, having proper sleep for at least seven hours a day and having healthy food mostly.

Now, doing exercise means that we are constantly engaged in some kind of physical activity and healthy food also means to have a balanced lifestyle.

Hence, the four ways to care for our nervous system are exercise, meditation, proper sleep and healthy food.

To know more about nervous system here

https://brainly.com/question/29355295

#SPJ4

As per the given differential equation, the minimum radius of convergence R of power series solutions about the ordinary point x = 0 is 9 and that about the ordinary point x = 1 is 10 units.

Differential equation:

Differential equation refers the equation which contains one or more terms and the derivatives of one variable with respect to the other variable

And it can be written as,

=> dy/dx = f(x)

Given,

The given differential equation is  (x² - 81)y"+ 7xy' + y = 0 R = 9 (x = 0) R = (x = 1).

Now we have to find the minimum radius of convergence R of power series solutions about the ordinary point x = 0 and x = 1.

Here we know that the minimum radius of convergence is defined as the distance between the ordinary point and the singularity of the differential equation.

And the Singularity point is the root of the polynomial attached with the second derivative. So, the singularity points will be calculated as,

=> x² - 81

=> (x + 9) (x - 9)

=> x = 9, - 9

So, the singularity points are 9, - 9.

So, the minimum radius of convergence can be calculated as,

Now, the ordinary points are 1 + 0i  and 1 - 0i.

So,

=> r1 = | 1 + 0i - 9|

=> r1 = 9

=> r2 = | 1 + 0i + 9|

=> r2 = 10

Therefore, the minimum radius of convergence R of power series solutions about the ordinary point x = 0 is 9 and that about the ordinary point x = 1 is 10 units.

To know more about differential equation here.

https://brainly.com/question/14620493

#SPJ4

The correct equation is tan θ = 6 / 13, and the value of angle θ will be 24.775°. Then the correct option is C.

Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.

The right-angle triangle is shown below.

The length of the perpendicular is 6 cm and the length of the base is 13 cm. Then the angle θ is written as,

tan θ = P / B

tan θ = 6 / 13

Simplify the equation to get the value of the angle θ will be given as,

tan θ = 6 / 13

tan θ = 0.4615

θ = 24.775°

The correct equation is tan θ = 6 / 13, and the value of angle θ will be 24.775°. Then the correct option is C.

More about the trigonometry link is given below.

https://brainly.com/question/22698523

#SPJ1

The probability of choosing a person at random who is a junior and plays video games is of:

0.32 = 32%.

These are non-independent events.

A probability in the context of a problem is given by the division of the number of desired outcomes by the number of total outcomes.

For the probability in the context of this problem, the outcomes are given as follows:

Hence the probability is of:

p = 48/150 = 0.32 = 32%.

The probability of being a junior is of:

60/150 = 6/15.

The probability of playing videogames is of:

99/150

The multiplication of these probabilities is of:

6/15 x 99/150 = 0.264.

Different than 0.32, hence these two events are not independent.

More can be learned about probabilities at https://brainly.com/question/14398287

#SPJ1

Option A, which states that the ordered pair of point P' will be, is the appropriate response (-8.75, 5.25).

Given,

A scaling factor of 7/4 is used to enlarge the pentagon in the OPQRS.

In order to generate O'P'Q'R'S, we must identify the ordered pair of point P'.

Here,

To obtain the coordinates of P', multiply the coordinates of point P by the scale factor 7/4.

P(-5,3)

P' (x, y) = P (-5 x 7/4, 3 x 7/4).

= P(-8.75, 5.25) 

As a result, option A, which states that the ordered pair of point P' will be, is the appropriate response (-8.75, 5.25).

Learn more about scale factor here;

https://brainly.com/question/1698446

#SPJ4

The question is improper. Proper question is given below;

If pentagon OPQRS is dilated by a scale factor of 7/4 from the origin, to create O’P’Q’R’S’, what is the ordered pair of point P’?

A. (-8.75, 5.25)

B. (-1.25, 0.75)

C. (-3.5, 8.75)

D. (-1.75, 3.5)

Maura's driveway is 4.7 meters long and the distance from the garage into the lot is 3.6 meters

The length of Maura's drive way is solved using SOH CAH TOA

Sin = opposite / hypotenuse - SOH

Cos = adjacent / hypotenuse - CAH

Tan = opposite / adjacent - TOA

The information in the question describes a right angle triangle of

opposite = 3 meters

adjacent = distance into the lot = ?

hypotenuse = Maura's drive way = ?

angle of depression = 40

The length of the drive way

sin 40 = 3 / hypotenuse

hypotenuse = 3 / sin 40

hypotenuse = 4.667 m

The distance from the garage to the lot

tan 40 = 3 / adjacent

adjacent = 3 / tan 40

adjacent = 3.575 m

Learn more about SOH CAH TOA here:

https://brainly.com/question/29402966

#SPJ1

The measure of angle BDC = 100°

The smallest polygon with three sides and three internal angles is known as a triangle. According to the triangle's "angle sum property," a triangle's internal angles add up to 180°.

Sum of angles in a triangle = 180°

Here we have

3 triangles in the given picture

As we know the Sum of angles in a triangle = 180°

From triangle CBD

∠CBD + ∠BDC + ∠DCB = 180°

From figure  ∠DCB = 40° and ∠CBD = 40°

=> 40° + ∠BDC + 40° = 180°  

=> ∠BDC = 180° - 80°

=> ∠BDC = 100°

Therefore,

The measure of angle BDC = 100°

Learn more about the Angles of triangles at

https://brainly.com/question/27682397

#SPJ9

Plastic, wood, and rubber are the three materials that do not conduct electricity.

Conductors are materials that conduct heat or electricity. Insulators are the materials that do not allow to conduct heat or electricity.

Electrical insulators are materials that do not allow to pass electricity  through them.

Glass,  wood, rubber and plastic are examples of these materials. Air also acts as an insulator.

Thus,these non-conductors/insulators are useful in a variety of applications.

To learn more about non-conductors of electricity refer here

https://brainly.com/question/14969495

#SPJ4

Answer:

the answer is 88.36 inches

Step-by-step explanation:

because he wants a square painting and the painting each side length is 9.4 so, we use the formula l square and we get the answer

The main advantage of using a graphic calculator is that it speeds up the process of solving more difficult arithmetic problems for students.

A graphing calculator, often known as a graphics calculator or graphic display calculator, is a portable computer that can plot graphs, solve many equations at once, and carry out other variable-related activities. The most common graphing calculators are programmable calculators, which let the user design unique programs, generally for scientific, technical, or educational purposes. They feature big screens that show computations and several lines of text.

Numerous graphing calculators may be connected to sensors such as accelerometers, electronic thermometers, pH meters, weather stations, decibels, light meters, and other devices to operate as data recorders and as monitoring, polling, and communication tools with teachers. The use of such data in student laboratory tasks improves their understanding of math, particularly statistics and mechanics. 

To know more about calculators click the following link

https://brainly.com/question/17054946

#SPJ4

The percentage of 2000 from 50000 is 4%.

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.

The percentage therefore refers to a component per hundred. Per 100 is what the word percent means. It is represented by %.

The percentage of 2000 from 50000 will be:

= 2000/50000 × 100

= 4%

The percentage is 4%.

Learn more about percentages on:

brainly.com/question/24877689

#SPJ1

[tex]2^{10}\cdot 2^{15}\implies 2^{10+15}\implies 2^{25}\implies 2^{5\cdot 5}\implies (2^5)^5\implies {\Large \begin{array}{llll} 32^5 \end{array}}[/tex]

The rate of change of area is given as 27 π. The time at which radius of circle is increasing is 1.386 sec and change in radius is 3 cm.

What is rate of change?

The rate of change function is defined as the rate at which one quantity is changing with respect to another quantity. In simple terms, in the rate of change, the amount of change in one item is divided by the corresponding amount of change in another.

a) Given, radius of circle = 9 cm

rate of change of radius = 3/2

We know area of circle = πr^2

change in area =2πrr'

we get  2×π×9×2/3=27π

B) Given,

g(t) = 12 - 12e^0.5t

derivate it

g'(t) =-12×-1/2e^t/2

g'(t)=3

3= 6e^t/2

t = 1.386

c) f1(t) = t2-4t+4.

Integrate it we get

radius =3.

To know more about rate of change, visit:

https://brainly.com/question/14469078

#SPJ4

The value of expression 51 x 57 will be;

⇒ 51 x 57 = 2,907

What is Multiplication?

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

The expression is,

⇒ 51 x 57

Now,

Multiply the numbers as;

⇒    51

    x 57

   ---------

    357

+255×

------------

 2907

Thus, The value of expression 51 x 57 will be;

⇒ 51 x 57 = 2,907

Learn more about the multiplication visit:

https://brainly.com/question/28768606

#SPJ1

Answer:

x = 6

Step-by-step explanation:

3x - 1 = 34/2

3x - 1 = 17

3x = 17 + 1

3x = 18

3/3 x = 18/3

x = 6

Answer: A) Juan buys 3 packs of markers. Each pack has 6 markers. How many markers does Juan buy in all?

Answer: A) Juan buys 3 packs of markers. Each pack has 6 markers. How many markers does Juan buy in all?