Find the eigenvalues and eigenvectors

The minimum and maximum of the function f(x)=2x³+15x²-36x+1 are 38 and 39 respectively

The maximum value of a function f(x) is also called the absolute maximum value, or the  greatest value of the function f on the closed interval [0, 1]. on the other hand, the minimum value of f(x) at x = 0 is called the absolute minimum value,  or least value of the function f on the closed interval [0, 1)

How to find the minimum and maximum functions?

From the function f(x) = 2x3 − 15x2 + 36x + 1.

Using differential calculus , dy/dx = 6x2 - 30x + 36

= 6(x2 - 5x + 6)

f(x) is a maximum when x = 2 and the maximum value of f(x) = f(2).

This implies that f(2) = 2(23) − 15(22) + 36(2) + 11 = 39

d2y/dx2|x=3 = 12 x 3 - 30 = 6 > 0

This also implies that  f(x) is a minimum when x = 3 and the minimum value of f(x) = f(3) = 2(3)3 − 15(3)2 + 36(3) + 11 = 38

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Answer:

Step-by-step explanation:

Let the required amount of 5% milk is x quartz, then the amount of 2% milk is 90 - x quartz.

Set equation for the fat content:

Considering the quadratic equation, it is found that:

a) The initial height of the object is of 58.8 meters.

b) The object first hits the ground after 39.2 seconds.

c) The maximum height reached by the object is of: 1912 meters.

The quadratic equation that models the projectile's height is defined as follows:

s(t) = -4.9t² + 190.6t + 58.8.

Which has the coefficients given as follows:

a = 4.9, b = 190.6, c = 58.8.

The initial height is obtained as follows:

s(0) = -4.9(0)² + 190.6(0) + 58.8 = 58.8 meters.

It hits the ground at the positive root for which s(t) = 0, hence, using a quadratic equation calculator, this root is of:

t = 39.2 seconds.

The maximum height obtained by the object is the y-coordinate of the vertex, hence:

hMAX = -(b² - 4ac)/4a = -(190.6² - 4(-4.9)(58.8))/(4(-4.9)) = 1912 meters.

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Answer:

160.1 divided by 22.3 = 7.179 miles per litre.

This is 7.179 x 4.544 = 32.62 miles per gallon.

hope that will help

keeping in mind that there are about 1.609 Km in 1 mile and that there are about 3.78L in 1 gallon(US)

[tex]\cfrac{24~~\begin{matrix} Km \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ }{1~~\begin{matrix} L \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ }\cdot \cfrac{mile}{1.609~~\begin{matrix} Km \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ }\cdot \cfrac{3.78~~\begin{matrix} L \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ }{gallon(US)} \\\\\\ \cfrac{24(3.78)}{1.609}\cfrac{mile}{gallon(US)} ~~ \approx ~~ 56.38\frac{mile}{gallon}[/tex]

The probability of the person favoring rock music is 0.257, favoring country music is 0.285, and favoring something other than rock, country, or classical music is 0.342.

Given that:

Total people = 70

Chose rock = 18

Chose country = 20

Chose classical = 8

Chose something other than rock, country, or classical = 24

a) The empirical probability that the next person entering the store favors rock music is = Total people choosing rock music/ Total people

                                = 18/70 = 9/35 = 0.257

b) The empirical probability that the next person entering the store favors country music is = Total people choosing country music/ Total people = 20/70 = 2/7 = 0.285

c) The empirical probability that the next person entering the store favors something other than rock, country, or classical music is = Total people choosing something other than rock, country, or classical music/ Total people = 24/70 = 12/35 = 0.342.

Hence, the empirical probability that the next person favors rock music is 0.257, favors country music is 0.285, and favors something other than rock, country, or classical music is 0.342.

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Answer:-8

Step-by-step explanation:

You are basically adding -4+(-4)

Answer:

Step-by-step explanation:

2(-4)

2 x -4

answer: -8

The function is y = 3(x+3)^2-9

The equation of a parabola is

y=a(x-h)^2+k

where (h,k) are the coordinates of the vertex and a, is a constant.

From the question, we have

(h,k)=(-3,-9)

⇒y=a(x+3)^2-9

To find a, substitute x=-2,y=-6

-6=a(-2+3)^2-9

⇒a=3

The equation, y=3(x+3)^2-9

Multiplication:

Mathematicians use multiplication to calculate the product of two or more numbers. It is a fundamental operation in mathematics that is frequently utilized in everyday life. When we need to combine groups of similar sizes, we utilize multiplication. The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors. Repeated addition of the same number is made easier by multiplying the numbers.

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The graph of the polar curve r = 3 – 2cos(θ) is in the attachment

A graph is a diagram representation on a coordinate system.

A polar curve is a curve represented by the equation r = a + bcosθ where

To find the graph of the polar curve r = 3 – 2cos(θ), we need to determine its maximum and minimum values and also the value as it crosses the axis.

Since r = 3 – 2cos(θ), the maximum value of r is obtained at the minimum value of cos(θ) = -1 at θ = π

So, substituting this into the equation, we have

r = 3 – 2cos(θ)

r = 3 – 2(-1)

r = 3 + 2

r = 5

Since r = 3 – 2cos(θ), the minimum value of r is obtained at the maximum value of cos(θ) = 1 at θ = 0

So, substituting this into the equation, we have

r = 3 – 2cos(θ)

r = 3 – 2(1)

r = 3 - 2

r = 1

Since r = 3 – 2cos(θ), the value of r at the origin is when θ = π/2 and θ = 3π/2

So, substituting this into the equation, we have

r = 3 – 2cos(θ)

r = 3 – 2cos(π/2)

r = 3 – 2(0)

r = 3 - 0

r = 3

So, in polar form, the points we require for the polar curve graph are

Find the graph of the polar curve in the attachment

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Answer:

C: The third graph.

Step-by-step explanation:

Took the quiz

Answer:

Roman numeral representing thousand (1000)

Round 8.879 to the nearest tenth is 8.9.

Rounding to the nearest tenth:

The combination of a whole number and a fraction, separated by a decimal point, is known as a decimal number in mathematics. The place value of the digits is divided by 10 starting from left to right. Determining the place values of tenths, hundredths, and thousands will therefore be aided by the decimal place value. For instance, the definition of the place value tenth is 1/10.

Think about the decimal 12.345.

Tenth place value in this case is 3.

By substituting the actual number with an approximation, the decimal value can be rounded. To the nearest integer, the decimal number 5.8 is rounded to 6, for instance. The decimal number can also be rounded to the nearest tenths place value. The first integer that appears after the decimal point is the tenth place value. Look at the hundredth number to round the decimal number to the nearest tenth. If it's more than 5, add one to the tenth value. Remove all the numbers that are present after the tenth place and leave the tenth place value alone if it is less than 5.

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The area of the given trapezium is 16x + 8

Area of trapezium:

The general formula to calculate the area (A) of a trapezium is written as,

A = ½ (a + b) h where,

where

a, b = bases of trapezium, and,

h = height

Given,

Here we have the figure of trapezium and the measures are written in it.

Now, we have to find the area of the trapezium.

According to the formula of the area of the trapezium,

We need the value of base and height.

By looking into the given figure, we have identified the value of

a = x cm

b = 3x + 2 cm

h = 8 cm.

Then the area of the trapezium is calculated as,

A = ½ (x + (3x +2)) 8

A = ½ (4x + 2) 8

A = 4 (4x + 2)

A = 16x + 8

Therefore, the area of the trapezium is 16x + 8.

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A system of linear equations to describe this situation is given by:

A + O = 11.

0.80A + 0.95O = 9.95.

Harry bought six (6) apples and five (5) oranges from this store.

In order to write a system of linear equations to describe this situation, we would assign variables to the amount of apples and oranges respectively, and then translate the word problem into algebraic equation as follows:

Since Harry bought a total of 11 pieces of fruit, we have:

A + O = 11              .....equation 1.

Since the cost of apples is $0.80 each and oranges cost $0.95 each, we have:

0.80A + 0.95O = 9.95      .....equation 2.

From equation 1, we have:

O = 11 - A                   .....equation 3.

Substituting equation 3 into equation 2, we have:

0.80A + 0.95O = 9.95

0.80A + 0.95(11 - O) = 9.95

Apples, A = 0.90/0.15

Apples, A = 6.

For the number of oranges, we have:

Oranges, O = 11 - A

Oranges, O = 11 - 6

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Complete Question:

At a store, apples cost $0.80 each and oranges cost $0.95 each. Harry buys some apples and oranges and spends $9.55 . He buys a total of 11 pieces of fruit.

Part a. Write a system of linear equations to describe this situation.

Part b. How many of each fruit did Harry buy?

Answer:

below

Step-by-step explanation:

(7p^9)^-4     a negative exponent means move the number up or down in the fraction

=   1 / [ (7 p^9) ^4  ]

           = 1 / ( 7^4 p^36) =   1/(2401 p^36)   <===don't omit the parentheses!

According to the concept of translation, the function of g(x) = x² + 2.

Translation:

The concept of translation is defined by using the function f(x) then f(x + a) is a horizontal translation of f(x)

If the value of a > 0 then a shift to the left of a units

If the value of  a < 0 then a shift to the right of a units

Given,

Here we have the function f(x) = x².

Now, we have to find  the equation of the graph of g(x) and how it change in corresponds to f(x).

While we looking the graph, the function f(x) has curved on the origin (0, 0).

Where the function g(x)  has curved the point (2,0).

Which tells the the graph is move left side by 2 units.

So, according to the rule of translation, the value of a is 2.

Then the function g(x) is written as,

=> g(x) = x² + 2.

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Answer:8 experiments

Step-by-step explanation:

she has 8 feet of copper and she needs one foot for each experiment she can do 8 experiments.

Answer: 247.97

Step-by-step explanation:

The nearest cent is two decimal places.

to get the equation of any straight line, we simply need two points off of it, let's use those two in red in the picture below

[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{12}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{12}-\stackrel{y1}{6}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{1}}} \implies \cfrac{ 6 }{ 2 } \implies 3[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{6}=\stackrel{m}{ 3}(x-\stackrel{x_1}{1}) \\\\\\ y-6=3x-3\implies {\Large \begin{array}{llll} y=3x+3 \end{array}}[/tex]

Answer:

There are two pairs of numbers:

-8      -18

and

18        8

Step-by-step explanation:

a * b = 144      EQ. 1

a - b = 10         EQ. 2

From EQ. 2:

a = 10 + b          EQ. 3

Replacing EQ. 3 in EQ. 1:

(10+b)b = 144

10*b + b*b = 144

b² + 10b - 144 = 0

b = {-10±√((10²)-(4*1*-144))} / (2*1)

b = {-10±√(100+576)} / 2

b = {-10±√676} / 2

b = {-10±26} / 2

b₁ = {-10-26} / 2 = -36/2 = -18

b₂ = {-10+26} / 2 = 16/2 = 8

a₁ - b₁ = 10

a₁ - (-18) = 10

a₁ + 18 = 10

a₁ = 10 - 18

a₁ = -8

a₂ - b₂ = 10

a₂ - 8 = 10

a₂ = 10 + 8

a₂ = 18

Check:

a₁ * b₁ = -8 * -18 = 144

a₂ * b₂ = 8 * 18 = 144

The time that it took Zane to reach the edge of the volcano is of:

35 seconds.

The variables that are graphed in this problem are listed as follows:

The edge of the volcano is the point at which the elevation relative to the volcano is of 0, hence the coordinate is:

y = 0.

y = 0 is the x-intercept of the function, which is the value of x at which the function crosses the x-axis.

Hence, looking at the graph, the time that it took Zane to reach the edge of the volcano is of:

35 seconds.

(as 35 is the x-intercept of the graph, and we previously explained that the edge of the volcano is the x-intercept).

The question is:

How long did it take Zane to reach the edge of the volcano?

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Answer:

17.8

Step-by-step explanation:

You have to add 9.2 and 63 and the subtract from 90. Hope this helped! <3

$225 was earned from the craft sales

and $40 was earned from the play.

Given, During a school carnival, students from the middle school raised money by selling crafts, food, game tickets, and school play admissions.

Of each dollar earned, $0.15 came from games. Craft sales earned 3 times as much as games. Food sales were 4 times the amount earned from the play.

Let the amount earned by play be x,

Now, Games earned = 0.15×500 = $75

Also, crafts earned 3×75 = $225

Now, as play earned x, then food earned 4x.

According to question,

x + 75 + 225 + 4x = 500

5x + 300 = 500

5x = 200

x = 40

So, the amount earned by Play be, $40

and the amount earned by Food be $160.

Hence, $225 was earned from the craft sales

and $40 was earned from the play.

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Answer:

P = 84

Step-by-step explanation:

Area = length* width or A = lw

We know that the length is 5 times its width which can also mean

[tex]l = 5*w[/tex] or [tex]l=5w[/tex]

Use the formula for area and replace [tex]l[/tex] with [tex]5w[/tex] and the total area with 245

[tex]A = lw\\245=5w(w)[/tex]

Multiply:

[tex]245=5w^{2}[/tex]

Divide by 5

[tex]49=w^2[/tex]

Square root of [tex]w^2[/tex]

[tex]\sqrt{49}=\sqrt{w^2}[/tex]

Simplify

[tex]7=w[/tex]

Now that we know w = 7 we can input this into the Perimeter formula

(P = 2l +2w)

P = 2(5*7)+2(7)   // Note: Remember [tex]l[/tex] = 5*w and w = 7

P = 84

There is also a formula for this type of problem, but this explanation is for when you forget. Hope that explains things :)  

Answer:

volume is approximately 73.6 to the nearest tenth

Step-by-step explanation:

The volume of a pipe is volume = π * radius² * length

diameter = 2.5

radius = 2.5/2 = 1.25 inches

volume = π * 1.25² * 15

volume = π * 1.5625 * 15

volume =  π * 23.4

which is approximately 73.6 to the nearest tenth

The money spent on the plates which are very expensive is: $133.44

Given,

The plates that mom bought are very fragile and expensive.

Each  plate costs $16.68.

Total plates bought by her mom are = 8

we are asked to determine the total cost of the plates bought = ?

let y represent the total cost of the plates.

and x represent the number of plates bought.

based on the conditions, we can formulate:

total cost pf plates = 16.38(number of plates bought)

⇒ y = 16.68x

we know that plates bought = 8

⇒ total cost is:

⇒ y = 16.68(8)

⇒ y = 133.44

Hence total cost of 8 plates is $133.44

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Answer:

C) The y-intercept of Function A is 1 unit greater than the y-intercept of Function B

Step-by-step explanation:

The y-int of Function A is (0,1), while the y-int of Function B is (0,0).

Answer:

C

Step-by-step explanation:

For Function A, the y-intercept occurs at 1. For B, it occurs at 0. Therefore, the y-intercept of Function A is 1 unit greater than the y-intercept of Function B.

A number line which represents the given inequality (-1 ≥ x) is: number line C.

In Mathematics, a number line can be defined as a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.

This ultimately implies that, a number line primarily increases in numerical value towards the right from zero (0) and decreases in numerical value towards the left from zero (0).

Next, we would determine a solution for the given inequality (-1 ≥ x) in order to graph it on a number line:

-1 ≥ x

x ≤ -1

In conclusion, we can logically deduce that the value of x is less than or equal to -1 as shown in number line C, which is shaded because of the less than or equal inequality symbol.

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Answer:

[tex]m=38[/tex]

Step-by-step explanation:

An interior angle and its corresponding exterior angle are supplementary, so:

[tex]3m-12+2m+2=180 \\ \\ 5m-10=180 \\ \\ 5m=190 \\ \\ m=38[/tex]

Answer:

Step-by-step explanation:

7 1/4 is what i think