Find the following answers:

The absolute maximum is 56 and absolute minimum values is 24 of a function f given by f(x) = 2x³−15x² + 36x +1 on the interval [1, 5] .

A function is defined as a relationship between a set of inputs, each having an output. In short, a function is a relationship between inputs where each input relates to exactly one output. Each function has a domain and a password domain or scope. Functions are usually denoted by f(x), where x is the input.

Given that:

f(x) = 2x³ −15x²+ 36x+ 1

f'(x) = 6x² −30x + 36

Putting f'(x) = 0

⇒ 6x² − 30x+ 36 = 0

⇒ x² −5x+6 = 0

⇒ (x−2)(x−3) = 0

⇒ x=2 or 3

We are given interval [1,5]

Hence, calculating f(x) at 2, 3, 1, 5,

f(2) = 29

f(3) = 28

f(1) = 24

f(5) = 56

Hence, absolute maximum value is 56 at x=5.

Absolute minimum value is 24 at x=1.

Complete Question:

Find the absolute maximum and absolute minimum values  of a function f given by f(x)=2x³−15x² + 36x +1 on the interval [1, 5] .

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A positive semi-definite operator's rayleigh quotient must have a minimum value of zero to be considered positive.

Let A be a non-positive definite positive semi-definite operator. This proves that a non-zero vector x exists such that Ax = 0. The Rayleigh quotient of A with regard to x may thus be defined as follows:

[tex]R(x) = (x^T)Ax / (x^T)x[/tex]

A is positive semidefinite, hence for each vector x, (xT)Ax >= 0 is true. However, there is a non-zero vector x such that Ax = 0 if A is not a positive definite. In this instance, the Rayleigh quotient's numerator is 0, and as a result, the Rayleigh quotient is also 0. Since there is always a non-zero vector x such that Ax = 0, we may infer that the Rayleigh quotient's lowest value for a positive semi-definite but not positive definite operator is 0.

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We can use trigonometry to solve this problem. Let's call the horizontal distance from the boat to the lighthouse "x". We can use the tangent function to find x:

tangent(8 degrees) = opposite / adjacent

tangent(8 degrees) = 148 / x

To solve for x, we can rearrange the equation:

x = 148 / tangent(8 degrees)

x ≈ 1041.87 feet

So the ship's horizontal distance from the lighthouse (and the shore) is approximately 1041.87 feet or 1041.87 rounded to the nearest hundredth of a foot if necessary.

Answer:

Your answer is 1053.07

Hope I helped!

Step-by-step explanation:

Important points to conduct a survey are; to gather information, make informed decisions, evaluate programs or services, identify trends, assess needs.

Surveys are conducted for a variety of reasons, including gathering information, making informed decisions, evaluating programs or services, identifying trends, and assessing needs. By using surveys, organizations can collect valuable data that can be used to inform decisions, improve programs or services, and better understand their target audience.

Surveys, also known as questionnaires, are used to gather information from a targeted group of individuals or a population. Surveys are an important tool for collecting data in a structured manner and can be used for a variety of reasons. Here are some of the reasons why surveys are conducted:

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If x is an integer, the least possible value of x is 4. So the option D is correct.

The triangle's third side should be less than the sum of the other two sides and more than the difference of the other two sides.

11 - 7.5 < x < 11 + 7.5

Simplify

3.5 < x < 18.5

So the value of the x is between 3.5 and 18.5.

From the option the value 4 and 5 lies between 3.5 and 18.5.

As we have to determine the least possible value of x, so the value of x should be 4. So the option D is correct.

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The complete question is:

The sides of a triangle have lengths 7.5, 11, and x. If x is an integer, what is the least possible value of x?

A. 1

B. 2

C. 3

D. 4

E. 5

After answering the provided question, we can conclude that slant height  of pyramid  [tex]= \sqrt((2/2)^2 + 5^2) = \sqrt(29) = 5.39 units.[/tex]

A pyramid is a polygon formed by connecting points known as bases and polygonal vertices. For each hace and vertex, a triangle known as a face is formed. A cone with a polygonal shape. A pyramid with a floor and n pyramids has n+1 vertices, n+1 vertices, and 2n edges. Every pyramid is dual in nature. A pyramid contains three dimensions. A pyramid is made up of a flat tri face and a polygonal base that come together at a single point known as the vertex. A pyramid is formed by connecting the base and peak. The edges of the base form triangle faces known as sides, which connect to the top.

            /\

          /    \

        /         \

      /______\

         5

         |

         |

         |

         |

         |

         2

The square pyramid in the diagram above has a two-unit-long square base and four five-unit-high triangular faces. The Pythagorean theorem can be used to calculate the slant height of each triangular face:

slant height [tex]= \sqrt((2/2)^2 + 5^2) = \sqrt(29) = 5.39 units.[/tex]

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The particular solution of Differential equation y" – 2y' + 2y = et sin x is yp = (1/2et - 1/2et cos(x))sin(x).

We assume the particular solution is of the form of given differential equation is

yp = (Aet + Bcos(t))sin(x) + (Cet + Dsin(t))cos(x)

where A, B, C, and D are constants to be determined.

Taking the first and second derivative of yp with respect to t:

yp' = Aet sin(x) - Bsin(t)sin(x) + Cet cos(x) + Dcos(t)cos(x)

yp'' = Aet sin(x) - Bcos(t)sin(x) - Cet sin(x) + Dsin(x)cos(t)

Substituting these into the differential equation and simplifying, we get:

(et sin x) = (A - C)et sin(x) + (B - D)cos(x)sin(t)

Since et sin x is not a solution to the homogeneous equation, the coefficients of et sin x and cos(x)sin(t) on both sides of the equation must be equal. Therefore:

A - C = 1 and B - D = 0

Solving for A, B, C, and D, we get:

A = 1/2, B = 0, C = -1/2, D = 0

So the particular solution is:

yp = (1/2et - 1/2et cos(x))sin(x)

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Answer:

4.3

Step-by-step explanation:

Answer:

Step-by-step explanation:

1st find v solving 3v + 1 = 7

3v + 1 = 7

3v = 7 - 1

3v = 6

v = 6 : 3

v = 2

v + 8 =

replace v with 2

2 + 8 = 10

Answer:

10

Step-by-step explanation:

Solve for the value of the variable, v, in the given equation of 3v + 1 = 7, by isolating the variable. Do the opposite of PEMDAS.

PEMDAS is the order of operations, and stands for:

Parenthesis

Exponents (& Roots)

Multiplications

Divisions

Additions

Subtractions

~

First, subtract 1 from both sides of the equation:

[tex]3v + 1 = 7\\3v + 1 (-1) = 7 (-1)\\3v = 7 - 1\\3v = 6[/tex]

Next, divide 3 from both sides of the equation:

[tex]3v = 6\\\frac{3v}{3} = \frac{6}{3} \\v = \frac{6}{3} \\v = 2[/tex]

Then, plug in 2 for v in the first given expression:

[tex]v + 8\\=(2) + 8\\=10[/tex]

10 is your answer for v + 8 when 3v + 1 = 7.

~

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Answer: To determine the number of accidents on highways and rural roads after 4 years, we need more information. The given data only tells us about the distribution of accidents in a sample of 100 accidents investigated, but it doesn't provide any information about the rate of change or trend of accidents over time.

Assuming that the rate of accidents on highways and rural roads remains the same, we can make a projection based on the given data. If 60% of the road accident deaths occur on highways and 40% on rural roads, we can estimate the number of accidents on highways and rural roads after 4 years as follows:

Number of accidents on highways after 4 years = 80 * (100/60) = 133.33 (rounded to 133)

Number of accidents on rural roads after 4 years = 20 * (100/40) = 50

Note that this is only a projection based on the assumption that the rate of accidents remains the same. In reality, the number of accidents can vary depending on various factors such as changes in traffic volume, weather conditions, road infrastructure, and driver behavior, among others. Therefore, this projection should be taken as an estimate and not as an accurate prediction.

Step-by-step explanation:

Answer:

Hence, factors are 3x,(x−4y).

Step-by-step explanation:

We need to factorise 3x 2 −12xy

Here we can take 3x common.

Thus we have 3x 2−12xy=3x(x−4y)

Hence, factors are 3x,(x−4y).

Answer: 3x ( x - 4y )

Step-by-step explanation:

Factorizing 3x²-12xy

3x ( x - 4y )

Answer:

1.Neither

2.Perpendicular

3.Perpendicular

4.Neither

5.Perpendicular

6.Perpendicular

7.Neither

8.Neither

9.Perpendicular

10.Neither

11. Perpendicular

12.Perpendicular

13.Neither

14.Neither

15.Neither

16.Neither

17.Parallel

18.Neither

here are the answers in order from top to bottom

Answer:

True.

Step-by-step explanation:

Alternate interior angles are congruent, meaning they have equal measure. When we have two parallel lines that are intersected by a transversal, and again my parallel lines are identified by using the same number of arrows, then two special angles are congruent and that is alternate interior angles.

Answer:

Let's call the unknown number "x".

According to the problem:

x - (-17) = 25x

Simplifying:

x + 17 = 25x

Subtracting x from both sides:

17 = 24x

Dividing by 24:

x = 17/24

Therefore, the unknown number is 17/24.

As the triangles are similar to each other, using congruent theorem, we get the value of side JK = 63.8.

Comparable triangles are those that resemble one another but may not be precisely the same size. Comparable items are those that share the same shape but differ in size.

This shows that when shapes are amplified or demagnified, they superimpose one another. This feature of similar shapes is often known as "similarity".

As per the triangles,

Let JK be = x.

GF/GH = JI/JK

⇒ 11/18 = 36 /x

⇒ x = 36 × 18/11

⇒ x = 63.8.

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The correct option A) There is a cluster, and as x decreases, y increases.

The table represents a set of data containing two variables, x and y. By analyzing the data, we can observe a cluster of values around x = 4 with corresponding y values in the range of 42-45. As we move towards smaller x values, there is a general trend of increasing y values. However, there are a few outliers. Based on these observations, statement A is the most accurate description of the data in the table. It is important to note that the accuracy of the statement is limited to the given data, and further analysis or additional data may reveal a different trend or pattern.

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Complete question:

The table below shows a set of data. Which statement about the table is true?

x: 1.6, 1.9, 2.3, 3.4, 3.8, 4.2, 4.3, 4.6, 4.8.

y: 39, 38, 42, 40, 41, 44, 42, 45, 44

Which statement about the table is true?

A) There is a cluster, and as x decreases, y increases.

B) There is a cluster, and as x increases, y increases.

C) There is not a cluster, and as x increases, y increases.

D) There is not a cluster, and as x decreases, y increases.

The decimal number 555 is written as 4210 in base-5.

Answer:  [tex]555_{10} =4210_{5}[/tex]

Step-by-step explanation:

Decimal to base five conversion

here

                                    D   Q            Remainders

                                    5  |555               0

                                     5  |111                   1

                                      5  |22                  2

                                       5  |4                     4

                                             0  

Step-by-step explanation:

7eh8heusvush0wio0w92726 2is 3the world ydgugd8jd8djkd0jd9jd8hd7hd

Answer:

gdiduusuehfuehvv

Step-by-step explanation:

bbzbhshxhdhhd are the best and my mom I WINNNNNN you want it to be over with you guys to come in and your mom are doing ghhdhhsuwuwhsh and your family are doing well and your family are doing well and your family are doing well and your family are doing well and your family and my wife was the best and I WINNNNNN and my mom are doing ghhdhhsuwuwhsh and what is the only ones I WINNNNNN with the kids I WINNNNNN and I will be over and I can do i and eat early for you and Darshanie and I WINNNNNN and my friend and your mom and my mom ever had a great day I love ever and your mom are the kids I will get you a great mom and I will send you a link and I WINNNNNN with the only ones I WINNNNNN with you don't need me I can get it and I will be over and your mom and your mom I will send it out tomorrow night I will send it out tomorrow night with you guys and I can send the best ones that have to do i I will send you and Darshanie and your mom I will send it and your family and I WINNNNNN and my friend are doing errands to run out to do i you guys and I WINNNNNN you want me I will send you and Darshanie is done now we have a great day for a great mom I will be over there and I WINNNNNN you and everyone and my friend and my friend and what time do the kids have a whole new world we live together I will be home tomorrow night with the only one that has to wait until the way home tomorrow morning to run out of wo you guys to run out with the best ones that w with the kids I will get you guys want me when we good day for you it

Answer: A positive whole number multiplied by any whole number will remain positive. In the case of the squares of 4, it will always end in a 6 which is a positive number.

Step-by-step explanation:

4^2= 16

16^2 = 256

256^2= 65,536

etc.

The slope of the sole sequence's perpendicular line is [tex]-\frac{3}{2}[/tex].

As two lines meet at right angles, the word "perpendicular" refers to an angle. Every direction, including up and down, across, and side to side, can be faced by a pair of perpendicular lines.

A perpendicular is a straight line in mathematics that forms a correct angle (90 °) with another line. In other words, two lines are parallel to one another if they connect at a right angle.

[tex]y = mx + b[/tex], where [tex]m[/tex] is the slope:

[tex]4x - 6y = -24[/tex]

[tex]-6y = -4x - 24[/tex]

[tex]y = (4/6)x + 4[/tex]

[tex]y = (2/3)x + 4[/tex]

So the slope of the given line is [tex]2/3[/tex].

To find the slope of a line perpendicular to this line, we need to take the negative reciprocal of [tex]2/3[/tex]:

[tex]-1/(2/3) = -3/2[/tex]

Therefore, the slope of a line perpendicular to the given line is [tex]-\frac{3}{2}[/tex].

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Answer: 2/13

Step-by-step explanation:

There are four jacks and four tens in a standard deck of 52 cards. However, the jack of spades and the ten of spades are counted twice since they are both a jack and a ten. Therefore, there are 8 cards that are either a jack or a ten, and the probability of drawing one of these cards at random is:

P(Jack or Ten) = 8/52 = 2/13

So the answer is 2/13.

Step-by-step explanation:

a probability is airways the ratio

desired cases / totally possible cases

in each of the 4 suits there is one Jack and one 10.

that means in the whole deck of cards we have

4×2 = 8 desired cases.

the totally possible cases are the whole deck = 52.

so, the probability to draw a Jack or a Ten is

8/52 = 2/13

The first limit,  [tex]\lim_{x\to \→-2^- } -3(x+2)/x²+4x+4[/tex]  , evaluates to negative infinity, while the second limit, [tex]\lim_{ x\to \-2^+}-3(x+2)/x²+4x+4[/tex] , evaluates to positive infinity.

Function in maths is a relation between two sets of values. It is a type of mathematical equation in which each input value has a unique output value. In a function, each input value must correspond to only one output value. This means that for any input value, the output must be the same.

This indicates that the function has a vertical asymptote at x=-2.

In order to understand why this is the case, we can first rewrite the function as follows:

f(x) = -3(x+2)/(x+2)(x+2)

The denominator of the function is (x+2)(x+2), which has a double root at x=-2. This means that the denominator is equal to zero when x=-2. As a result, the function f(x) will have a vertical asymptote at x=-2, since the denominator will be equal to zero and the function will approach negative or positive infinity. This is why the two limits mentioned above both evaluate to either negative or positive infinity.

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The limit of the given functions are:

[tex]\lim_{x \to \--2^-}[/tex]-3(x+2)/ x²+4x+4 = positive infinity

[tex]\lim_{x \to \--2^+}[/tex] -3(x+2)/ x²+4x+4 = negative infinity

[tex]\lim_{x \to \--2[/tex] -3(x+2)/ x²+4x+4 = Undefined

Function is a relation between two sets of values. In a function, each input value must correspond to only one output value. This means that for any input value, the output must be the same.

[tex]\lim_{x \to \--2^-}[/tex]-3(x+2)/ x²+4x+4

= -3(-2+2)/(-2)²+4(-2)+4

= -3/0 + 8 + 4

= +∞  (infinity)

[tex]\lim_{x \to \--2^+}[/tex] -3(x+2)/ x²+4x+4

= -3(-2+2)/(-2+2)²+4(-2+2)+4

= -3/4 + 0 + 4

= -∞

[tex]\lim_{x \to \--2[/tex] -3(x+2)/ x²+4x+4

= -3(-2+2)/(-2+2)²+4(-2+2)+4

= -3/0 + 0 + 4

= Undefined

Therefore, the limit of the functions given are:

[tex]\lim_{x \to \--2^-}[/tex]-3(x+2)/ x²+4x+4 = +∞

[tex]\lim_{x \to \--2^+}[/tex] -3(x+2)/ x²+4x+4 = -∞

[tex]\lim_{x \to \--2[/tex] -3(x+2)/ x²+4x+4 = Undefined

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if we  that Abby spent 50% of her time on School, 30% on Work, and 20% on Sleep, we can estimate that she spent:

100% - (50% + 30% + 20%) = 100% - 100% = 0% on Other.

If Abby divided her time into four categories (School, Work, Other, and Sleep), the percentage she spent on Other would be 100% less the sum of the percentages she spent on School, Work, and Sleep.

So, assuming Abby spending 50% of her time at school, 30% at work, and 20% sleeping, we can estimate she spent:

On Other, 100% - (50% + 30% + 20%) = 100% - 100% = 0%.

However, this is just a guess based on assumptions about how Abby spent her time. It's difficult to provide a more accurate estimate without more information.

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The answer of the given question based on the compound interest to find  total amount Nicole ended up paying for the machinery and the interest did Nicole pay on the loan is (A) the total amount Nicole ended up paying for the machinery is $14,342.52. (B) Nicole paid $2,342.52 in interest on the loan.

Compound interest is type of interest that is calculated not only on initial principal amount but also on accumulated interest from previous periods. In other words,  interest earned in each period is added to  principal amount, and  interest for the next period is calculated on  new, larger principal amount.

Compound interest can be thought of as "interest on interest" and is used in many financial transactions, like loans, investments, and savings accounts.

(a) The total amount Nicole ended up paying for the machinery is the sum of her down payment and all of her monthly loan payments over the 3-year period. We can calculate this as follows:

Total amount paid = Down payment + (Monthly payment x Number of payments)

Total amount paid = 1200 + (365.07 x 36)

Total amount paid = 1200 + 13142.52

Total amount paid = $14,342.52

Therefore, the total amount Nicole ended up paying for the machinery is $14,342.52.

(b) To calculate how much interest Nicole paid on the loan, we first need to calculate the total amount of the loan. We can do this by subtracting her down payment from the total cost of the machinery:

Total loan amount = Total cost of machinery - Down payment

Total loan amount = $13,200 - $1,200

Total loan amount = $12,000

Next, we can calculate the total amount of interest paid over the 3-year period by subtracting the total loan amount from the total amount paid:

Total interest paid = Total amount paid - Total loan amount

Total interest paid = $14,342.52 - $12,000

Total interest paid = $2,342.52

Therefore, Nicole paid $2,342.52 in interest on the loan.

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The final answer is $\frac{1}{12}$.

We need to evaluate the triple integral $\iiint e y , dv$ over the region $e$ bounded by the planes $x = 0$, $y = 0$, $z = 0$, $x + y + z = 1$, and $x + y = 2$.

To evaluate this triple integral, we can use the limits of integration obtained by considering the intersection of the planes. From the plane equations $x+y+z=1$ and $x+y=2$, we can solve for $z$ and $x$ in terms of $y$ to obtain the limits:

0≤z≤1−x−yand0≤x≤2−y.

Since $e$ is bounded by the planes $x=0$ and $y=0$, we have $0 \leq x \leq 2-y$ and $0 \leq y \leq 2$. Thus, we can set up the triple integral as follows:

Next, integrating with respect to $x$, we obtain∫

02[22−22]

02−∫ 02 [eyx− 2eyx 2 − 2ey 2 x​ ] 02−ydy.Simplifying this expression, we get

∫02(2−522+32)

.∫ 02​ (2ey− 25​ ey 2 + 2ey 3 )dy.

Evaluating the integral, we get the final answer of $\frac{1}{12}$.

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question:-Evaluate the triple integral $\int!!\int!!\int e y ,dv$, where $e$ is bounded by the planes $x = 0$, $y = 0$, $z = 0$, $x + y + z = 1$ and $x + y = 2$.

Answer: 62°

Step-by-step explanation:

All angles of a triangle add up to 180°.

So, add up all the other angles.

15 + 25 + 39 = 79

180 - 79 = 101

Then, to find x, subtract 39 from 101, to get 62!

Answer:

1 cubic meter = 1000000 cm cubed

Step-by-step explanation:

[tex]1m^3*10^6=1000000cm^3[/tex]

Answer:

1 cubic meter = 10000000 cm cube