Find the absolute extrema of f(x) =3x? -2x+ 4 over the interval [0,5].
Find the absolute extrema of f(x) =3x? -2x+ 4 over the interval [0,5].

I'm sorry the photo is on a side. I'm too lazy to text it on here lol

Answer:

irrational

Step-by-step explanation:

The area of R is ln(4) - ln(√2) and the value of k is √2.

a) To find the area of the region R, we need to find its definite integral with respect to x. Using substitution, we can write the integral as follows:

Let u = \(x^{2}\) + 2, du/dx = 2x, dx = du/2x

Area of R = ∫[0,√6] x/(\(x^{2}\) + 2) dx = ∫[2,8] (1/2) du/u = (1/2) ln(u) evaluated from 2 to 8 = (1/2) ln(8) - (1/2) ln(2) = ln(4) - ln(√2)

b) The line x = k divides the region R into two regions of equal area if the definite integral of R with respect to x from 0 to k is equal to the definite integral of R with respect to x from k to √6.

Letting k = x in the definite integral, we have:

∫[0,k] x/( \(x^{2}\)  + 2) dx = ∫[k,√6] x/( \(x^{2}\)  + 2) dx

(1/2) ln(\(k^{2}\) + 2) - (1/2) ln(2) = (1/2) ln(6 - \(k^{2}\) ) - (1/2) ln(2)

Solving for k, we get:

ln( \(k^{2}\)  + 2) = ln(6 - \(k^{2}\) )

\(k^{2}\) + 2 = 6 - \(k^{2}\)

2 \(k^{2}\)  = 4

k = ±√2

Since k must be in the first quadrant, k = √2.

So, the line x = √2 divides the region R into two regions of equal area.

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Answer:

solution = (3, 11)

Step-by-step explanation:

4x + 2y = 10

*subtract 4x from both sides*

2y = -4x + 10

*divide by 2* --> y = -2x +5

12x - 3 y = 3

*add 3y to both sides*

12x = 3y + 3

*subtract 3 form both sides*

12x - 3 = 3y

*divide by 3* --> y = 4x - 3)

2x + 5 = 4x - 1

*subtract 2x form both sides*

5 = 2x -1

*add 1 to both sides*

6 = 2x

*divide by 2x* --> x = 3

y = 2(3) + 5   (plug in 3 for x to solve for y)

y = 6 + 5

y = 11

Slope can be found using the following equation:

slope (m) = \(\frac{y_2 - y_1}{x_2 - x_1}\)

7) Let:

\((x_1 , y_1) = (-1 , -11)\\(x_2 , y_2) = (-6 , -7)\)

Plug in the corresponding numbers to the corresponding variables:

m = \(\frac{-7 - (-11)}{-6 - (-1)} = \frac{-7 + 11}{-6 + 1} = \frac{4}{-5} = -\frac{4}{5}\)

Slope: \(-\frac{4}{5}\)

8) Let:

\((x_1 , y_1) = (-7 , -13)\\(x_2 , y_2) = (1 , -5)\)

Plug in the corresponding numbers to the corresponding variables:

m = \(\frac{-5 - (-13)}{1 - (-7)} = \frac{-5 + 13}{1 + 7} = \frac{8}{8} = 1\)

Slope: \(1\)

9) Let:

\((x_1 , y_1) = (-5 , 3)\\(x_2 , y_2) = (8 , 3)\)

Plug in the corresponding numbers to the corresponding variables:

m = \(\frac{3 - (3)}{8 - (-5)} = \frac{0}{8 + 5} = \frac{0}{13} = 0\)

Slope: \(0\)

10) Let:

\((x_1 , y_1) = (3 , -2)\\(x_2 , y_2) = (15 , 7)\)

Plug in the corresponding numbers to the corresponding variables:

m = \(\frac{7 - (-2)}{15 - 3} = \frac{7 + 2}{15 - 3} = \frac{9}{12}\)

Simplify the slope. Divide common factors from both the numerator and denominator:

\((\frac{9}{12})/(\frac{3}{3} ) = \frac{3}{4}\)

Slope: \(\frac{3}{4}\)

11) Let:

\((x_1 , y_1) = (-5 , -10)\\(x_2 , y_2) = (-5 , -1)\)

Plug in the corresponding numbers to the corresponding variables:

m = \(\frac{-1 - (-10)}{-5 - (-5)} = \frac{-1 + 10}{-5 + 5} = \frac{9}{0} =\) undefined.

Slope: undefined

12) Let:

\((x_1 , y_1) = (-4 , -2)\\(x_2 , y_2) = (-12, 16)\)

Plug in the corresponding numbers to the corresponding variables:

m = \(\frac{16 - (-2)}{-12 - (-4)} = \frac{16 + 2}{-12 + 4} = \frac{18}{-8} = -\frac{18}{8} = ((-\frac{18}{8})/( \frac{2}{2}) = -\frac{9}{4}\)

Slope: \(-\frac{9}{4}\)

~

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These professionals have the expertise and knowledge regarding the specific requirements and policies of academic programs. They can provide accurate and up-to-date information about class registration, course sequencing, major requirements, and any relevant academic policies or procedures. Academic advisors can guide students in making informed decisions about their course schedules, ensuring that they meet the necessary requirements for their chosen majors or academic goals.

It is recommended to reach out to the academic advising department at your institution to get personalized guidance and support regarding class registration and major requirements.

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Answer:(6,14)

Step-by-step explanation: x+y≤22   &   .05+.10y≥ 1.40

y≤22-x                                                        y≥14- 1/2x

The system of the inequalities will be 0.05x + 0.10y ≥ 1.40 and x + y ≤ 22. And the graph is given below.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

Anna has a nickels and y dimes. She has at most 22 coins worth a minimum of $1.40 combined.

Let x be the number of nickels and y be the number of dimes. Then the equation is given as,

0.05x + 0.10y ≥ 1.40

x + y ≤ 22

The system of the inequalities will be 0.05x + 0.10y ≥ 1.40 and x + y ≤ 22. And the graph is given below.

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The slope of the least-squares regression line is 4.340, which represents the rate of change in the standardized test score (y) for each unit increase in the age of an elementary school student (x). The y-intercept is -13.586, which represents the estimated score on the standardized test when the age of the student is zero.

The least-squares regression line is a mathematical model that best fits the relationship between the age of an elementary school student (x) and their score on a standardized test (y). In this case, the slope of 4.340 indicates that for each additional year in age, the student's standardized test score is expected to increase by 4.340 points. This positive slope suggests a positive correlation between age and test performance, implying that older students tend to have higher scores.

On the other hand, the y-intercept of -13.586 indicates the estimated test score when the age of the student is zero. However, in practical terms, it may not have a meaningful interpretation since it is highly unlikely for an elementary school student to be aged zero. It is important to note that extrapolating beyond the range of available data can lead to unreliable predictions.

In conclusion, the slope of 4.340 signifies the rate of change in test scores per unit increase in age, while the y-intercept of -13.586 represents the estimated score when the student's age is zero, albeit this value may not hold practical significance in the context of elementary school students.

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Answer:

x≥-2

Step-by-step explanation:

dark circle means equality and all numbers are greater than -2

it can also be written as

[-2,∞)

Answer:2

Step-by-step explanation:

▬▬▬▬▬▬▬▬▬▬▬▬▬

→ Base = 15m

→ Height = 6m

→ Sides = 9m

→ Perimeter of the triangle

→ Perimeter of triangle = Sum of all sides

= a + b + c

= 15 + 9 + 9

= 33 m

▬▬▬▬▬▬▬▬▬▬▬▬▬

Answer:

B and C are correct

Step-by-step explanation:

1 cm=10 mm

1 mm=10 m

10 cm=1 kmm

The generated value X of the Exponential random variable is approximately 2.3817. This means that the Exponential random variable with an average lifetime of 5.8 years and a generated standard uniform value of 0.5647 has a value of approximately 2.3817 years. The answer is 2.3817.

To find the generated value X of the Exponential random variable, we can use the formula X = - (1 / λ) * ln(U), where λ is the rate parameter and U is the given standard uniform value.

To start, we need to calculate the rate parameter λ. The average lifetime of the Exponential distribution is given as 5.8 years, which means that the mean or expectation E(X) is also 5.8 years. We can calculate λ as follows:

E(X) = 1 / λ

5.8 = 1 / λ

λ = 1 / 5.8

Now, we can substitute the values of λ and U into the formula to find the generated value X:

X = - (1 / λ) * ln(U)

X = - (1 / (1/5.8)) * ln(0.5647)

X = - 5.8 * ln(0.5647)

X ≈ 2.3817

Therefore, the generated value X of the Exponential random variable is approximately 2.3817. This means that the Exponential random variable with an average lifetime of 5.8 years and a generated standard uniform value of 0.5647 has a value of approximately 2.3817 years. The answer is 2.3817.

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The solution set of the example inequality, 2•x + 3 ≤ -3, is the option;

A possible inequality that can be used to get one of the options, (the inequality is not included in the question) is as follows;

Solving the above inequality, we have;

2•x + 3 ≤ -3

2•x ≤ -3 - 3 = -6

2•x ≤ -6

Therefore;

x ≤ -6 ÷ 2 = -3

x ≤ -3

Which gives;

-∞ < x ≤ -3 in interval notation is (-∞, -3]

The solution set of the inequality, 2•x + 3 ≤ -3, is therefore the option;

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Can't see full image

Answer:

28:12

Step-by-step explanation:

When we take 7 and 3 and multiply them both by 4 we get 28 and 12.

hope this helps!

if s and l are independent, both should be accepted False.

If s and l are independent, it means that the occurrence of one event does not affect the occurrence of the other event. However, this does not necessarily mean that both events should be accepted. It depends on the specific criteria and requirements for acceptance of each event.

Therefore, the statement "if s and l are independent, both should be accepted" is false.


If s and l are independent, it means that they have no direct influence on each other. However, this does not necessarily mean that both should be accepted. The acceptance of s and l will depend on their individual merits and the specific context or criteria being considered.

The independence of s and l does not automatically imply that both should be accepted. Instead, evaluate each one separately based on the relevant factors.

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True. If s and l are independent variables, then accepting one does not affect the acceptance or rejection of the other. Therefore, both can be accepted if they meet the necessary criteria.

However, it's important to note that this assumption of independence should be confirmed through statistical analysis before making any conclusions.

If s and l are independent variables, then accepting one does not affect the acceptance or rejection of the other. This means that both can be accepted if they meet the necessary criteria. However, it's important to ensure that this assumption of independence is valid before making any conclusions. The independence of the variables can be tested through statistical analysis. Therefore, it's essential to examine the relationship between s and l before accepting or rejecting them. In general, if s and l are independent, then both can be accepted without any issues.

In conclusion, if s and l are independent variables, then both can be accepted. However, the independence assumption should be confirmed before making any decisions. This can be achieved through statistical analysis, which is a crucial step in data analysis.

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Step-by-step explanation: Okay so ther is 2 blue and 1 red and 5 white. 1/8 chance you would get red and then 2nd try 2/8 chance so... Im pretty sure its 1/32

Answer:

22 times.

Step-by-step explanation:

3 minutes = 180 seconds.

180 divided by 8 = 22.5

The light only flashed 22 times.

Answer: 5y + 2x - 3

(In simplest form)

750=y²-5y is the equation that can be used to solve for y, the length of the room.

The area of Rectangle is length times of width.

Given that the area of a rectangular room is 750 square feet.

The width of the room is 5 feet less than the length of the room.

Let y be the length of the room

Width=y-5.

Area=Length×Width

750=y(y-5)

750=y²-5y

Hence, 750=y²-5y is the equation that can be used to solve for y, the length of the room.

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There will  total of 987 outcomes involving at least 8 heads when a coin is tossed ten times

We will be using the formula of combination for calculating the outcomes. Since we have tossed a coin 10 times , so total number of possible outcomes: 2¹⁰ = 1024 .Since at least 8 heads means we will get tail, exactly after two tosses exactly. we will find the outcomes for no head, one head, and 2 head .So, the number of outcomes involving will be 8 heads :

= 1024 - ⁸C₀ ( + ⁸C₁ + ⁸C₂ )

= 1024 - ( 1+8+28) = 1024 - 37

= 987

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Answer:

x = -2, y = -5 and x = 5, y = 2

Step-by-step explanation:

The slope-intercept equation of line is -1 and equation will be y = -x - 1.

What is the slope?

m = (y2 - y1) / (x2 - x1) is the formula for calculating slope from two points on a line, (x1, y1) and (x2, y2). Here,

m = the line's slope

x1 is equal to the initial point's x-coordinate.

y1 is the first point's y-coordinate.

x2 is equal to the second point's x-coordinate.

The second point's x-coordinate is equal to y2.

x1 = -3, y1 = 4; x2= -2, y2=3

m = (3-4)/(-2 - (-3))

= -1 / (-2+3)

= -1/1

m = -1

Substitute the value in given equation:

y = -x + (-1)

y = -x - 1

Hence, the slope-intercept equation of line is -1 and equation will be y = -x - 1.

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Answer:

\(\textsf{If\;\;$A + B + C = \pi$\;\;and\;\;$\sin A = \sin B\sin C$,\;\;then\;\;$\cot B + \cot C = 1$.}\)

Step-by-step explanation:

We are given that:

\(\textsf{Equation 1:} \quad A + B + C = \pi\)

\(\textsf{Equation 2:} \quad \sin A = \sin B \sin C\)

We need to prove that:

\(\cot B + \cot C = 1\)

Begin by rearranging the first equation to isolate (π - A):

\(\implies \pi-A=B+C\)

Use this and the identity sin(A) = sin(π - A) to rewrite sin(A) in terms of B and C:

\(\implies \sin A=\sin(\pi - A)\)

\(\implies \sin A=\sin(B+C)\)

Expand sin(B + C) using the identity sin(x + y) = sin(x)cos(y) + cos(x)sin(y):

\(\implies \sin A=\sin(B+C)\)

\(\implies \sin A=\sin B \cos C +\cos B \sin C\)

Given that sin(A) = sin(B)sin(C), substitute the two equations for sin(A) to create an equation in B and C only:

\(\implies \sin B \cos C + \cos B\sin C=\sin B \sin C\)

Divide both sides of the equation by sin(B)sin(C):

\(\implies \dfrac{\sin B \cos C + \cos B \sin C}{\sin B \sin C}=\dfrac{\sin B \sin C}{\sin B \sin C}\)

\(\implies \dfrac{\sin B \cos C}{\sin B \sin C} + \dfrac{\cos B \sin C}{\sin B \sin C}=1\)

Cancel the common factors:

\(\implies \dfrac{\cos C}{ \sin C} + \dfrac{ \cos B}{\sin B}=1\)

Use the identity cos(x)/sin(x) = cot(x):

\(\implies \cot C +\cot B=1\)

Rearrange the terms on the left side of the equation:

\(\implies \cot B+ \cot C=1\)

Therefore, we have proved that cot(B) + cot(C) = 1, given that A + B + C = π and sin(A) = sin(B)sin(C).

The theme of each epic poem is sublime, elegant, and has universal significance. It may not be an insignificant theme, which is only limited to the personality or the locality of the poet. It deals with the entire humanity.

Epic poem

An epic poem, or simply an epic, is a lengthy narrative poem typically about the extraordinary deeds of extraordinary characters who, in dealings with gods or other superhuman forces, gave shape to the verse mortal universe their descendants.

'epic' could refer to all poetry in dactylic hexameter , which included not only Homer but also the wisdom poetry of Hesiod, the utterances of the Delphic oracle.

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