Find the equation of a line containing the points (5,1) and (5,−4).

Indefinite integral using integration by parts from x2 ln(x) dx is

\(\frac{1}{3}\) \(X^{3\\}\) (ln(x) - \(\frac{1}{3}\)) + C

The given choice of u and dv

∫ \(x^{2} ln(x) dx\)

we can use the formula

∫ u dv = uv - ∫ v du

Then split the component

u =  \(ln(x)\)     du = \(\frac{1}{x}\)\(dx\)

dv = \(x^{2}\)         v = \(\frac{1}{3}x^{3}\)

∫ u dv = uv - ∫ v du

∫ \(x^{2} ln(x) dx\)   =  ln(x) \(\frac{1}{3}x^{3}\) - ∫ \(\frac{1}{3}x^{3}\) \(\frac{1}{x}\) dx

                    = \(\frac{1}{3}x^{3}\) ln(x) - \(\frac{1}{3}\) ∫ \(x^{3}\) \(\frac{1}{x}\) dx

                    = \(\frac{1}{3}x^{3}\) ln(x) - \(\frac{1}{3}\) ∫ \(x^{3} . x^{-1}\) dx

                    = \(\frac{1}{3}x^{3}\) ln(x) - \(\frac{1}{3}\) ∫ \(x^{2}\) dx     ----> ∫ \(x^{2}\) dx = \(\frac{1}{3} x^{3} + C\)

                    =  \(\frac{1}{3}x^{3}\) ln(x) - \(\frac{1}{3}\) \(\frac{1}{3} x^{3} + C\)

                    = \(\frac{1}{3} x^{3} ( ln(x) - \frac{1}{3} ) + C\)

Therefore Indefinite integral using integration by parts

∫ \(x^{2} ln(x) dx\)  is  \(\frac{1}{3} x^{3} ( ln(x) - \frac{1}{3} ) + C\)

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Answer:

how much is one pound of grapes you have to divide 15 by that number

The magnitute of a vector can be calculated by calculating the distance beteen its endpoints.

The vector starts at point (2, 5) and ends at point (-3, -2), so the distance between them is:

To calculate the direction, we must calculate the angle from the x-axis, just like in the unit circle.

Firstly, we calculate using the arc tangent to calculate the angle in the first quadrant, but then we need to figure out the actual value considering the quadrant the vector is.

Firstly, we calculate the x and y differences from the start point to the endpoint:

So, we calculate the arctanent of the absolute values of these differences:

Now, since the differences of the x and y coordinates of the endpoint are negative, this means that the vector is in the third quadrant, so we need the equivalent angle that gives this tangent but is in the third quadrant.

The tangent values repeat every 180°, so the value that gives the same tangent and is in the third quadrant is:

So, the vector has magnitute of approximately 8.602 and a direction of approximately 234.462°, which second alternative.corresponds to the

Answer:

Marilyn Iturri

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

1212112

Answer:

yeah every time Charlie takes 30 dollars more than previous salary

To find the average rate of change of the function f(x) = 1.85x^2 over the interval 10 ≤ x ≤ 20, we need to find the difference in the function values at the endpoints of the interval and divide by the length of the interval.

The function value at x = 10 is:

f(10) = 1.85(10)^2 = 185

The function value at x = 20 is:

f(20) = 1.85(20)^2 = 740

The length of the interval is:

20 - 10 = 10

So the average rate of change of the function over the interval 10 ≤ x ≤ 20 is:

(f(20) - f(10)) / (20 - 10) = (740 - 185) / 10 = 55.5

Rounding to the nearest tenth, the average rate of change of the function over the interval 10 ≤ x ≤ 20 is approximately 55.5.

Answer: 22

Step-by-step explanation:

The linear equation to determine the cost to ship 8 packages is x=22.

Given that, Jeff's shipping service charges $8 for the first package and $2 for each additional package.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form linear equation is Ax+B=0.

Let the total charge be $x.

Now, x=8+(8-1)2

⇒x=8+14

⇒x=22

Therefore, the linear equation to determine the cost to ship 8 packages is x=22.

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Let's begin by identifying key information given to us:

Reflection is done over the line y = x, we have:

Explanation:

Tangent lines touch the circle at exactly one point.

Answer:

b. False

Step-by-step explanation:

Let A and B be matrices with the rows a1a2 and b1b2 respectively. Suppose the other two columns are c1,c2 and d1d2 having a value equal to zero.

A=   a1   c1                      B=  b1       d1

      a2  c2                            b2      d2

Multiplying

AXB= a1b1+c1b2         a1d1+c1d2

          a2b1+c2b2       a2d1+c2d2

AB=║ a1b1         0║

      ║a2b1        0 ║

Hence the given statement is false.

Each column of AB is a linear combination of the ROWS of A using weights from the corresponding column of B.

The matrix multiplication is "row by column" i.e the rows of the first matrix are multiplied with the columns of the second matrix.

The rows are also used in multiplication.

Answer:

I think the correct answer is A

Answer:

A

Step-by-step explanation:

Plot the points on the coordinate plane in order to find out which one is the correct polygon.

In this case, A has all of the correct points and is therefore the correct answer.

Hope this helps!

Answer:

Step-by-step explanation:

\(x^{2} + 6x-6= 10\\x^{2} +6x-16=0\\x^{2} -2x+8x-16=0\\x(x-2)+8(x-2)=0\\(x-2)(x+8)=0\\x = 2\\or\\x = -8\)

Answer:

X = 2 and X = -8

Step-by-step explanation:

X2 + 6X - 6-10 = 0 ....... when +10 pass the equality sign it will become -10

X2 + 6X -16 =0

here we need to find if there are two numbers there sum is +6 and there product is -16.

here we need to find if there are two numbers there sum is +6 and there product is -16.The two numbers are -2 and +8

-2+8= +6

-2*8= -16

( X - 2 ) * ( X + 8 ) =0

X - 2 = 0 ...... when -2 pass equality sign it will become+2

X = 2

X + 8 =0 ..... when +8 pass equality sign it will become -8

X = -8

The percentage of those that did not like both of them is 76%

Let the total number of people in the community be 100%

n(u) = 100

If 58% like to listen to the radio only and 18% like to watch the T.V. only, then;

n(R) = 58 - x

n(T) = 118 - x

where x is the percentage of people who do not like both of them. Taking the sum;

58 + x + 18 = 100

x + 76 = 100

x = 100 - 76

x = 24

Hence 24% of people like both of them.

The percentage of those that did not like both of them is 76%

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The first equation that represents 42 - p -p= 21 is correct.

An equation is a mathematical statement that express the equality between two or more number of expressions. An equal sign is mandatory for equation. An equation is used to determine unknown values in terms of variables. In our everyday life equation is used by many professionals necessarily. By using equation many complicated problems can be easily solved within a limited time.

Isaac has $42 cash in hand when arrived Saturday market.

He buys two posters that each cost selling price or SP.

when he leaved the market had $21 cash in hand.

assume, each poster has a price = p

The situation is represented by the following.

initial amount - cost for two posters = final amount

42 - p - p = 21

hence, the first equation that given in the question is correct.

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Whwn the line of sight from the park ranger station, P, to the lifeguard chair, L, the length of PL is 0.76 miles.

It should be noted that since the line of sight from the park ranger station, P, to the lifeguard chair, L, on the beach of a lake is perpendicular to the path joining the campground, C, and the first aid station, F, then the path from the park ranger station to the lifeguard chair is the hypotenuse of a right triangle with legs of 0.35 miles and 0.65 miles.

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the legs. Therefore, the length of PL is equal to:

= ✓(0.35² + 0.65²)

= 0.76 miles.

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The answer after simplifying the expression is 8x .

Quotient rule simply states that as long as the base is the same, we can just divide two powers by subtracting the exponents.

This is a shortcut to simplify exponents.

The given expression is

\(\rm\dfrac{\sqrt{192 x^{3}}}{\sqrt{3x}}\)

now simplifying

as they both have square root so can be written as

\(\rm\sqrt{\dfrac{{192 x^{3}}}{{3x}}}\)

now we can divide the x³ and x to get x² and 192 can be divide by 3 to get 64

\(\rm\sqrt{64x^{2}}\)

now this can written as 8x.

Therefore after simplifying the equation we get 8x .

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Answer:

Table B

Step-by-step explanation:

The table B shows possible outcomes of flipping 3 coins.

A probability experiment is a test in which we execute a series of trials to determine the likelihood of an event occurring in the future. A probability experiment's results may reveal a previously unknown truth or lead us to learn anything about the likelihood (or chance) of an occurrence occurring in the future.

Given:

If three coins are flipped then the possible outcomes are:

{ HHH,

HHT,

HTH

THH,

TTT,

TTH,

THT,

HTT}

So, there total 8 number of outcomes.

But in table 1 the number of outcomes is 5.

Thus, table B shows possible outcomes of flipping 3 coins.

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Answer:

C

Step-by-step explanation:

Although I don't see the graph, I will assume it's a graph about the relationship between time and distance walked.

Here's the logic:

If you walk a longer time, your distance increases.

Answer:

The common difference in the given sequence is 5.

Step-by-step explanation:

The common difference in the sequence is 5 because they all add by 5 each time for example 5 + 5= 10 and 10+5=15

Answer and Step-by-step explanation:

The independent variable is m, and the dependent variable is h.

This is because you can plug in any value for m, making m NOT have to depend on any other value to become m.

With h, it needs the result of m and its other values to become the result of h. H relies/depends on the values in the equation to become a value.

#teamtrees #PAW (Plant And Water)

The sum of angles ∠D and ∠F in quadrilateral DEFG, inscribed in circle P, is equal to 180∘.

To prove that m∠D + m∠F = 180∘, we can use the property of angles inscribed in a circle.

In a circle, an inscribed angle is equal to half the measure of its intercepted arc. Therefore, if we can show that arc DE + arc FG = 360∘, we can conclude that m∠D + m∠F = 180∘.

Let's start the proof:

1. Quadrilateral DEFG is inscribed in circle P. This means that all the vertices of the quadrilateral lie on the circumference of the circle.

2. Let's consider arc DE and arc FG. These arcs are intercepted by angles ∠D and ∠F, respectively.

3. By the property of angles inscribed in a circle, we know that the measure of an inscribed angle is equal to half the measure of its intercepted arc.

4. Therefore, m∠D = 1/2(arc DE) and m∠F = 1/2(arc FG).

5. We want to prove that m∠D + m∠F = 180∘. This is equivalent to showing that 1/2(arc DE) + 1/2(arc FG) = 180∘.

6. Combining the fractions, we have 1/2(arc DE + arc FG) = 180∘.

7. Now, we need to show that arc DE + arc FG = 360∘.

8. Since quadrilateral DEFG is inscribed in circle P, the sum of the measures of all the arcs intercepted by the sides of the quadrilateral is equal to 360∘.

9. This means that arc DE + arc EF + arc FG + arc GD = 360∘.

10. However, we can observe that arc EF and arc GD are opposite sides of the same chord, so they have equal measures. Therefore, arc EF = arc GD.

11. Substituting arc GD with arc EF in the equation from step 9, we have arc DE + arc EF + arc FG + arc EF = 360∘.

12. Simplifying the equation, we get 2(arc DE + arc EF + arc FG) = 360∘.

13. Dividing both sides by 2, we have arc DE + arc EF + arc FG = 180∘.

14. Comparing this result with step 7, we can conclude that arc DE + arc FG = 180∘.

15. Finally, going back to our initial goal, we can now substitute arc DE + arc FG with 180∘ in the equation from step 6: 1/2(180∘) = 180∘.

16. Simplifying, we have 90∘ = 180∘, which is a true statement.

17. Therefore, we have proven that m∠D + m∠F = 180∘.

Thus, we have successfully proved that the sum of angles ∠D and ∠F in quadrilateral DEFG, inscribed in circle P, is equal to 180∘.

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Answer:

D) A search warrant

Step-by-step explanation:

A search warrant is required before the search and collection of evidence to ensure legal authorization and protection of individuals' rights against unreasonable searches and seizures.

Option B, "A crime", is incorrect because the presence of a crime is not a prerequisite for conducting a search and collection of evidence. There are various situations where searches and evidence collection may occur without a crime being involved, such as regulatory inspections, consented searches, or investigations into potential threats or risks.

By your logic when you say law enforcement can conduct a search without a search warrant if there is consent by the owner, that would mean option A would be right, but of course, it's not.

Answer:

x = 20

Step-by-step explanation:

The sides are similar so they equal each other proportionally.

8/14 = 4/7

49 - 14 = 35

Segment MU is 4/7 the size of segment NT.

So x will be 4/7 the size of segment VN.

35 x 4/7 = 20

x = 20

The motivations for producers and consumers in the black market are largely driven by financial incentives and a desire to avoid legal consequences.

The black market refers to the illegal trade of goods and services that are not permitted by law, such as drugs, counterfeit items, and stolen goods. Producers and consumers in the black market are motivated by a variety of factors, including:

High profits, Producers in the black market can earn higher profits than they would in legal markets due to the lack of regulation and taxes.

Escaping legal consequences: Producers and consumers may participate in the black market to avoid legal consequences, such as fines or imprisonment, for engaging in illegal activities.

Limited availability, Some goods and services are only available on the black market due to legal restrictions or limited supply.

Low prices, Consumers in the black market can often purchase goods and services at lower prices than in legal markets due to the lack of taxes and regulations.

Desire for anonymity, The black market can provide anonymity for both producers and consumers, allowing them to engage in illegal activities without fear of detection or retribution.

However, participating in the black market also comes with significant risks, including the possibility of arrest, fines, and even violence.

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The solution to the equation x - 25 = 2 is x = 27.

What is the equation?

An equation is a mathematical statement that asserts the equality of two expressions. In other words, it is a statement that states that two values are equal.

To solve the equation x - 25 = 2, we first add 25 to each side of the equation:

x - 25 + 25 = 2 + 25

Simplifying the right side of the equation, we get:

x = 27

Hence, The solution to the equation x - 25 = 2 is x = 27.

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The absolute humidity is 500g/m³, specific humidity = 16.67% and mixing ratio = 20%.

Absolute humidity is a measure of the amount of water vapor in a given volume of air, regardless of the total mass of the air. It is expressed as the mass of water vapor per unit volume of air, typically in units of grams per cubic meter (g/m³).

First, we need to find the mass of dry air in the package. Since the total volume of air is 1m³ and the volume of dry air is 2.5m³, the volume of water vapor is 1 -2.5 = -1.5 m³. This means that the water vapor must have condensed and become liquid water, which we can ignore for the purposes of this problem. So the mass of dry air is:

mass of dry air = density of air * volume of dry air

mass of dry air = 1000g/m³ × 2.5m³

mass of dry air = 2500 g

Now we can use this value, along with the given mass of water vapor, to calculate the three measures of humidity:

       absolute humidity = 500g/ 1m³

       absolute humidity =  500g/m³

       specific humidity = 500g/(2500g + 500g)

       specific humidity = 0.1667 (or 16.67% as a percentage)

       mixing ratio = 500g/2500g

       mixing ratio = 0.2 (or 20% as a percentage)

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The value of the x is 3.22 if the eˣ = 25 after taking the log both side and lne is 1.

It is another way to represent the power of numbers, and we say that 'b' is the logarithm of 'c' with base 'a' if and only if 'a' to the power 'b' equals 'c'.

\(\rm a^b = c\\log_ac =b\)

We have:

\(\rm e^x = 25\)

Taking ln both side:

\(\rm lne^x = ln25\)

xlne = 3.218

x = 3.218   (lne = 1)

or

x = 3.22

Thus, the value of the x is 3.22 if the eˣ = 25 after taking the log both side and lne is 1.

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