Whats the answer for this

Find f when f"(x) = x^-2, x > 0, f(1) = 0, f(8) = 0

Integrate twice. Do not forget the constants of integration.

f'(x) = -1/x + C                    f(x) = - ln x + Cx + D

To find C and D, apply f(1) and f(2)

f(1) =  - ln (1) + C + D = 0    

C + D = 0     equation 1

f(8) = - ln 8 + 8C + D = 0  

8C + D = ln 8   equation 2

Solve for C and D from equations 1 and 2

C = ln 2/7   and D = - ln2/7

f(x) = - ln x  + (ln 2/7) x - ln 2/7

In mathematics, an integral lends numerical values to functions to represent concepts like volume, area, and displacement that result from combining infinitesimally small amounts of data. Integration is the action of locating integrals. Integration, along with differentiation, is a fundamental, crucial calculus operation.

It can be used to solve issues in mathematics and physics involving, among other things, the volume of a solid, the length of a curve, and the area of an arbitrary shape.

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Answer:

[tex]\frac{2\pi}{3}\text{units}^2[/tex]

Step-by-step explanation:

[tex]\displaystyle A=\frac{r^2\theta}{2}=\frac{4^2*\frac{\pi}{12}}{2}=\frac{16\pi}{24}=\frac{2\pi}{3}\text{units}^2[/tex]

The quotient from the model of the number line is 0.05.

A quotient is an outcome of a division process carried out by two numbers in which one is a divisor and the other is a dividend. The divisor is the number that is being used to divide the dividend.

A quotient is the output of a division operation in more generic terms. It is the result of dividing one quantity by another. Aside from its mathematical use, the term "quotient" can also refer to the outcome of any division or separation process.

From the number line, we have 20 spaces between 0 to 1. So, it implies that 1 is the dividend and 20 is the divisor.

i.e.

[tex]\dfrac{1}{20}[/tex]

= 0.05  ... The result of this division process is known as the quotient.

Therefore, we can conclude that the quotient that models the division of the number line is 0.05.

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Answer: y = ±√ 0.500 = ± 0.70711

Step-by-step explanation:

Solve  :    2y2-1 = 0  Add  1  to both sides of the equation :                       2y2 = 1 Divide both sides of the equation by 2:                     y2 = 1/2 = 0.500   When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:                        y  =  ± √ 1/2  

Answer:

Answer: y = ± √0.500 = ± 0.70711

For the given equations the value of x is 3 and the value of y is -7.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the system of equation is 5x + 7y = -34 and 10x + 17y = -89​. The value of x and y will be calculated as,

5x + 7y = -34   ........................(1)

10x + 17y = -89​ ........................(2)

Multiply the first equation by 2 and subtract the second equation from the first equation,

10x + 14y = -68

-10x - 17y = +89

____________

0    - 3y = 21

          y = -7

The value of x will be,

5x + (7 x -7 ) = -34

5x - 49 = -34

5x = -34 + 49

5x = 15

x =3

Hence, the values are x = 3 and y = -7.

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Douglas McGregor distinguished between these two techniques' fundamental assumptions about human motivation in his well-known "Theory X and Theory Y."

In his well-known "Theory X and Theory Y," Douglas McGregor distinguished between these two approaches' underlying assumptions about human motivation as follows: According to Theory X, employees must be forced, managed, and persuaded to work toward organizational objectives since they detest it.

Additionally, the majority of people prefer to be treated in this manner so they can evade accountability.

Theory Y, or the integration of aims, highlights the typical person's innate interest in his work, desire to be self-directing and seek responsibility, and the ability for originality in problem-solving for organizations.

Therefore, Douglas McGregor distinguished between these two techniques' fundamental assumptions about human motivation in his well-known "Theory X and Theory Y."

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The probability of needing at most 3 rolls is 1/2.The probability of needing an even number of die rolls is 1/2.

(a) The probability of needing at most 3 rolls is 1/6 + 1/6 + 1/6 = 3/6 = 1/2. This can be calculated by considering the probability of getting a 4 on the first, second and third rolls. The probability of getting a 4 on the first roll is 1/6, the probability of getting a 4 on the second roll is 1/6 and the probability of getting a 4 on the third roll is 1/6. This adds up to 3/6 which is the same as 1/2.

(b) The probability of needing an even number of die rolls is 1/2. This is because the probability of getting a 4 on an even roll is the same as the probability of getting a 4 on an odd roll. For example, the probability of getting a 4 on the first roll is 1/6, the probability of getting a 4 on the third roll is also 1/6. Therefore, the probability of needing an even number of die rolls is 1/2.

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The solution of the polynomial ; subtracting a² - 3ab - 4b² from the sum of 3a² - ab - 2b² and 2a² + 5ab - 3b² is 4a² + 7ab - b².

Polynomials are algebraic expressions that consist of variables and coefficients. Therefore, let's perform the operation with the polynomials as follows:

Let's subtract a² - 3ab - 4b² from the sum of 3a² - ab - 2b² and 2a² + 5ab - 3b².

Hence,

3a² - ab - 2b² + 2a² + 5ab - 3b²

combine like terms

3a² + 2a² - ab + 5ab - 2b² - 3b²

5a² + 4ab - 5b²

Finally let's subtract a² - 3ab - 4b²  from 5a² + 4ab - 5b².

Therefore,

5a² + 4ab - 5b² - ( a² - 3ab - 4b²)

5a² + 4ab - 5b² - a² + 3ab + 4b²

5a² - a² + 4ab + 3ab - 5b² + 4b²

4a² + 7ab - b²

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The linear function f(x) has a slope of -5 and intersects the y-axis at the point (0, 45).  The function g(x) intersects the x-axis closer to zero than the function f(x). Option D

Generally, To find the x-intercepts of a linear function, you can set the y-value equal to zero and solve for x.

For the function f(x), we have:

f(x) = -5x + 45

0 = -5x + 45

5x = 45

x = 9

So the x-intercept of f(x) is (9, 0).

For the function g(x), we have:

g(x) = -5x - 10

0 = -5x - 10

5x = 10

x = 2

So the x-intercept of g(x) is (2, 0).

Since the x-intercept of g(x) is closer to zero than the x-intercept of f(x), the correct answer is D. The function g(x) intersects the x-axis closer to zero than the function f(x).

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Triangle JKL is right. Triangle XYZ is acute.

To classify a triangle you need to know the measure of each angle.

For triangle JKL, if we measure the angles, we can see that angle JKL is 90 degrees, which makes it a right triangle.

For triangle XYZ, if we measure the angles, we can see that all angles are less than 90 degrees, which makes it an acute triangle.

Triangle JKL is a right triangle and triangle XYZ is an acute triangle.

Triangle JKL is right. Triangle XYZ is acute.

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Answer: b and a

Step-by-step explanation:

one angstrom, symbolized as å, is 10-10 m, so

1 cm^3 = 10^24 angstrom^3

The angstrom, sometimes known as a ångström, is a metric length unit equal to 10^(-10)m, or one ten billionth of a metre, one hundred millionth of a centimeter, 0.1 nanometer, or one hundred picometres. The Swedish alphabet letter serves as its symbol. The Swedish physicist Anders Jonas Angström is commemorated by the unit's name.

The length of an object is measured in centimeters, which are metric units of measurement. The abbreviation is cm.

100 centimeters make up a meter.

One centimeter is equal to ten millimeters.

so one angstrom is 10^-10 m, or 10^-8 cm, so there are 10^8 angstroms in 1 cm.

1 cm^3 = 1 cm 1 cm * 1 cm

1 cm^3 = 10^8 10^8 10^8 angstrom^3

1 cm^3 = 10^24 angstrom^3

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From the rectangle, the value of x is 4.9 or -2.4

A rectangle is a four sided polygon whose opposite sides are equal and parallel, The area can be defined as the amount of space covered by a flat surface of a particular shape. It is measured in terms of the "number of" square units (square centimeters, square inches, square feet, etc.)

The parameters given for the solution are

Area = 24m

Length = x+2

width = 2x-9

Area = l*w

This implies that (x+2)(2x-9)=24

Collecting like terms we have

2x2-5x-24=0

Solving the equation we have

(5±√25+192)/4

⇒(5±√217)/4

⇒(5+14.7)/4 or( 5-14.7)/4

x=4.9 or x = 2.4

Therefore the value of x in the figure is 4.9 and -2.4 respectively

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Triangles can be categorized as scalene triangles, acute triangles, obtuse triangles, isosceles triangles, equilateral triangles, and right angles.

A triangle is a 3-sided polygon that is occasionally (though not frequently) referred to as the trigon. There are three sides and three angles in every triangle, some of which may be the same. A triangle is a polygon with three vertices and three sides. The triangle's three angles add up to 180 degrees in total. Triangles are a particular sort of polygon in geometry that have three sides and three vertices. Three straight sides make up the two-dimensional figure shown here. An example of a 3-sided polygon is a triangle.  

here ,

various triangles

Triangle of Scalene. a triangle without sides that are similar.

Sharp Triangle a triangle in which each of the three angles is less than 90 degrees.

Sharp Triangle. a triangle with one angle that is more than 90 degrees in length.

Triangles include: Right Triangle, Equilateral Triangle, and Isosceles Triangle.

Triangles can be categorized as scalene triangles, acute triangles, obtuse triangles, isosceles triangles, equilateral triangles, and right angles.

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Answer:

2 is correct answer.

The coordinates of the vertices after the reflection over the line y = -x is K'(-5, -4), L'(-7, -7), M'(-9, -4) and N'(-7, 1).

Reflection is a type of geometric transformation where the figure is flipped. In other words, a figure when undergoes reflection becomes it's mirror image.

Given a quadrilateral KLMN.

The coordinates of the vertices are,

K(4, 5), L(7, 7), M(4, 9) and N(-1, 7)

The point (x, y) after the reflection over the line y = -x is the point (-y, -x).

K(4, 5) becomes K'(-5, -4)

L(7, 7) becomes L'(-7, -7)

M(4, 9) becomes M'(-9, -4)

N(-1, 7) becomes N'(-7, 1)

Hence the coordinates are K'(-5, -4), L'(-7, -7), M'(-9, -4) and N'(-7, 1).

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the answer is 1

x = 1 is an extraneous solution for the equation 1/(x - 1) = (x - 2)/(2x² - 2).

The sum of the interior angle measures of this polygon is 540 degrees

A convex polygon is simply described as closed figure having all its interior angles less than 180° and its vertices  pointing outwards.

The word 'convex' is used to described a shape that has a curve or a protruding surface.

Also, all the lines across the outline are straight and they all point outwards.

From the diagram shown, we have that;

Sum of the interior angles of a pentagon = (n - 2) 180

Substitute n as 5 in the equation

= (5 -2 ) 180

= 3(180)

= 540 degrees

Hence, the sum is 540 degrees

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The Answer is 84, because 36 x 2 =72 and then 1/3 of 36 is 12 and 12+72=84.

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answer: more likely because its a bunch of school-aged kids so obviously they want a new park.

Answer:

π/4

Step-by-step explanation:

(I cannot attach a unit circle here, sorry :)

Recall the function of the (x,y) values of the unit circle. X represents the cosine value, and y is the sine value.

If you look at a unit circle, π/2 has the coordinates (0,1), so the sine value of π/2 is 1.

To find arctangent, remember that the range of tangent is -π/2 < x < π/2. In terms of the unit circle, these are the minimum and maximum values, and we cannot use -π/2 and π/2 since x is 0, which means it'll be undefined. The angle where the coordinates can be found is the arctangent of the function.

So, find the coordinate where both x and y have the same value (√2/2, √2/2) at π/4. Therefore, the answer for the arctan(sin(π/2)) =  π/4.

Using simultaneous equations, Kieran and Louise's numbers are 20 and 8 respectively.

Kieran and Louise each think of a number. 4 less than Kieran's number is equal to 2 lots of Louise's number.

let's

x = Kieran's number

y = Louise's number.

x - 4 = 2y

x - 2y = 4

3 lots of Kieran's number added to Louise's number is 68.

Hence,

3x + y = 68

Hence, let's combine the system of equation.

x - 2y = 4

3x + y = 68

multiply equation(i) by 3

3x - 6y = 12

3x + y = 68

-7y = -56

y = -56 / -7

y = 8

Therefore, let's find x

x = 4 + 2y

x = 4 + 2(8)

x = 4 + 16

x = 20

Hence,

Kieran number = 20

Louise number = 8

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Answer:

[tex]f^{-1}(x)=\sqrt{x+4}+1[/tex]

Step-by-step explanation:

[tex]f(x)=(x-1)^2-4\\y=(x-1)^2-4\\[/tex]

Swap x and y and solve for y:

[tex]x=(y-1)^2-4\\x+4=(y-1)^2\\\sqrt{x+4}=y-1\\\sqrt{x+4}+1=y\\f^{-1}(x)=\sqrt{x+4}+1[/tex]

Hence, the inverse function is [tex]f^{-1}(x)=\sqrt{x+4}+1[/tex]

We must take into account the number of options for each PIN digit in order to get the total number of 4-digit personal identification numbers (PINs) that can exist. There are nine options available because the first digit must be 0. (1, 2, 3, 4, 5, 6, 7, 8, or 9). There are a total of 10 options available for each of the remaining 3 digits, which can all be any of the digits 0 through 9. Thus, there are a total of 9 * 10 * 10 * 10 = 9000 different 4-digit PIN combinations.

  However, since we're looking for 4-digit PINs that are odd, the last digit must be one of the following: 1, 3, 5, 7, or 9. This indicates that there are 5 options available for the final digit.

  As a result, there are 4500 4-digit PINs that are odd and cannot start with 0. This is calculated as 5 * 9 * 10 * 10. This is the right response, which goes with option b.

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Answer:

y = -5x/4 + 9

Step-by-step explanation:

Slope-intercept Form: y=mx+b where m=slope

In order to put the equation into slope-intercept form, solve for y:

10x + 8y = 72

8y = -10x + 72 ==> subtract 10x on both sides to isolate y

y = (-10x + 72)/8  ==> divide both sides by 8 to isolate y

y = -10x/8 + 72/8  ==> divide each term by 8

y = -5x/4 + 9  ==> simplify

The solution is : y = -5x/4 + 9, equation of a line into slope-intercept form, simplifying all fractions.

A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.

here, we have,

we know that,

Slope-intercept Form:

y=mx+b

where m=slope

In order to put the equation into slope-intercept form, solve for y:

10x + 8y = 72

8y = -10x + 72 ==> subtract 10x on both sides to isolate y

y = (-10x + 72)/8  ==> divide both sides by 8 to isolate y

y = -10x/8 + 72/8  ==> divide each term by 8

y = -5x/4 + 9  ==> simplify

Hence, The solution is : y = -5x/4 + 9, equation of a line into slope-intercept form, simplifying all fractions.

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Answer:

its b

Step-by-step explanation:

Answer: b

Step-by-step explanation:

We can give the following two conclusions:

From the information provided:

Since GFH and HFJ are adjacent, they share a common side or vertex. This means that the two figures are not only congruent, but they also share at least one common angle.

Since GFH and HFJ are congruent, they have the same size and shape. This means that corresponding angles and sides are equal in measure. It also means that the two figures can be superimposed on each other exactly.

In conclusion, since they are congruent and adjacent, we can say that they are part of a larger geometric figure.

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Answer:

Rectangle

Step-by-step explanation:

By putting the points in Desmos, it shows an image of a rectangle. It allows you to change the number of B and also A, and whatever number you change them to the image will still be a rectangle.

The test statistic by the given values is t = -2.

Test statistic is a value calculated from a statistical test of hypothesis. It describes the closeness of the observed data with the expected distribution under the null hypothesis.

Test statistic can be calculated from the formula,

t = (xₐ - μ) / (s/√n)

where xₐ is the sample mean, μ is the population mean, s is the standard deviation and n is the sample size.

Given,

n = 49, xₐ = 50, s = 7

Since null and alternate hypothesis are given, μ = 52.

So the test statistic,

t = (50 - 52) / (7/√49)

 = -2 / (7/7)

 = -2

Hence the test statistic is -2.

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Part 1

[tex]m=\frac{-7-(-5)}{8-0}=\boxed{-\frac{1}{4}}[/tex]

Part 2

[tex]y=-\frac{1}{4}x-5[/tex]

The answer of addition & multiplication are,

101,455,348 + 1,111,419 = 102566767

0.000000612 x 0.00031119 = 1.9044828E-10

297,060 + 0.0004839 =297060.0005

0.000000612 x 0.00031119 =

297,060 + 0.0004839 =

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

Here, given that,

101,455,348 + 1,111,419 = 102566767

0.000000612 x 0.00031119 = 1.9044828E-10

297,060 + 0.0004839 =297060.0005

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