Solve for all possible values of x.
√9x-9 = x + 1

Omg help someone i don’t get this

Mathematical modeling, in which equations are used to model the relationships between variables, is a technique used in various fields and disciplines. Some areas where mathematical modeling is commonly applied include:

Physics: Mathematical models are used to describe and predict physical phenomena, such as the motion of objects, the behavior of fluids, and the interactions of particles.

Engineering: Mathematical models are employed in engineering to design and analyze systems, such as electrical circuits, mechanical structures, and chemical processes. These models help engineers optimize performance, improve efficiency, and ensure safety.

Economics: Mathematical models are used in economics to understand and predict economic behavior, market dynamics, and the effects of various factors on economic systems. Models such as supply and demand curves, production functions, and macroeconomic models help economists study and analyze economic phenomena.

Biology: Mathematical models are used in biology to describe biological processes and systems, including population dynamics, biochemical reactions, ecological interactions, and genetic inheritance. These models help biologists understand complex biological phenomena and make predictions about their behavior.

Computer Science: Mathematical models are utilized in computer science to analyze algorithms, design computer networks, and optimize system performance. Models such as graph theory, automata theory, and computational complexity theory provide frameworks for understanding and solving computational problems.

Finance: Mathematical models play a crucial role in finance for pricing options, managing risks, and predicting market behavior. Models like the Black-Scholes model and portfolio optimization models help financial analysts make informed investment decisions.

These are just a few examples of the many fields where mathematical modeling is used.

The power of mathematical modeling lies in its ability to represent real-world phenomena in a precise and quantitative manner, allowing for analysis, prediction, and optimization.

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The final answer is: ∫(2x-1)÷[(x-3)(x+2)]dx = ln|x-3| + ln|x+2| + C

What is Integration ?

In calculus, integration is the inverse operation of differentiation. It is a mathematical technique used to find the integral of a function. The integral of a function f(x) is another function F(x), which gives the area under the curve of f(x) from a certain point to another.

To perform the integration of the given function:

∫(2x-1)÷(\(x^{2}\)-x-6)dx

First, we need to factor the denominator:

\(x^{2}\)- x - 6 = (x-3)(x+2)

So we can rewrite the integral as:

∫(2x-1)÷[(x-3)(x+2)]dx

Next, we need to decompose the fraction into partial fractions:

(2x-1)÷[(x-3)(x+2)] = A÷(x-3) + B÷(x+2)

Multiplying both sides by (x-3)(x+2), we get:

2x-1 = A(x+2) + B(x-3)

Substituting x=3, we get:

5A = 5

A = 1

Substituting x=-2, we get:

-5B = -5

B = 1

So we have:

(2x-1)÷[(x-3)(x+2)] = 1÷(x-3) + 1÷(x+2)

Substituting this back into the integral, we get:

∫(2x-1)÷[(x-3)(x+2)]dx = ∫[1÷(x-3) + 1÷(x+2)]dx

Using the first rule of integration, we get:

∫[1÷(x-3) + 1÷(x+2)]dx = ln|x-3| + ln|x+2| + C

where C is the constant of integration.

Therefore, the final answer is: ∫(2x-1)/[(x-3)(x+2)]dx = ln|x-3| + ln|x+2| + C

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\( \displaystyle \int \rm \: \dfrac{2x - 1}{ {x}^{2} - x - 6 } dx\)

Answer:

\( \underline{\boxed{\rm = ln |x + 2| + ln |x - 3| + C}}\)

Step-by-step explanation:

\( = \displaystyle \int \rm \: \dfrac{2x - 1}{ {x}^{2} - x - 6 } dx\)

\( = \displaystyle \int \rm \: \dfrac{2x - 1}{ {x}^{2} - 3x + 2x - 6 } dx\)

\( = \displaystyle \int \rm \: \dfrac{2x - 1}{ x(x - 3) + 2(x - 3) } dx\)

\( = \displaystyle \int \rm \: \dfrac{2x - 1}{ (x + 2) (x - 3)} dx\)

\( \rm \: Let : \displaystyle \rm \: \dfrac{2x - 1}{ (x + 2) (x - 3) } = \dfrac{A }{x + 2} + \dfrac{B}{x - 3} \)

\(\rm\implies\displaystyle \rm \: \dfrac{2x - 1}{ (x + 2) (x - 3) } = \dfrac{A(x - 3) + B(x + 2) }{(x + 2)(x - 3)} \\ \)

\( \rm \implies\displaystyle \rm \: {2x - 1}{ } = {A(x - 3) + B(x + 2) } \\ \)

Put x = 3 , we get

\( \rm \implies\displaystyle \rm \: {6 - 1}{ } = {A(3- 3) + B(3 + 2) } \\ \)

\( \rm \implies\displaystyle \rm \: {5}{ } = 5 B \\ \)

\( \implies \rm \: B = 1\)

Again

put put x = -2

\( \rm \implies\displaystyle \rm \: { - 4- 1}{ } = {A( - 2- 3) + B( - 2 + 2) } \\ \)

\( \rm \implies\displaystyle \rm \: { - 5}{ } = {A( - 5) } \\ \)

\( \rm \implies\displaystyle \rm A = 1 \\ \)

Thus ,

\( \displaystyle \int \rm \: \dfrac{2x - 1}{ (x + 2) (x - 3)} dx = \int\dfrac{1}{x + 2} dx + \int \dfrac{1}{x - 3} dx\)

\( \rm = ln |x + 2| + ln |x - 3| + C\)

\( \tt\int \dfrac{dx}{ {x}^{2} + {a}^{2} } = \frac{1}{a} { \tan}^{ - 1} \frac{x}{a} + c \\ \)

\( \tt\int \dfrac{dx}{ {x}^{2} - {a}^{2} } = \frac{1}{2a} log \frac{x - a}{x + a} + c \\ \)

\( \tt\int \dfrac{dx}{ {a}^{2} - {x}^{2} } = \frac{1}{2a} log \frac{a + x}{a - x} + c \\ \)

\( \tt\int \: \dfrac{dx}{ \sqrt{ {x}^{2} + {a}^{2} } } = log|x + \sqrt{ {a}^{2} + {x}^{2} } | + c \\ \)

\( \tt\int \: \dfrac{dx}{ \sqrt{ {x}^{2} - {a}^{2} } } = log|x + \sqrt{ {x}^{2} - {a}^{2} } | + c \\ \)

\( \tt \int \: \dfrac{dx}{ {a}^{2} - {x}^{2} } = { \sin }^{ - 1} \bigg(\dfrac{x}{a} \bigg) + c \\ \)

\( \tt \int \: \sqrt{ {x}^{2} + {a}^{2} } dx \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\= \tt \dfrac{x}{2} \sqrt{ {a}^{2} + {x}^{2} } + \dfrac{ {a}^{2} }{2} log |x + \sqrt{ {x}^{2} + {a}^{2} }| + c\)

Answer:

\(4x^2\left(3x-1\right)\)

Key:

• \(a^{b+c}=a^ba^c\)

• Factor out the last leading term standing to solve in the end.

Step-by-step explanation:

\(12x^3-4x^2\\x^3=xx^2\\=12xx^2-4x^2\\=4\cdot \:3xx^2-4\cdot \:1\cdot \:x^2\\=4x^2\left(3x-1\right)\)

Answer:

no

Step-by-step explanation:

0.06 = \(\frac{6}{100}\) ← that is 6 books out of 100

she requires to have 60 out of 100 , that is

\(\frac{60}{100}\) = 0.6

Answer:

see explanation

Step-by-step explanation:

(a)

OC = OB ( both radii of the circle )

Thus Δ BOC is isosceles with congruent base angles.

∠ BOC = ∠ BCO = 50°

(b)

∠ ACB = 90° ( angle in a semicircle ), then

∠ ACO = 90° - 50° = 40°

OA = OC ( both radii of the circle )

Thus Δ ACO is isosceles with congruent base angles.

∠ BAC = ∠ ACO = 40°

Answer: The answer is 36

Answer:

B

Step-by-step explanation:

solved using calculator.

7-2.50:4.5

4.5 - 0.45 is 10.0

ez dubs man

hirhgkjsdbgkgbdk kbfsbjd jsbfbdh jabjdbshd jsjdsfkj

Answer: x>11

Step-by-step explanation:

The solutions for the system of equations given by Substitution method is (27, 114), (-0.25, -5.625), (0, -3) and (0, -2).

Linear equations involve one or more expressions including variables and constants and the highest exponent of the variable is 1.

System of linear equations involve two or more linear equations.

1) -4x + y = 6

5x - y = 21

We are using Substitution Method.

From, -4x + y = 6, we get, y = 4x + 6

Substituting y = 4x + 6 in the equation 5x - y = 21, we get,

5x - (4x + 6) = 21

5x - 4x - 6 = 21

x = 27

So, y = 4x + 6 = 114

2) -7x - 2y = 13

x - 2y = 11 ⇒ x = 2y + 11

Substituting x = 2y + 11 in the first equation -7x - 2y = 13,

-7(2y + 11) - 2y = 13

-14y - 77 - 2y = 13

-16y = 90

y = -5.625

So, x = 2y + 11 = -0.25

3) -5x + y = -3 ⇒ y = 5x - 3

3x - 8y = 24

Substituting y = 5x - 3 in the second equation 3x - 8y = 24,

3x - 8(5x - 3) = 24

3x - 40x + 24 = 24

x = 0

y = 5x - 3 = -3

4) -5x + y = -2 ⇒ y = 5x - 2

-3x + 6y = -12

Substituting y = 5x - 2 in the second equation -3x + 6y = -12,

-3x + 6 (5x - 2) = -12

-3x + 30x - 12 = -12

x = 0

So, y = 5x - 2 = -2

Hence the system of equations are solved.

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Answer

-sqrt(18)<x<sqrt(18)

Step-by-step explanation:

Answer:

False.

Just because the name begins with J does not mean the name is Jim. For example: Jack, Joshua, James, Jacob, and so on.

Answer:

27

Step-by-step explanation:

\(3^{3}\) is basically just multiplying the number 3, three times. So 3x3x3. 3x3 is 9, and when you multiply 3 more, it is 27.

Answer:

Step-by-step explanation: 3, because when 3 is cubed you get 27.

In a queueing system with customer arrivals every 6 seconds and service times of 4 seconds, the task is to calculate the average number of customers in the queue

To calculate the average number of customers in the queue, we can use Little's Law, which states that the average number of customers in a stable queueing system is equal to the average arrival rate multiplied by the average time spent in the system.

First, we need to calculate the average arrival rate. Since customers arrive once every 6 seconds, the arrival rate is 1 customer per 6 seconds or 1/6 customers per second.

The total service time is 4 seconds, and the standard deviation is 5.9. Therefore, the average service time is 4 seconds.

Using Little's Law, we multiply the average arrival rate (1/6 customers per second) by the average service time (4 seconds) to obtain the average number of customers in the queue.

Average number of customers in the queue = (1/6) * 4 = 2/3 ≈ 0.667

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Answer:

d

Step-by-step explanation:

The point can be located on the curve at the corresponding z-value, which in this case is approximately z = 0.03.

To calculate the standard score, we use the formula:

z = (X - μ) / σ

Substituting the given values, we get:

z = (91.9 - 88.7) / 92.4

z ≈ 0.03

Rounding to two decimal places, we get z ≈ 0.03.

To indicate where z ≈ 0.03 is located on the standard normal curve, we can use a standard normal distribution table or a calculator that has a normal distribution function. From the table or calculator, we find that the area to the left of z ≈ 0.03 is about 0.5125. This means that z ≈ 0.03 is close to the center of the curve, since the area to the left and right of it is almost equal. The point can be located on the curve at the corresponding z-value, which in this case is approximately z = 0.03.

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Answer:

$2855.46

Step-by-step explanation:

$27,174.25 - $24,318.79= $2855.46

The requried domain of the given relation is {−5, 0, 3, 4}. Option A is correct.

The domain is defined as the values of the independent variable for which there is a certain value of the dependent variable exists in the range of the function.

Here,
We have the ordered pair of a relation given as,
(-5, -10), (0, 0) (3, 6) (4, 8)

From above, the x absciss of each ordered pair is termed as the domain of the relation.

So, set of domain = {−5, 0, 3, 4}]

Thus, the requried domain of the given relation is {−5, 0, 3, 4}. Option A is correct.

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Function:

65m + 45

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This is here to remove the 20 word minimum limit.

Answer:

I tiz6ez7zr7zrf7xf ohch8gcg IS C

Answer:

10 Letter B

Step-by-step explanation:

56.23 rounds down to 56 and 45.9 rounds up to 46. So 56 - 46 = 10

Answer:

Step-by-step explanation: Let x,y,z are in G.P.

⇔y  

2

=xz

⇔x is a factor of y (not possible)

Taking x=3,y=5,z=7, we have x,y,z, are in A.P.

Thus x,y,z  may be in A.P. but not in G.P.

Answer:-15+.2

Step-by-step explanation:

The sequence aₙ = {(4 + 3n²)/(n + 5n²)} converges to 3/5.

A value of the function, whenever the input values are substituted in the function then the function approaches some number.

And that number is a limit of the function.

Given:

A sequence,

aₙ = {(4 + 3n²)/(n + 5n²)}

To find the limit at n tends to infinity:

\(\lim_{n \to \infty} a_n = \frac {(4 + 3n^2)}{(n + 5n^2)}\)

                 = n²(4/n² + 3)/n²(1/n + 5)

                 = (4/n² + 3)/(1/n + 5)

Now, if n tends to infinity,

then \(\lim_{n \to \infty} a_n\) = 3/5

Therefore, 3/5 is the limit of the sequence.

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Answer:

2n-11

Step-by-step explanation:

-9, -7, -5

a+(n-1)d

-9+(n-1)2

-9+2n-2

2n-11

Answer:

B

Step-by-step explanation:

Basically, this question is asking the legs of the triangle shown in the graph.

In this right triangle, there are 2 legs and one of them is 6400 meters. We were asked to find out the length of the other led. And we know the angle is 16.5 deg.

Using Tangent  to find out:

set the length of the other leg is x meters.

tan(16.5) = 6400/x

x= 6400/tan(16.5)

x= 21606 m

Answer:

the slope is rise over run 5/4

the -9 is the y intercept so you start you slope from there

The volume of the solid obtained by rotating the region bounded by y = x^2 and y = 6 about the line x = -3 is approximately 481.39 cubic units.


To find the volume of the solid, we can use the method of cylindrical shells. The region bounded by y = x^2 and y = 6 in the first quadrant is a parabolic shape above the x-axis.
To set up the integral for the volume, we consider an infinitesimally small vertical strip of thickness Δx at a distance x from the line x = -3. The height of the strip is given by the difference between the two curves: h = 6 – x^2. The circumference of the cylindrical shell is given by the formula 2πr, where r is the distance between x and the line x = -3, which is r = x + 3.

The volume of the infinitesimal shell is then given by dV = 2π(x + 3)(6 – x^2)Δx. Integrating this expression from x = 0 to x = 3, we obtain the volume V = ∫[0,3] 2π(x + 3)(6 – x^2)dx. Evaluating this integral, we find V ≈ 481.39 cubic units.
In summary, the volume of the solid obtained by rotating the region bounded by y = x^2 and y = 6 about the line x = -3 is approximately 481.39 cubic units.

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The value of the copier after 3 years and 6 months can be found by substituting t = 3.5 into the function and solving for V. The salvage value of the copier can be found by substituting t = 5 into the function and solving for V.

After 3 years and 6 months of use, the copier is worth $5,800. This can be found by substituting t = 3.5 into the function V(t)-3600t+20000: V(3.5) = 3600(3.5) - 20000 + 20000 = $5,800.

The salvage value of the copier after 5 years of use is $4,000. This can be found by substituting t = 5 into the function V(t)-3600t+20000: V(5) = 3600(5) - 20000 + 20000 = $4,000. This is the value of the copier when it is sold or replaced after 5 years of use.

The domain of the function is all real numbers because time and value can take on any real value. However, since the function is only defined for the first 5 years of use, t must be between 0 and 5.

The graph of the function is a downward-sloping line with an intercept of $20,000 on the y-axis and a slope of -3600. This means that the value of the copier decreases by $3,600 each year. At t = 0, the copier is worth $20,000, and after 5 years, it is worth $4,000. The graph is a straight line because the function is linear.

Complete Question:

The function V(t)-3600t+20000, where V is value and t is time in years, can be used to find the value of a large copy machine during the first 5 years of use. a. What is the value of the copier after 3 years and 6 months? After 3 years and 6 months, the copier is worth $ b. What is the salvage value of the copier if it is replaced after 5 years? After 5 years, the salvage value of the copier is ts c. State the domain of this function. d. Sketch the graph of this function. 20000 18000 16000 14000 12000 10000 8000 6000+ 4000 2000 4 .

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Answer:

\(283x^3 + 10y^3 = C\)

Step-by-step explanation:

\(28.3x^2 dx=-y^2 dy \\ \\ \int 28.3 x^2 dx=-\int y^2 dy \\ \\ \frac{283x^3}{30}=-\frac{y^3}{3} +C \\ \\ 283x^3 =-10y^3 + C \\ \\ 283x^3 + 10y^3 = C\)

The population parameter being estimated is the confidence coefficient.

The confidence coefficient is the confidence level stated as a proportion, rather than as a percentage. For example, if you had a confidence level of 99%, the confidence coefficient would be . 99. In general, the higher the coefficient, the more certain you are that your results are accurate.

probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

Hence, The probability that the interval estimation procedure will generate an interval that does not contain the actual value of the population parameter being estimated is the confidence coefficient.

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Answer: To match the shapes produced by the slice through the triangular prism, we need to consider the orientation of the slice relative to the prism. Here are the matching options:

A. Perpendicular to the base: Rectangle

B. Parallel to the base: Triangle with dimensions equal to the base

C. Diagonal from vertex to vertex: Triangle with unknown dimensions