Find the composite functions (f - g) and (g-f) 1. What is the domain of each composite function? f(x) = 9/x
g(x) = x^2 - 25

Answer:

21 1/3

Step-by-step explanation:

8 + ( 2 × 5 ) × 3 4 ÷ 9

2 x 5 = 10

10 x 3 = 30

30 x 4 = 120

13 1/3

8 + 13 1/3 = 21 1/3

The proof for the given condition S ≤ T is justified using the product rule of differentiation.

The given function is given by f(x) = A sin(x) + B cos(2x).

Let us first find the derivative of this function.

Using product rule, we getf′(x) = A cos(x) – 2B sin(2x)

Now, let us calculate the second derivative of the function

f′′(x) = -A sin(x) – 4B cos(2x)

Now, we need to check if the function is concave or convex over the interval [0, π/2].

In order to do that, we will check the sign of the second derivative on this interval. We note that A is non-zero.

Hence, if we multiply the second derivative by A, we get

-A² sin(x) – 4AB cos(2x).

We observe that cos(2x) is greater than or equal to -1 for all real values of x.

Hence, -4AB cos(2x) is less than or equal to 4AB.

This implies that -A² sin(x) – 4AB cos(2x) is less than or equal to -A² sin(x) + 4AB.

Now, we need to find the maximum value of this expression for x between 0 and π/2.

Let us differentiate this expression w.r.t. x.

A² cos(x) + 8AB sin(x) = 0sin(x)/cos(x)

= -A²/8AB

= -A/8Btan(x)

= -A/8B or

x = -arctan(8B/A)

Let x = -arctan(8B/A).

Then sin(x) = -A/√(A² + 64B²) and cos(x) = 8B/√(A² + 64B²).

Putting these values in the expression, we get

Maximum value of the expression = √((A² + 64B²)/(A²))

= √(1 + (64B²)/(A²))

Hence, we have that for any function f in F,

f(x) ≤ f(a) + f′(a)(x-a) + (√(1 + (64B²)/(A²)) / 2)

f′′(a)(x-a)² for x between 0 and π/2.  

The equation  √√√((a) - arctan (2))³²dr ≤√√√ (f(a) — arctan(a))³d.r can be expressed as ∫ √(a - arctan2(x)) dx ≤ ∫ √(f(a) - arctan(a)) dx  over the interval (0, π/2).

Now, we just need to evaluate the integrals on both sides. We can do this numerically. We will use the trapezoidal rule for this. We will divide the interval into n subintervals of equal length.

Let xi be the point where the ith subinterval starts and let f(xi) be the value of the function at that point.

Then, the integral can be approximated by

∫ √(a - arctan2(x)) dx ≈ (π/(2n))(√(a - arctan2(0)) + 2

∑i=1n-1 √(a - arctan2(xi)) + √(a - arctan2(π/2)))

Similarly,

∫ √(f(a) - arctan(a)) dx ≈ (π/(2n))(√(f(a) - arctan(a)) + 2

∑i=1n-1 √(f(a) - arctan(a)) + √(f(a) - arctan(a)))

Let S = √√√((a) - arctan (2))³²dr and T = √√√ (f(a) — arctan(a))³d.r.

Then, we just need to show that S ≤ T. This can be done by choosing appropriate values of A and B.

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Answer:

D. {1}

Step-by-step explanation:

F(x)=3x−1

Let F(x) =2

2 = 3x-1

Add 1 to each side

2+1 = 3x-1+1

3 =3x

Divide by 3

3/3 = 3x/3

1 =x

Answer:

there is no question below therefore, we can't answer it

Answer:

The independent variable, x, represents the number of hours driven, and the dependent variable is the gallons of gas remaining, because the gallons of gas remaining depends on the number of hours driven.

A function relating these variables is K(x) =K(x)= 12-1.75x .

So K(4) = 5, meaning 4 hours of driving will result in 5 gallons left in the tank.

Step-by-step explanation:

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Have a good day :)

The most appropriate choice for domain of a  functions will be given by -

What is a domain of a function

A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.

There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.

The set of values for which the function is defined is called domain of the function.

Here, from the graph, the set of values of x axis for which the graph is drawn is \(-6\leq x \leq 6\).

And values of x - axis represents the domain.

So domain of function is {x ∈ \(\mathbb{R}\), \(-6 \leq x \leq 6\)}

Third option is correct.

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Answer:

3x²-4

Step-by-step explanation:

1 distribute

(-4x²-2x-6)+7x²+2x+2

2 eliminate redudant parentheses

-4x² -2x - 6+7x² +2x+2

3 Add the numbers

-4x²-2x-4+7x²+2x

4 Combine like terms

3x²-2x-4+2x

5 Combine like terms

3x²-4

Answer:

\(3x^{2} -4\)

Step-by-step explanation:

Before solving this you have to know that,

( - ) × ( - ) = ( + )

( + ) × ( + ) = ( + )

( - ) × ( + ) = ( - )

Let us solve now.

\((-4x^2-2x-6)-(-7x^2-2x-2)\)

\((-4x^2-2x-6)+7x^{2} +2x+2\)

\(-4x^2-2x-6+7x^{2} +2x+2\)

Now combine like terms

\(-4x^{2}+7x^{2} -2x+2x-6+2\)

\(3x^{2} -4\)

Hope this helps you .

Let me know if you have any other questions :-)

When x = 0 and y = 6, the partial derivatives ∂P/∂x and ∂P/∂y are ∂P/∂x = 12 and ∂P/∂y = 0, respectively.

To find the partial derivatives ∂P/∂x and ∂P/∂y using the Chain Rule, we start by computing the partial derivatives of P with respect to each variable u, v, and w, and then differentiate u, v, and w with respect to x and y.

Given expressions are:

\(P = u^2 + v^2 + w^2\)

\(u = xe^y\\ v = ye^x\\ w = e^{xy}\\\)

x = 0

y = 6

Let's begin with ∂P/∂x:

Using the Chain Rule, we have:

∂P/∂x = ∂P/∂u × ∂u/∂x + ∂P/∂v × ∂v/∂x + ∂P/∂w × ∂w/∂x

Differentiating each component:

∂P/∂u = 2u

∂u/∂x = \(e^y\)

∂P/∂v = 2v

∂v/∂x = \(ye^x\)

∂P/∂w = 2w

∂w/∂x = \(e^{xy}\)

Substituting the given values:

x = 0

y = 6

∂P/∂x = 2(0 × e^6) × e^0 + 2(6 × e^0) × 0 + 2(e^0 × 6) = 12

Next, let's find ∂P/∂y:

Using the Chain Rule, we have:

∂P/∂y = ∂P/∂u × ∂u/∂y + ∂P/∂v × ∂v/∂y + ∂P/∂w × ∂w/∂y

Differentiating each component:

∂u/∂y = x × \(e^y\)

∂v/∂y = x × \(e^y\)

∂w/∂y = \(e^x\) × y

Substituting the given values:

x = 0

y = 6

∂P/∂y = 2u × (0 × e^6) + 2v × (0 × e^6) + 2w × (e^0 × 6) = 0

Therefore, when x = 0 and y = 6, the partial derivatives are ∂P/∂x = 12 and ∂P/∂y = 0.

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Answer: B Stan has $42 and Cory has $108.

Step-by-step explanation:

The awnser is Stan has $42 and Cory has $108 and $108 + $42 = $150.

                            CAN YOU PLEASE MARK ME BRAINLY.

Given a linear operator T on a vector space V and an ordered basis {3}, we need to compute the matrix representation [T] with respect to this basis. Once we have the matrix [T], we can find its eigenvectors and eigenvalues

To address your question, we first need to understand the concepts involved:

1. A linear operator (T) is a function that maps a vector space V to itself, while preserving the structure of the space.
2. An ordered basis is a linearly independent set of vectors that spans the vector space V.
3. [T] is the matrix representation of the linear operator T with respect to the ordered basis.
4. Eigenvectors are non-zero vectors that satisfy the equation T(v) = λv, where λ is a scalar called an eigenvalue.

. If the eigenvectors of T form a basis for the vector space V (i.e., they are linearly independent and span the space), then we can say that F3 is a basis consisting of eigenvectors of T.

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Answer:

# of appointments is 3

Step-by-step explanation:

He makes $75 per appointment, which means this immediate value is directly dependent on the number of appointments (x). So it can be given by 75x.

Tips are simply added, tips are not directly dependent on the number of visits as customers will tip differently so we can add $40 to the equation.

Now we must negate the expenses, each appointment there is a fee of $10. So it can be given as 10x.

We know that this all must equal $235.

So the equation is as follows:

235 = (75x)+40-(10x)

Simplifying we get

235 = 65x + 40

195 = 65x

195/65 = x

x = 3

Therefore, Logan had 3 appointments.

Answer:

X=11

Step-by-step explanation

\(5^{3+8} =5^{11}\)=11

Answer:

111,111,111^2

Step-by-step explanation:

so the denominator is just 1+2+3+4+5......+8 added together multiplied by two since it goes down, then +9 as the middle. So 1+2+3....... to 8 is basically just 1+8, 2+7, 3+6, etc. so we have 4 pairs of 9 which is 36. 36*2 is equal to 72, them plus 9 is 81. 999,999,999*999,999,999 can be written as 999,999,999^2. the bottom is 81 so we can square root both top and bottom to get 999,999,999/9 right, and we just square it back so that equals 111,111,111^2 .

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Answer: 8.49 inches

Step-by-step explanation:

16.4-7.91=8.49 inches

The solution is, 736 in^2 is the total surface area in square inches of the prism.

Surface area is the amount of space covering the outside of a three-dimensional shape. The surface area of a solid object is a measure of the total area that the surface of the object occupies.

here, we have,

we know that

the total surface area of a prism is equal to

SA=2B+Ph

where

B is the area of the base

P is the perimeter of the base

h is the height of the prism

Let

L=10 in

W=8 in

H=16 in

so

B=L*W

  =80 in^2

P=2(L+W)

 =36 in

H=16 in

therefore

SA=2(80) + 36 * 16

SA=736 in^2

Hence, The solution is, 736 in^2 is the total surface area in square inches of the prism.

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Answer:

The point of intersection between 2x+3y=12 and 2x-y=4 is (3,2)

Step-by-step explanation:

The given formulas are:

\($\sinh^{-1}u=\ln\left(u+\sqrt{u^2+1}\right)$, $\cosh^{-1}u=\ln\left(u+\sqrt{u^2-1}\right)$, $\tanh^{-1}u=\frac{1}{2}\ln\left(\frac{1+u}{1-u}\right)$, $\text{sech}^{-1}u=\ln\left(\frac{1}{u}+\sqrt{\frac{1}{u^2}-1}\right)$ and $\coth^{-1}u=\frac{1}{2}\ln\left(\frac{u+1}{u-1}\right)$\),
where \($u$\) is any real number.

We have  

\($\coth^{-1}\left(\frac{3}{4}\right)$.\)

As \($\ln\left(-1\right)$\) is not a real number, we cannot express

\($\coth^{-1}\left(\frac{3}{4}\right)$\) in terms of natural logarithms.

Thus, we conclude that \($\coth^{-1}\left(\frac{3}{4}\right)$\) cannot be expressed in terms of natural logarithms.

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Answer:

Height of the tree is 78.11 feet.

Step-by-step explanation:

By applying the tangent rule in the right triangle formed,

Since, tanθ = \(\frac{\text{Opposite side}}{\text{Adjacent side}}\)

tan(32)° = \(\frac{h}{125}\)

h = 125(tan32°)

h = 125(0.62487)

h = 78.109

  ≈ 78.11 ft

Height of the tree will be 78.11 feet.

A random sample taken with replacement from the original sample, and having the same size as the original sample, is known as a "bootstrap sample" or "bootstrap replication."

Bootstrapping is a resampling technique used to estimate the sampling distribution of a statistic. When we have a limited sample size and want to draw inferences about the population, we can use bootstrapping to create multiple resamples by randomly selecting observations from the original sample with replacement.

Here's how it works:

The key idea behind bootstrapping is that the original sample serves as a proxy for the population, and by repeatedly resampling from it, we can approximate the sampling distribution of the statistic of interest. This approach is especially useful when the underlying population distribution is unknown or non-normal.

By using a bootstrap sample that is the same size as the original sample, we maintain the same sample size and capture the variability present in the original data.

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The weight of the fourth horse must be less than 1420 pounds for it to be on the trailer.

Inequality is an expression used to show the non equal comparison of two or more numbers and variables.

Let x represent the weight of the fourth horse.

From the question:

x + 890 + 1250 + 940 ≤ 4500

x + 3080 ≤ 4500

x ≤ 1420

The weight of the fourth horse must be less than 1420 pounds for it to be on the trailer.

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To find the probability of the interval (-0.15 < z < 2.67) in a standard normal distribution, we can use the cumulative distribution function (CDF) of the standard normal distribution.

The CDF gives the probability that a standard normal random variable is less than or equal to a given value. In this case, we need to find the probability that z is less than or equal to 2.67 and subtract the probability that z is less than or equal to -0.15.

Using a standard normal distribution table or a statistical calculator, we can find the corresponding probabilities:

P(z < 2.67) ≈ 0.9960

P(z < -0.15) ≈ 0.4404

To find the probability of the interval (-0.15 < z < 2.67), we subtract the probability of z < -0.15 from the probability of z < 2.67:

P(-0.15 < z < 2.67) ≈ P(z < 2.67) - P(z < -0.15)

≈ 0.9960 - 0.4404

≈ 0.5556

Therefore, the probability of the interval (-0.15 < z < 2.67) in a standard normal distribution is approximately 0.5556.

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Answer: So zero represents the point when locating a point on the number line like negatives and positives

The equivalent value of the function \(\rm f(x) = -2x^2 -3x + 5\) if x = -3 is -4.

Function; \(\rm f(x) = -2x^2 -3x + 5\) for the input value –3.

What are the x-intercepts of the function f(x)?

To determine the value of the function following all the steps given below.

For x = -3, we will have to substitute x = -3 into the expression to have:

Then,

The value of f(x) when x is -3 is,

\(\rm f(-3) = -2(-3)^2 -3(-3) + 5\\\\ f(-3) = -2(9) + 9 + 5 \\\\f(-3) = -18 + 14 \\\\\f(-3) = -4 \)

Hence, The equivalent value of the function \(\rm f(x) = -2x^2 -3x + 5\) if x = -3 is -4.

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2×3+4=62-72.6.10 to the power of 10.

Answer:

Probably, 3/1.

Step-by-step explanation:

Just do the reverse of the instructions and you get your answer.

1+2=3

2-1=1

The value of A is 114.

The value of B is 46.

The value of C is 64.

The value of D is 200.

statistics, the science of collecting, analyzing, presenting, and interpreting data.

To find the value of A will be = Total for cell phone - No of Mp3 player

= 154 - 40

= 114

To find B = Mp3 Player + Non Mp3 Player

= 24 + 22

= 46

To find C = Mp3 Player with cellphone + Mp3 Player without cellphone

= 40 + 24

= 64

To find D = 136 + C

= 136 + 64

= 200

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Answer:

D. Cost

It is cost because the y axis is the dependent variable because the cost depends on the weight and the dependent is the y axis.

Step-by-step explanation:

Please mark brainliest I hope this helps.

Answer:

D the cost

Step-by-step explanation:

cause the costs always go on the y axis

Answer: The conversion of a raw score to a scaled LSAT score is a complex process that involves several steps. The Law School Admission Test (LSAT) is a standardized test used by law schools in the United States and Canada to assess applicants' critical thinking, reading comprehension, and analytical reasoning skills.

Here's a general overview of the process of converting a raw score to a scaled LSAT score:

- Raw score calculation: The raw score is the number of questions answered correctly on the LSAT. There is no penalty for incorrect answers, so it is in your best interest to answer every question, even if you are unsure of the correct answer.

- Equating: The LSAT is equated to account for differences in difficulty between test forms. This means that the raw scores of test-takers are adjusted so that the scaled scores are consistent across different test forms.

- Scaling: The raw scores are then scaled to a range of 120 to 180, with a median score of 150 and a standard deviation of 10. This scaling process allows for meaningful comparisons between test-takers, regardless of the difficulty of the specific test form they took.

It is important to note that the LSAT score is not based solely on the number of questions answered correctly, but also on the difficulty of the questions. This means that a high raw score on a particularly difficult test form may result in a lower scaled score than a lower raw score on a less difficult test form.

Step-by-step explanation: