if f(x)=6x^3-4 and g(x)=2x+2 find (f-g)(x)​

According to  Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function: \(g(s)=\int_{5}^{s}\left(t-t^{2}\right)^{8} d t\) is

\(g^{\prime}(s)=f(s)=\left(s-s^{2}\right)^{8}\)

A Fundamental Theorem of Calculus is a powerful theorem that defines the relationship among differentiation and integration and provides a method for evaluating definite integrals without the use of Riemann sums or calculating areas.

The theorem is divided into two parts, the first of which is stated below, called Fundamental Theorem of Calculus, Part 1. Part 1 introduces the concept of differentiation and integration.

Given a function defined in the context of an integral, as follows:

\(G(x)=\int_{a}^{x} f(t) d t\)

A derivative for G(x) is then as follows:

\(G^{\prime}(x)=f(x)\)

This is Part 1 of the Calculus Fundamental Theorem.

Now, according to the question;

Consider function; \(f(t)=\left(t-t^{2}\right)^{8}\)

The, function becomes; \(g(s)=\int_{5}^{s} f(t) d t\)

Part 1 of a Fundamental Theorem of Calculus states that;

\(g^{\prime}(s)=f(s)=\left(s-s^{2}\right)^{8}\)

Therefore, the derivatives of the following functions is \(g^{\prime}(s)=f(s)=\left(s-s^{2}\right)^{8}\).

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The complete question is-

Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function:

\(g(s)=\int_{5}^{s}\left(t-t^{2}\right)^{8} d t\)

Mary used 96 pounds of type b coffee this month.

Using algebraic expression and equation, we can solve how much of each type of coffee did Mary used that month.

An algebraic expression is a number, variable, or the combination of both and operational symbols. On the other hand, an equation is the equality of two expressions separated by "=".

Given that that month, Mary made 181 pounds of the blend that is a mixture of two types of coffee, we can express this as:

181 = a + b

where a = pounds of type a coffee that costs $5.35 per pound

b = pounds of type b coffee that costs $4.15 per pound

Also, the total cost of the blend that month is $853.15, which is the sum of the total cost of the two types of coffee. We can express that as:

$853.15 = $5.35(a) + $4.15(b)

Using substitution method to solve the two equations,

181 = a + b   ⇒   a = 181 - b

$853.15 = $5.35(181 - b) + $4.15(b)

853.15 = 968.35 - 5.35b + 4.15b

5.35b - 4.15b = 968.35 - 853.15

1.2b = 115.2

b = 96

a = 181 - b

a = 181 - 96

a = 85

Hence, Mary used 85 pounds of type a coffee and 96 pounds of type b coffee that month.

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Answer:

56

Step-by-step explanation:

Zoe : hanna

3         7

Zoe got 24

3*8 = 24

so multiply each side by 8

Zoe : hanna

3*8         7*8

24           56

Hanna got 56

The equation of the graphed function is given as follows:

f(x) = x³ + 2x² - 5x - 6.

The equation of the function is obtained considering the Factor Theorem, as a product of the linear factors of the function.

From the graph, the zeros of the function are:

Hence the function is:

f(x) = a(x + 3)(x + 1)(x - 2).

In which a is the leading coefficient.

Expanding the product, we have that:

f(x) = a(x² + 4x + 3)(x - 2)

f(x) = a(x³ + 2x² - 5x - 6).

When x = 0, y = -6, hence the leading coefficient a is obtained as follows:

-6a = -6

a = 1.

Hence the function is:

f(x) = x³ + 2x² - 5x - 6.

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Answer:

Which statements are true about the figure? Select two options.

Line JM intersects line GK at point N.

Horizontal line G K intersects vertical line J M at point N, forming a right angle. A line extends from point N to L, down and to the right.

Step-by-step explanation:

please mark me as brainliest

∠MNL and ∠KNL are complementary angles while ∠GNM and ∠JNK are supplementary angles

An angle is formed from the intersection of two or more lines. Types of angles are acute, obtuse and right angled.

Complementary angles add up to 90 degrees while supplementary angle add up to 180 degrees.

∠MNL + ∠KNL = 90° (complementary angles)

∠GNM + ∠JNK = 180° (supplementary angles)

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Percentage change = 10%

We can use the formula:

Percent change = \(\frac{New-Old}{Old}\) x 100

Percent change = \(\frac{77-70}{70}\)x100

Percent change = \(\frac{7}{70}\) x 100

Percent change = 0.1 x 100

Percent change = 10%

Answer: 53.9

Step-by-step explanation:

Answer:

-7x(to the power of 2)-2x-16

Explanation:

The firm should hire workers until the MRP of the last worker hired equals the wage rate.

Based on the information given in Figure 18-1, we can see that the profit maximizing level of employment for the firm is where the marginal revenue product (MRP) equals the wage rate (MPL x P = w). At a selling price of $12 per unit and a wage rate of $700 per week, the MRP is $60. Therefore, the firm will hire workers up to the point where the MRP equals $60, which occurs at 4 workers (as shown in the graph). Thus, the answer is c.4. The firm will hire 4 workers to maximize its profit. Word count: 100 words. To determine the number of workers a firm will hire to maximize its profit, we need to analyze the marginal revenue product (MRP) of labor. MRP is calculated by multiplying the marginal product of labor (MPL) by the price of output. In this case, the output price is $12 per unit, and the wage rate is $700 per week. The firm should hire workers until the MRP of the last worker hired equals the wage rate.

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Given :

A number 789.13 .

To Find :

7.74% of 789.13 .

Solution :

Let, 7.74% of 789.13 is x.

So,

\(x = \dfrac{789.13\times 7.74}{100}\\\\x = \dfrac{6107.8662}{100}\\\\x = 61.08\)

Therefore, 7.74% of 789.13 upto 2 decimal place 61.08 .

Answer:

3 pictures are giraffes

Step-by-step explanation:

1/3 of 9 is 3. Caleb took 3 pictures of giraffes.

3,6,9...

1/3, 2/3, 3/3=1

Hope this helps!

Answer:

cucuffuifb use I'll I EB ten nu TV cell GB EEC to reef GRB decry

Let,

Number of Advance Tickets = a

Number of Same-Day tickets = s

Given,

Total 45 tickets sold

We can write

Also, each advance ticket cost $15 and same day tickets cost $20 for a total of $825. Thus, we can write:

We will multiply the first equation by - 15 and then add both equations. Then, solve for "s". The steps are shown below:

Now, we can use this value of "s" and put it into Equation 1 and find the value of "a". Shown below:

The length of AB = 5 units

We have a point B is between A and C.

We have to determine the length of AB.

According to the question, we have -

AB = x + 4

BC = 2x - 2

AC = 4x - 1

Now -

AC = AB + BC

4x - 1 = x + 4 + 2x - 2

4x - 1 = 3x + 2

3x = 3

x = 1

Therefore -

AB = 1 + 4 = 5 units

Hence, the length of AB = 5 units

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The solution to the provided differential equation with the initial condition y(0) = 5 and u as a step change of unity is y = -2

The provided differential equation is: \(\[\frac{{dy}}{{dt}} = y + 2u\]\) with the initial condition: y(0) = 5 where u is a step change of unity.

To solve this differential equation, we can use the method of integrating factors.

First, let's rearrange the equation in the standard form:

\(\[\frac{{dy}}{{dt}} - y = 2u\]\)

Now, we can multiply both sides of the equation by the integrating factor, which is defined as the exponential of the integral of the coefficient of y with respect to t.

In this case, the coefficient of y is -1:

Integrating factor \(} = e^{\int -1 \, dt} = e^{-t}\)

Multiplying both sides of the equation by the integrating factor gives:

\(\[e^{-t}\frac{{dy}}{{dt}} - e^{-t}y = 2e^{-t}u\]\)

The left side of the equation can be rewritten using the product rule of differentiation:

\(\[\frac{{d}}{{dt}}(e^{-t}y) = 2e^{-t}u\]\)

Integrating both sides with respect to t gives:

\(\[e^{-t}y = 2\int e^{-t}u \, dt\]\)

Since u is a step change of unity, we can split the integral into two parts based on the step change:

\(\[e^{-t}y = 2\int_{{-\infty}}^{t} e^{-t} \, dt + 2\int_{t}^{{\infty}} 0 \, dt\]\)

Simplifying the integrals gives:

\(\[e^{-t}y = 2\int_{{-\infty}}^{t} e^{-t} \, dt + 0\]\)

\(\[e^{-t}y = 2\int_{{-\infty}}^{t} e^{-t} \, dt\]\)

Evaluating the integral on the right side gives:

\(\[e^{-t}y = 2[-e^{-t}]_{{-\infty}}^{t}\]\)

\(\[e^{-t}y = 2(-e^{-t} - (-e^{-\infty}))\]\)

Since \(\(e^{-\infty}\)\) approaches zero, the second term on the right side becomes zero:

\(\[e^{-t}y = 2(-e^{-t})\]\)

Dividing both sides by \(\(e^{-t}\)\) gives the solution: y = -2

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The equation of the line that passes through the point (-1, 1) and has a slope of -1 is y = -x.

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁)

Where:

At data point (-1, 1), a linear equation of this line can be calculated in point-slope form as follows:

y - y₁ = m(x - x₁)

y - 1 = -1(x - (-1))

y - 1 = -1(x + 1)

y = -x -1 + 1

y = -x.

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The equation of the line is y = -x

The general formula for the equation of a line is expressed with the equation;

y = mx + c

Given that the parameters are;

From the information given, we have that;

slope, m =-1

The points are (-1, 1)

Now, let's substitute the values

1 = -1(-1) +  c

expand the bracket

1 = 1 + c

collect like terms

c = 0

The equation of the line is y = -x

Hence, the equation is y = -x

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Answer:Except -1 for all real values of k given the equations has a unique solution.

Step-by-step explanation:

Except -1 for all real values of k given the equations has a unique solution.

Explanation:

Compare given linear pair of equations

(3k+1)x+3y-2 = 0 ----(1)

(k²+1)x+(k-2)y-5=0 ----(2)

with

----(2)

----(3)

we get ,

and

\* Given linear equations have unique solution *\

=> 3k(k-2)+1(k-2)≠3k²+3

=> 3k²-6k+k-2≠3k²+3

=> 3k²-5k-3k²≠3+2

=> -5k ≠ 5

Divide each term by (-5) , we get

=> k ≠-1

Therefore,

Except -1 for all real values of k given the equations has a unique solution.

Answer:

0

Step-by-step explanation:

Answer:

a) 72

b) 1/72

c) 1/36

Step-by-step explanation:

a) number of ways she can choose route= 3C1 = 3

   number of ways she can choose parking lots= 4C1 = 4

number of ways she can choose entrances= 3C1 = 3  

number of ways she can choose elevators= 2C1 = 2

number of ways she can go to office= number of ways she can choose route×number of ways she can choose parking lots×number of ways she can choose entrances×number of ways she can choose elevators

      number of ways she can go to office= 3×4×3×2

                                                                      = 72

b) Probability of morning side= number of morning side/ total number of routes=  1/3

probabiltiy of Parking lot A=  number of parking lot A/ total number of parking lot= 1/4

probability of south entrance= number of south entrance/ total number of entrances=  1/3

probablity of elevator 1=  number of elevator 1/ total number of elevator= 1/2

combine probability= 1/3× 1/4×1/3×1/2 = 1/72

c) Probability of Industrial Avenue= number of industrial avenue/ total number of avenue= 1/3

Probability of parking lot D= number of parking lot D/ total number of parking lot after deducting number of parking lots A and B = 1/2

Probability of north entrance= number of north entrance/ total number of entrance= 1/3

probablity of elevator 2= number of elevator 2/ total number of elevator

                                      = 1/2

combine probability= 1/3 × 1/2 × 1/3 ×1/2

                                  = 1/36

Answer:

-4x+12=10

-4x+12-12=10-12

-4x= -2

-4x/-4=-2/-4

x=0.5

Step-by-step explanation:

Answer:

1) $10b

2) 20

3) $5a

The hypothesis test aims to determine whether female college students score higher than 3.0 on the emotional empathy scale. The null hypothesis states that there is no significant difference, while the alternative hypothesis suggests that there is a significant difference.

a. The null hypothesis (H₀) states that the mean emotional empathy score for female college students is equal to or less than 3.0 (μ ≤ 3.0), while the alternative hypothesis (H₁) proposes that the mean emotional empathy score for female college students is greater than 3.0 (μ > 3.0). To compute the test statistic, we use the formula:

t = (sample mean - population mean) / (population standard deviation / √sample size)

In this case, the sample mean response is 3.28, the population mean is 3.0, the population standard deviation is 0.5, and the sample size is 30. Plugging these values into the formula, we calculate the test statistic. To find the observed significance level (p-value) of the test, we compare the test statistic to the appropriate t-distribution with (sample size - 1) degrees of freedom. By looking up the p-value associated with the test statistic in the t-distribution table or using statistical software, we determine the significance level.

With a significance level of α = 0.01, we compare the observed significance level (p-value) from part c to α. If the p-value is less than α, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis. The choice of significance level α depends on the desired level of confidence in the results. The smaller the α-value, the stronger the evidence required to reject the null hypothesis. As long as the observed significance level (p-value) is smaller than the chosen α-value, we can reject the null hypothesis and conclude that there is sufficient evidence to support the alternative hypothesis.

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Answer: He can use 3 x 5 = 15 and 15 + 3.

Step-by-step explanation:

Since a small car is $3, and the large car is 5x the price of the small car, he can use the equation 3 x 5 = 15, because the small car is $3, and the large car is 5x the price. You can use 15 + 3 = 18, because the small car is $3, so you also have to add that.

Here to help!

The equation is x + 5x = 18 , where x is the cost of small toy car and the total cost of the two cars = $ 18

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the total cost of the two cars be A

Now , the equation will be

Let the cost of the small toy car be = x

The cost of small toy car = $ 3

The cost of the large car = 5 x cost of small toy car

Substituting the values in the equation , we get

The cost of the large car = 5 x 3

The cost of the large car = $ 15

So , the cost of two cars = x + 5x

Substituting the values in the equation , we get

The total cost of the two cars A = 15 + 3

The total cost of the two cars A = $ 18

Therefore , the value of A is $ 18

Hence , the equation is A = x + 5x

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Answer:

See below

Step-by-step explanation:

Odds AGAINST are 3 to5        then odds FOR are  2 to 5

    2/5   = .4 = 40%   chance of winning

For a second order differential equation t²y'' - 4ty' + 6y = 0, general solution is of the form y(t) = c₁t² + c₂t³, so another solution other than y₁(t) = t² is y₂(t) = t³.

Given solution to t²y'' - 4ty' + 6y = 0 is

y₁(t) = t²

Using the method of reduction of order, let us assume, y₂(t) = v(t)y₁(t) is a solution to t²y'' - 4ty' + 6y = 0 for suitable choice of v(t). So,

y₂ = vt²

y₂' = 2vt + t²v'

y₂'' = 2v + 2tv' + 2tv' + t²v''

y₂'' = 2v + 4tv' + t²v''

Substituting this

t²×( 2v + 4tv' + t²v'') - 4t×(2vt + t²v') + 6×(vt²) = 0

t⁴v'' = 0

v'' = 0

v' = c, c is a constant

v = ct

Therefore, y₂(t) = ct×t²

y₂ (t) = ct³

Therefore general solution will be y(t) = c₁t² + c₂t³

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Answer:

Supplementary angles add up to 180 degrees. The key phrase "less than" signifies you are going to subtract angle X from angle Y. Angle Y is 2 times the measure of angle X so you are going to multiply Y by 2. So right now you should have the equation 2y - 19 = 180. Then, plug it in. Add 19 to 180 to move it to the other side and then divide by 2.

Answer:

<P = 41

Step-by-step explanation:

we can consider this first figure as a quadrilateral and the trianlgle attached to be is equilateral triangle (as it is already shown in the figure that sides are equal)

we know that each angle of equalateral triangle is 60°

we can see that angle 79° is attached to it and even other angle is also attached

let the other angle be x

we can notice that x and the angle of equi triangle make a linear pair

so 180 - 60

= 120°

the opposite angle to the angle x will be also equal as angles on the same side of qual sides will be equal

now we know that total angle sum of quadrilateral is 360°

so

79 + 120 + 120 + <P = 360

319 + <P = 360

<P = 360 - 319

<P = 41

Answer:

3:2

Step-by-step explanation:

42:28

21:14

3:2

The statement is true.Similarly to the case of R4, a set of three vectors in R47 could not span all of R47 since each of these vectors only has 47 components. They are a subset of R47 but they do not encompass the whole space of R47.

A set of three vectors in R4 could not span all of R4. This statement is true.Explanation:In order for a set of vectors to span a space, they need to be able to create any point within that space by linearly combining the vectors in the set.A set of three vectors in R4 could not span all of R4 since each of these vectors only has four components. They are a subset of R4 but they do not encompass the whole space of R4.

When n is less than m, a set of n vectors in Rm could not span all of Rm. This statement is false.Since each of the n vectors has m components, they can be combined in a way that creates any point within Rm. Thus, a set of n vectors in Rm could span Rm when n is less than m.

A set of three vectors in R47 could not span all of R47. This statement is true.Similarly to the case of R4, a set of three vectors in R47 could not span all of R47 since each of these vectors only has 47 components. They are a subset of R47 but they do not encompass the whole space of R47.

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Answer:

Step-by-step explanation:

So because Howard wants to divide the granola evenly among all of his friends, we have to divide the amount of pounds he has by the number of friends he has.

(3/5) / 4

Dividing by four is the same as multiplying by the reciprocal of 4 which is 1/4.

So (3/5) * (1/4) is 3/20 which is .15 pounds