Evaluate the integral. (Use C for the constant of integration.
∫9/(1 + t^2) I + te^(t^2)j +5√t k) dt

Derivative of the following functions are:f(x)= x/(2x−3)^2g(x)=(3x^2 −1)^2 (2x+1)^4h(x)=5x*2^(x ^2+1)s(x)= cos

The given function is `f(x)= x/(2x−3)^2`.To find its derivative, we apply the quotient rule of derivative.The quotient rule is as follows,`[f(x)/g(x)]' = [f'(x)*g(x) - f(x)*g'(x)] / g^2(x)`So, applying the quotient rule, we get:`

f'(x) = [x*2(2x-3)*1 - 1*(2x-3)^2*1] / (2x-3)^4`Simplifying,

`f'(x) = [-4x + 9] / (2x-3)^3`Therefore, the derivative of `f(x)` is `[-4x + 9] / (2x-3)^3`.b) The given function is

`g(x)=(3x^2 −1)^2 (2x+1)^4`.To find its derivative, we apply the product rule of derivative. The product rule is as follows,

`(f(x)*g(x))' = f'(x)*g(x) + f(x)*g'(x)`So, applying the product rule, we get:

`g'(x) = 2(3x^2-1)*6x*(2x+1)^4 + 4(3x^2-1)^2*(2x+1)^3*2`Simplifying,

`g'(x) = 12x*(2x+1)^3(3x^2-1) + 8(3x^2-1)^2*(2x+1)^3`Therefore, the derivative of \

`g(x)` is `12x*(2x+1)^3(3x^2-1) + 8(3x^2-1)^2*(2x+1)^3`.c) The given function is

`h(x)=5x*2^(x^2+1)`.To find its derivative, we apply the product rule of derivative. The product rule is as follows,

`(f(x)*g(x))' = f'(x)*g(x) + f(x)*g'(x)`So, applying the product rule, we get:

`h'(x) = 5*2^(x^2+1)*(x*ln2*2x)`Simplifying,

`h'(x) = 10x^2*ln2*2^(x^2+1)`Therefore, the derivative of `h(x)` is `10x^2*ln2*2^(x^2+1)`.d) The given function is `s(x)= cosx/x`.To find its derivative, we apply the quotient rule of derivative.The quotient rule is as follows,

`[f(x)/g(x)]' = [f'(x)*g(x) - f(x)*g'(x)] / g^2(x)`So, applying the quotient rule, we get:

`s'(x) = [x*(-sinx) - cosx*1] / x^2`Simplifying,

`s'(x) = [-sinx - cosx/x]`Therefore, the derivative of `s(x)` is `[-sinx - cosx/x]`.

To know more about Derivative visit:

https://brainly.com/question/29144258

#SPJ11

To find the volume of the solid generated by revolving the region bounded by the graphs of the equations, either the disk method or the shell method can be used.

When finding the volume of a solid generated by revolving a region around a line, we have two methods at our disposal: the disk method and the shell method.

1. Disk Method:

The disk method involves dividing the region into infinitesimally thin disks perpendicular to the axis of rotation. The volume of each disk can be calculated using the formula for the volume of a cylinder (V = πr^2h), where r represents the radius of the disk and h represents its height. By summing up the volumes of all the disks, we obtain the total volume of the solid.

2. Shell Method:

The shell method, on the other hand, involves dividing the region into infinitesimally thin cylindrical shells parallel to the axis of rotation. Each shell has a thickness of Δx, where x is the variable that defines the boundaries of the region. The volume of each shell is calculated by multiplying the height of the shell (given by the difference in the y-values of the two bounding curves) by the circumference of the shell (given by 2πx). By summing up the volumes of all the shells, we obtain the total volume of the solid.

Both methods yield the same result for the volume of the solid. The choice between the two methods depends on the shape of the region and the convenience of integrating with respect to either x or y.

Learn more about disk method and the shell method

brainly.com/question/28184352

#SPJ11

Answer:

Step-by-step explanation:

Only a straight line can be formed at the intersection of a plane with another plane. The faces of a cube are planes, so a 2-dimensional (planar) cross section of a cube cannot be a curve. It cannot be an ellipse or circle.

The intersection of a plane with a cube can be a polygon with 3, 4, 5, or 6 sides. That is, the 2-D cross section of a cube can be ...

  triangle, rectangle, square, pentagon, hexagon

__

The attachment shows some possibilities.

Answer:

3rd option

Step-by-step explanation:

Substitute x = 0 into f(x) and check if the result is - 6

f(0) = (0 + 1)(0 + 2)(0 + 3) = 1 × 2 × 3 = 6 ≠ - 6

f(0) = (0 + 1)(0 - 2)(0 - 3) = 1 × - 2 × - 3 = 1 × 6 = 6 ≠ - 6

f(0) = (0 - 1)(0 + 2)(0 + 3) = - 1 × 2 × 3 = - 1 × 6 = - 6 ✔

Thus the 3rd option crosses the y- axis at (0, - 6 )

Answer:

D

Step-by-step explanation:

Linear Functions will never have curve lines in the graph.

the answer is D. Linear functions are those whose graph is a straight line

The level of significance, in hypothesis testing, is the probability of rejecting a null hypothesis when it is actually true.

This is why it is important to set a proper level of significance before conducting the hypothesis testing to minimize the risk of making a type I error (incorrectly rejecting a true null hypothesis). This criterion is known as (alpha) and is usually always set to in null hypothesis testing.  0.05, and 0.01 are typical values. The level of significance is typically set at 0.05 or 0.01, meaning that there is a 5% or 1% chance of rejecting the null hypothesis when it is actually true.

Learn more about hypothesis testing at https://brainly.com/question/12860075

#SPJ11

The level of significance, in hypothesis testing, is the probability of  rejecting null hypothesis. accepting a true rejecting a true rejecting a false accepting a false

In hypothesis testing, the level of significance (often denoted as α) is a predetermined threshold used to make a decision about the null hypothesis. It represents the maximum probability of making a Type I error, which is rejecting a true null hypothesis.

The null hypothesis (H0) is a statement or assumption that suggests there is no significant difference or relationship between variables in a population. The alternative hypothesis (Ha) is the statement that contradicts or opposes the null hypothesis, suggesting that there is a significant difference or relationship.

To perform a hypothesis test, we collect sample data and calculate a test statistic. Then, we compare the test statistic to a critical value determined by the level of significance.

If the test statistic falls in the rejection region (beyond the critical value), we reject the null hypothesis. If the test statistic falls within the acceptance region (below the critical value), we fail to reject the null hypothesis.

To know more about the null hypothesis, here

brainly.com/question/13135308

#SPJ11

The rate at which the water level is rising when the water level is 6 cm is approximately 2.67 cm/s. if an inverted pyramid is filled with water at a constant rate of 55 cubic centimeters per second, the top of pyramid is in square shape with length of 8 cm and height of 14 cm.

Let's call this rate "r".

Volume of pyramid = (1/3) * base area * height

Since the pyramid has a square base, the base area is given by

Base area = (side length)^2

Substituting the given values

Base area = (8 cm)^2 = 64 cm^2

Height = 14 cm

V = (1/3) * 64 cm^2 * 14 cm = 298.67 cm^3

We know that the water is being added to the pyramid at a constant rate of 55 cm^3/s. Therefore, the rate at which the volume is increasing is

dV/dt = 55 cm^3/s

We also know that the volume of water in the pyramid at any given time is given by

V_water = (1/3) * base area * h_water

where h_water is the height of the water at that time.

To find the rate at which the water level is rising (r), we need to find dh_water/dt. We can do this by taking the derivative of both sides of the equation for V_water with respect to time

dV_water/dt = (1/3) * base area * dh_water/dt

Substituting the known values

dV_water/dt = (1/3) * (8 cm)^2 * dh_water/dt

dV_water/dt = (64/3) cm^2 * dh_water/dt

dh_water/dt = 3 * dV_water/dt / 64

dh_water/dt = 3 * 55 cm^3/s / 64 = 2.67 cm/s

To know more about rate here

https://brainly.com/question/24020169

#SPJ4

In a 4x3x2x2 factorial experiment, you have 4 independent variables and potentially 4 main effect hypotheses.

The 4 independent variables are represented by the four numbers in the experimental design

(i.e., 4 levels of variable A, 3 levels of variable B, 2 levels of variable C, and 2 levels of variable D).

The potentially 4 main effect hypotheses are one for each independent variable, which states that there is a significant effect of that independent variable on the outcome variable.

A factorial experiment includes multiple factors simultaneously, each consisting of two or more

levels. Many factors simultaneously influence what is studied in a factorial experiment, and

experimenters consider the main effects and interactions between factors.

To know more about Factorial experiment:

https://brainly.com/question/18402941

#SPJ11

Answer:

True, True, False, True, False for part 1

Step-by-step explanation:

Make me brainliest

Answer:true,true,false,true part one

Step-by-step explanation:

The correct response is (f) 26 ft. The radius of the cylinder is approximately 26 ft.

To solve for the radius, we can use the formula for the volume of a cylinder, V = πr²h, where V is the volume, r is the radius, and h is the height. We can plug in the given values to get:

63,679 = πr²(30)

Dividing both sides by 30π gives:

r² = 676

Taking the square root of both sides gives:

r ≈ 26

Rounding to the nearest whole number gives the answer of 26 ft. Therefore, the correct response is (f) 26 ft.

Learn more about the Radius of the Cylinder:

https://brainly.com/question/28247116
#SPJ4

Complete Question:

A cylinder has a height of 30 ft and a volume of 63,679 ft³. what is the radius of the cylinder? round your answer to the nearest whole number. responses

a) 676 ft

b) 676 ft  

c)338 ft

d) 338 ft

e) 52 ft

f) 26 ft.  

Answer:

You know a table is a function when each element inside the domain matches with only one element within the range.

Answer: You know a table is a function when each element inside the domain matches with only one element within the range.

Step-by-step explanation:  hope this helps

Answer:

66m, 35in?, 12m, 2km, 26cm

Step-by-step explanation:

22/17 = 1.294x51 = 66m

7/3 = 2.333x15? = 35in not sure if the number on the pic is 15

18/12 = 1.5x8 = 12m

6/27 = .2222x9 = 2km

6.5/2.5 = 2.6x10 = 26cm

The probability that the first person picked will be female is 2/5.

Two quantities are compared to form a ratio. Discover how to calculate the ratio of two items, such as apples to oranges.

Total audience = 120

Ratio of males to females; 3:2

Total males : 3*120/ 5 = 72

Total females: 2*120/5 = 48

Probability that the first person picked will be female = total females / total audience

Probability = 48 / 120

Probability = 2/5

Thus, the probability that the first person picked will be female is 2/5.

To know more about the ratio of numbers, here

https://brainly.com/question/12024093

#SPJ1

The question states that 1/4 of students at International are in the blue house, with 1/5 votes for Adam and 1/4 for Franklin. To analyze the results, calculate the fraction of votes for each candidate and multiply by the total number of students.

Based on the information provided, 1/4 of the students at International are in the blue house. The vote went as follows: 1/5 of the votes were for Adam, and 1/4 of the votes were for Franklin.

To analyze the vote results, we need to calculate the fraction of votes for each candidate.

Let's start with Adam:
- The fraction of votes for Adam is 1/5.
- To find the number of students who voted for Adam, we can multiply this fraction by the total number of students at International.

Next, let's calculate the fraction of votes for Franklin:
- The fraction of votes for Franklin is 1/4.
- Similar to before, we'll multiply this fraction by the total number of students at International to find the number of students who voted for Franklin.

Remember, we are given that 1/4 of the students are in the blue house. So, if we let "x" represent the total number of students at International, then 1/4 of "x" would be the number of students in the blue house.

To summarize:
- The fraction of votes for Adam is 1/5.
- The fraction of votes for Franklin is 1/4.
- 1/4 of the students at International are in the blue house.

Please note that the question is incomplete and doesn't provide the total number of students or any additional information required to calculate the specific number of votes for each candidate.

To know more about fraction Visit:

https://brainly.com/question/10708469

#SPJ11

The transfer price set by the selling division should be equal to the selling price less the variable costs plus the foregone contribution to the organization of making the transfer internally. Option D.

The transfer price refers to the price at which goods or services are transferred between divisions within the same organization. When the selling division sets the transfer price, it needs to consider various factors. Option D, selling price less the variable costs plus the foregone contribution to the organization of making the transfer internally, is the most appropriate choice.

The selling price less the variable costs ensures that the selling division covers its direct costs associated with the transferred goods or services. This ensures that the division remains financially viable and does not incur losses. However, it is also important to consider the opportunity cost of making the transfer internally.

The foregone contribution to the organization represents the potential profit or contribution that the selling division could have made if it had sold the goods or services to external customers instead of transferring them internally. By including this foregone contribution in the transfer price, the selling division accounts for the potential value it could have added to the organization.

In conclusion, the transfer price set by the selling division should consider both the variable costs associated with the transfer and the foregone contribution to the organization. Option D, selling price less the variable costs plus the foregone contribution to the organization of making the transfer internally, captures both of these factors and provides a comprehensive approach to setting the transfer price.

Learn more about divisions here: https://brainly.com/question/28598725

#SPJ11

Answer:

It represents the product of two rational numbers and is equivalent to a rational number.

Step-by-step explanation:

\( \sqrt{25} = 5\)

because

\(5 \times 5 = 25\)

and

\( \sqrt{4} = 2\)

because

\(2 \times 2 = 4\)

The numbers are all rational because they can all be put into fraction form.

Given that profits decrease by 13.8% when the degree of operating leverage (DOL) is 3.8.

The decrease in sales is: We have to determine the percentage decrease in sales Let the percentage decrease in sales be x.

Degree of Operating Leverage (DOL) = % change in Profit / % change in Sales3.8

= -13.8% / x Thus, we have: x

= -13.8% / 3.8

= -3.63%Therefore, the decrease in sales is 3.63%.Hence, the correct option is C) 3.63%. Percentage decrease in sales = % change in profit / degree of operating leverage

= 13.8 / 3.8

= 3.63% The percentage decrease in sales is 3.63%.

To know more about profits, visit:

https://brainly.com/question/29987711

#SPJ11

Answer:

\(\displaystyle m = \frac{7}{10}\)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

Point (0, -4)

Point (10, 3)

Step 2: Find slope m

Simply plug in the 2 coordinates into the slope formula to find slope m

Answer:

Equation: 4x = 128

\(m\angle 1 = 84\degree\)

\(m\angle 2 = 96\degree\)

Step-by-step explanation:

Answer:

y = -6 + 2/3x can I get brainliest?

Step-by-step explanation:

Just add 2/3x to both sides

y-2/3x=-6

 +2/3.      +2/3

cannot combine like term with number so..

y = -6 + 2/3x

Therefore, the 90% confidence interval for the mean repair cost for the VCRs is ($82.40,$90.12).

Subject to the exclusions outlined in this clause, the repair cost is defined as the cost of the parts and labor required to fix or replace any covered component as a result of a covered mechanical breakdown. We reserve the right to substitute components of comparable sort and quality, whether they are new, OEM, swapped, rebuilt, remanufactured, or used. The suggested retail price of a part of a like type and quality, or the manufacturer's indicated retail price for Your Vehicle, whichever is higher, may not be exceeded when pricing out parts. A current, widely used flat-rate labor guide will be used to calculate labor costs. According to state-specific rules, the Repair Cost includes the necessary taxes related to the covered Mechanical Breakdown.

To learn more about repair costs, Visit:

https://brainly.com/question/15065307

#SPJ4

Answer:

6n-5

Step-by-step explanation:

let 'n' equal 'a number'

the equation above means you are multiplying 6 and that number, then reducing it by 5

4 gallons of ice cream would we required to serve 125 portions.

The size of a scoop is equal to the numbers of scoops you can yield from a quart.
If we are using a 8 scoop to serve ice cream, the amount of ice cream is calculated by multiplying the number of servings by the amount of ice cream in a scoop.
125 portions of ice cream would need (125 / 8) quarts of ice cream= 15.625 quarts of ice cream
To convert quarts to gallons, divide by 4:15.625 quarts ÷ 4 = 3.91 gallons of ice cream, approximately 4 gallons of ice cream.

Therefore, 4 gallons of ice cream would we required to serve 125 portions.

To know more about gallons, click here

https://brainly.com/question/31702678

#SPJ11

Answer:

42 divided by 3

this would be the answer because one of the thirds we are multipling by would be devons age and the other two are ebonys age.

(ebony is 14 and devon is 7 btw)

Answer:

x+2x=42

Step-by-step explanation:

Devon's age=x

ebony is x times 2

The sum of their ages is 42 meaning x+2x=42

Devon is 14 and Ebony is 28

this is because 14+28=42

Answer:

C.

Step-by-step explanation:

You have use slope form.

Answer:

Step-by-step explanation:

To find the difference between -82 and 93, we need to subtract the smaller number from the larger number. In this case, 93 is the larger number and -82 is the smaller number. So, we have:

93 - (-82)

To subtract a negative number, we can change it to addition of its absolute value. So, we can rewrite the above expression as:

93 + 82

Now, we can add the numbers:

93

82

175

Therefore, the difference between -82 and 93 is 175.

To reduce the third-order ordinary differential equation y - y" - 4y + 4y = 0 into a companion system of linear equations, we introduce new variables u and v:

Let u = y,

v = y',

w = y".

Taking the derivatives of u, v, and w with respect to the independent variable (let's denote it as x), we have:

du/dx = y' = v,

dv/dx = y" = w,

dw/dx = y"'.

Now we can rewrite the given differential equation in terms of u, v, and w:

u - w - 4u + 4u = 0.

Simplifying the equation, we get:

-3u - w = 0.

This equation can be expressed as a system of first-order linear differential equations as follows:

du/dx = v,

dv/dx = w,

dw/dx = -3u - w.

Now we have a companion system of linear equations:

du/dx = v,

dv/dx = w,

dw/dx = -3u - w.

To solve this system completely, we need to find the solutions for u, v, and w. By solving the system of differential equations, we can obtain the solutions for u(x), v(x), and w(x), which will correspond to the solutions for y(x), y'(x), and y"(x), respectively.

The exact solutions for this system of differential equations depend on the initial conditions or boundary conditions that are given. By applying appropriate initial conditions, we can determine the specific solution to the system.

To learn more about derivatives : brainly.com/question/25324584

#SPJ11

Answer: So, the question that will fit best will be, "the monthly depreciation of the laptop."

Explain: So, Pamela doesn't know how many months because the most important sentence is, "Its value depreciates monthly". And Pamela doesn't need to know about the original price of the laptop, the number of months, and the total depreciates value of the laptop.

The volume of the sphere is option (d) 904.32 cm³

Volume is a measure of the amount of three-dimensional space occupied by a substance, object, or region of space

The formula for the volume of a sphere is V = (4/3)πr³, where r is the radius of the sphere.

Substituting r = 6 cm and π ≈ 3.14 into the formula, we get:

V = (4/3) × 3.14 × 6³

Find the cube of the number

V = (4/3) × 3.14 × 216

Multiply the numbers

V ≈ 904.32

Rounding the answer to the nearest hundredth, we get approximately 904.32 cm³.

Therefore, the correct option is (d) 904.32 cm³.

Learn more about volume here

brainly.com/question/27933834

#SPJ4

The given question is incomplete, the complete question is:

What is the approximate volume of the sphere when the radius is 6 cm?

Use 3.14 to approximate pi and round the answer to the nearest hundredth if necessary.

a) 48 cm³

b) 150.72 cm³

c) 288.00 cm³

d) 904.32 cm³

Answer:

-7/4

Step-by-step explanation:

Recall that slope, m, is defined as the ratio rise to run:  rise/run.

Note that if we start at x = -2 (an arbitrary choice), and move 6 units to the right, we end up at x = 4.  This is the 'run.'  Simultaneously, y starts at 1 and decreases to - 6, a change of -7.  

Thus, the slope of the line through these two points is m = rise/run = -7/4

Answer:

Well, actually it's missing something to your question. I think...

but the question says "The points in the table lie on a line. What is the slope of the line?"

The answer might be "X"

why? still not sure but hope this other one helps...

Step-by-step explanation:

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

(8,-8)  (1,-2)

\(x_{1}\) \(y_{1}\)   \(x_{2}\) \(y_{2}\)

there and you can solve it easy