Solve the equation using the multiplicative property of equality and the reciprocal. -2(a-5)=-1/2)10. (-1/2)(-2)(q-5)=(-1/2)10. q-5=-5.
q=

The final result of the integral is:

∫ (log(1 + x²) / (x + 1)²) dx = log(x + 1) - 2 (log(x + 1) / x) - 2Li(x) + C,

where Li(x) is the logarithmic integral function and C is the constant of integration.

We have,

To solve the integral ∫ (log(1 + x²) / (x + 1)²) dx, we can use the method of substitution.

Let's substitute u = x + 1, which implies du = dx. Making this substitution, the integral becomes:

∫ (log(1 + (u-1)²) / u²) du.

Expanding the numerator, we have:

∫ (log(1 + u² - 2u + 1) / u²) du

= ∫ (log(u² - 2u + 2) / u²) du.

Now, let's split the logarithm using the properties of logarithms:

∫ (log(u² - 2u + 2) - log(u²)) / u² du

= ∫ (log(u² - 2u + 2) / u²) du - ∫ (log(u²) / u²) du.

We can simplify the second integral:

∫ (log(u²) / u²) du = ∫ (2 log(u) / u²) du.

Using the power rule for integration, we can integrate both terms:

∫ (log(u² - 2u + 2) / u²) du = log(u² - 2u + 2) / u - 2 ∫ (log(u) / u³) du.

Now, let's focus on the second integral:

∫ (log(u) / u³) du.

This integral does not have a simple closed-form solution in terms of elementary functions.

It can be expressed in terms of a special function called the logarithmic integral, denoted as Li(x).

Therefore,

The final result of the integral is:

∫ (log(1 + x²) / (x + 1)²) dx = log(x + 1) - 2 (log(x + 1) / x) - 2Li(x) + C,

where Li(x) is the logarithmic integral function and C is the constant of integration.

Learn more about integrations here:

https://brainly.com/question/30217024

#SPJ1

Answer:  3×22+c≤85

Step-by-step explanation: i think the answer is 3×22+c≤85 because 3x 22 represent the total cost of azaleas + c the cost of salvia is less than or equal to 85 because the buget is 85 and it cannot be greater

Hope this helped

The inequality for the given situation is 66+c ≤ 85.

Given that, Frank plans to spend no more than $85 on plants for his front garden. He purchases a salvia and 3 azaleas. The azaleas cost $22 each.

In mathematics, inequality refers to a relationship that makes a non-equal comparison between two numbers or other mathematical expressions.

Let c be the cost for a salvia.

Three azaleas + A salvia ≤ 85

3×22+c ≤ 85

⇒ 66+c ≤ 85

Therefore, the inequality for the given situation is 66+c ≤ 85.

To learn more about the inequality visit:

https://brainly.com/question/20383699.

#SPJ5

Answer:

y=55 when x is 33

Step-by-step explanation:

Use the direct variation formula:

\(\frac{y}{x} =k\)  or \(\frac{y}{x} =\frac{y}{x}\)

Insert the given values:

\(\frac{15}{9}=\frac{y}{33}\)

To simplify the equation, cross multiply:

\(15(33)=9(y)\\\\495=9y\)

Isolate the variable. Divide both sides by 9:

\(\frac{495}{9} =\frac{9y}{9} \\\\55=y\)

Therefore, when x is 33, y is 55.

:Done

Answer:

I). X= 1,0. II) 1.72

Step-by-step explanation:

Using quadratic formula

Answer: 1296 square inches

Step-by-step explanation:

1 square yard is 36 times 36 square inches

36 times 36 is 1296 square inches

Answer:

I think its Yes!

Step-by-step explanation:

Hope this helps!!!

To determine the total number of apples pies done, multiply the number of apple pies done each day by 14:

Hence, the company made a total of 798 apple pies.

The data that appears to have a consistent rate of change over time or with respect to another variable often appears to be linear.

The data that has a clear trend or pattern that can be represented by a straight line is best modeled using a line.

Linear graphs are useful because they allow us to easily visualize and analyze trends or patterns in data. The equation of a line can also be used to make predictions or forecasts based on the data. Linear graphs can be used to identify correlations between variables and to assess the strength and direction of those correlations.

Read more about linear

brainly.com/question/28732353

#SPJ1

Answer:

let the breadth of room be 'x'm

so the lenghth of room is 'x+8'm

Given

Area of room=48m²

i.e length ×breadth =48m²

or,(x+8)x=48

or,x²+8x-48=0

or,x²+12x-4x-48=0

or,x(x+12)-4(x+12)=0

or,(x+12)(x-4)=0

Either x+12=0

or,x=-12(which is not possible)

Or,x-4=0

or,x=4

Thus,breadth is 4m.

length=x+8=4+8=12m

The dimensions of room are 8m and 12m respectively.

"s" can be concluded from the premises

To use the rules of inference to show that "s" is a conclusion, we can use modus ponens,

This is a rule that allows us to infer a conclusion from a premise and its conditional statement.

Thus, "s" can be concluded from the premises "p → q", "q → r", "(q → r) → s", and "p".

Read more about premises and conclusion at

https://brainly.com/question/12486203

#SPJ1

I think C would equal 15, because 14 + 14 = 28; 15 + 15 = 30 which is greater than 28.

The graph of the quadratic equation y = 6x² is an upward parabola with vertex (0,0) and axis of symmetry as y-axis.

What is a quadratic equation?

The polynomial equations of degree two in one variable of type f(x) = ax² + bx + c = 0 and with a, b, c, ∈ R and  a ≠ 0 are known as quadratic equations. It is a quadratic equation in its general form, where "a" stands for the leading coefficient and "c" is for the absolute term of f(x). Where it equals zero is where the quadratic equation finds its solutions. They are also known as the equation's roots.

Assuming the question is to graph the quadratic function y = 6x².

The x-intercept can be found by substituting y = 0

0 = 6x²

x = 0

x-intercept = (0,0)

y-intercept can be found by substituting x=0

y = 6 * 0

y = 0

y-intercept = (0,0)

The given quadratic equation is the equation of an upward parabola with the vertex as (0,0).

The axis of symmetry is x = 0 i.e y-axis.

Hence the graph of the quadratic equation y = 6x² is an upward parabola with vertex (0,0) and axis of symmetry as y-axis.

To learn more about quadratic equations, follow the link.

https://brainly.com/question/1214333

#SPJ1

Answer:

x+y=40 and 6x+9y=288

Nathaniel drinks 3 glasses of water in one hour.

To find out how many glasses of water Nathaniel drinks in one hour, we need to calculate his drinking rate per hour.

In 2 2/5 hours, Nathaniel drinks 4/5 of a 10-ounce glass of water.

Let's convert the mixed number of hours to an improper fraction:

\(2\frac{2}{5} = \frac{(5 \times2 + 2)}{5}\)

\(=\frac{12}{5}\)

Now, we can set up a proportion to find his drinking rate per hour.

We know that \(\frac{12}{5}\) hours corresponds to \(\frac{4}{5}\) of a glass of water.

Let's assign "x" as the number of glasses he drinks in one hour.

The proportion is then

\(\frac{(\frac{12}{5} hours) }{(x glasses) } =\frac{(\frac{4}{5} glass)}{(1 hour)}\)

Cross-multiplying gives us

\((\frac{12}{5} )\times1=\frac{4}{5}\times(x)\)

Simplifying, we get

\(\frac{12}{5} =\frac{4}{5}\times x\)

Dividing both sides by \(\frac{4}{5}\), we find x:

\(x=\frac{(\frac{12}{5} )}{\frac{4}{5} }\)

\(x=\frac{12}{4}\)

\(x = 3.\)

Therefore, Nathaniel drinks 3 glasses of water in one hour.

For such more such question on glasses

https://brainly.com/question/11980886

#SPJ8

Total water bill for the month is $62.37.

It seems that you may have accidentally left out the total amount of your water bill.

The total amount by simply adding the amounts of the individual bills together:

Total water bill =\($36.34 + $26.03\)

= \($62.37\)

You have not provided enough information to determine your total water bill.

You have only given the amounts of your individual bills from Metro Water Services and Madison Suburban Utility District.

To find your total water bill, you simply need to add the two bills together.

So, the total amount you owe for water this month would be:

Total water bill = \($36.34 + $26.03\)

= \($62.37\)

It appears that you may have forgotten to include the full amount of your water bill by accident.

Simple addition of the separate bill amounts yields the following sum:

Water bill total = \($36.34 + $26.03\)

= \($62.37\)

Your total water bill cannot be calculated because not enough information has been given.

Only the amounts of your individual Metro Water Services and Madison Suburban Utility District bills have been provided.

You just need to combine the two invoices together to get your total water bill.

As a result, this month's total water bill for you would be:

Water bill total =  \($36.34 + $26.03\)

= \($62.37\)

For similar questions on water bill

https://brainly.com/question/31119915

#SPJ11

A confidence interval that will capture the true population mean with 95% confidence. The value is ( 23.6459    , 24.8293 ) .

What is population mean?

A population in statistics is a group of comparable objects or occurrences that are relevant to a particular topic or experiment. A statistical population can be a collection of real things or a hypothetical, possibly limitless collection of objects derived from experience.

Data: 18

for given data

\($$\begin{aligned}\bar{X} & =\frac{\sum X i}{n} \\& =2448 / 101 \\& =24.2376\end{aligned}$$\)

as population variance is unknown so we used sample variance

\($$\begin{aligned}S^2 & =\frac{1}{n-1}\left(\sum X i^2-n \times \bar{X}^2\right) \\S^2 & =\frac{1}{100}\left(60232-101 \times 24.2376^2\right) \\& =8.9830\end{aligned}$$\)

Now

\(\frac{\bar{X}-\mu}{S / \sqrt{n}} \sim t_{n-1}$$\)

hence 95 % of population mean is

As n=101 which is large so critical value is 1.98397

\($$\begin{aligned}& =\left(\bar{X}-\sqrt{\frac{S}{n}} \times t_{(n-1, \alpha / 2)}, \bar{X}+\sqrt{\frac{S}{n}} \times t_{(n-1, \alpha / 2)}\right) \\& =\left(24.2376-\sqrt{\frac{8.9830}{101}} \times 1.98397,24.2376+\sqrt{\frac{8.9830}{101}} \times 1.98397\right) \\& =(23.6459,24.8293)\end{aligned}$$\)

To learn more about statistics visit:https://brainly.com/question/29093686

#SPJ4

Answer:

13

Step-by-step explanation:

use distance formula \(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\d= \sqrt{(7-2)^2+(7-(-5))^2} =13\)

Answer:

y = 5^(x+1)

Step-by-step explanation:

y = 5^(x+1)

x = 1 for the initial step

Answer:

4x+11

Step-by-step explanation:

−2x+11+6x

Combine Like Terms:

=−2x+11+6x

=(−2x+6x)+(11)

=4x+11

After simplifying the expression is 11 + 4x .

Given,

-2x+11+6x

Now,

Equation : -2x+11+6x

Combine the like terms and simplify further ,

So,

11 -2x + 6x

11 + 4x

Thus the simplified form is 11 + 4x .

Know more about equation,

https://brainly.com/question/17181370

#SPJ6

Answer:

Step-by-step explanation:

The first digit is 9

the 2nd one from the right = 2

So far what you have is

911, 121

941,121

There seems to be a second 4 implied. What is it? I'll edit if you get it to me in the next hour.

Answer:

4 1/2 cups of flour

4 1/2 tablespoons baking powder

4 1/2 teaspoon salt

4 1/2 eggs

5 cups of milk

5 cups of blueberries

Step-by-step explanation:

Not all intersecting lines are perpendicular.

Perpendicular lines require a 90-degree angle of intersection, creating the formation of right angles.

Nonetheless, unlike perpendicular lines that necessitate exactly 90 degrees of intersections, other types of driven lines can be at varying angles beside these.

As such, it is critical to highlight that in general intersecting lines come with different angles of intersection, and only those featuring exact 90-degree angle of intersection become normal cases of intersecting lines, becoming one among many subtypes existing today.

Learn more about perpendicular lines at

https://brainly.com/question/1202004

#SPJ1

\( { (x - 5) }^{2} = {x}^{2} - 10x + 25\)

Answer:

you can do 2^12=4096

there are 4096 different ways nick can answer the question

After answering the provided question, we can conclude that rotations equation per minute = angular speed divided by (2pi) = 1656.19 rad/min divided by (2pi) = 263.02 revolutions/min

An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x + 3" equals the value "9". The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. The variable x is raised to the second power in the equation "x2 + 2x - 3 = 0." Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.

Secondly, we must convert the speed from miles per hour to inches per minute since we want our final result in radians per minute.

1 mile equals 63360 inches (by definition)

1 hour equals 60 minutes

Therefore:

55 miles per hour = 55 * 63360 inches per hour / (1 mile per hour) = 3,484,800 inches per minute

We can now calculate the linear speed of a point on the wheel's rim:

Wheel circumference = pi * diameter = pi * 42 in. = 131.95 in.

3.484,800 in/min linear speed

angular speed = linear speed / (diameter/2) = (3,484,800 in/minute) / (42 in./2) = 1656.19 rad/min (rounded to two decimal places)

To get the number of revolutions per minute, divide the angular speed by 2*pi:

rotations per minute = angular speed divided by (2pi) = 1656.19 rad/min divided by (2pi) = 263.02 revolutions/min

To know more about equation visit:

https://brainly.com/question/649785

#SPJ1

Answer:

I believe that it is the first one. N+89=12.

the answer is 89-n=12

To solve the equation 3,532.5 = (3.14)(r^2)(x/3) for the variable r, we can follow these steps:

Multiply both sides of the equation by 3/3 to eliminate the fraction:

3,532.5 * 3/3 = (3.14)(r^2)(x/3) * 3/3

This simplifies to:

10,597.5 = (3.14)(r^2)(x)

Divide both sides of the equation by (3.14)(x) to isolate the variable r:

10,597.5 / (3.14)(x) = (r^2)

Take the square root of both sides of the equation to solve for r:

r = sqrt(10,597.5 / (3.14)(x))

Therefore, the solution to the equation 3,532.5 = (3.14)(r^2)(x/3) for the variable r is:

r = sqrt(10,597.5 / (3.14)(x))

The integral is ln|x + cos(x)| + C, where C represents the constant of integration.

To find the integral of the function 1/(x + cos(x)), we can employ a combination of algebraic manipulation and the use of standard integration techniques. Here's the solution:

First, let's rewrite the integral in a slightly different form to simplify the process:

∫(1/(x + cos(x))) dx

We notice that the denominator, x + cos(x), is not amenable to direct integration. To overcome this, we employ a substitution. Let's set u = x + cos(x). Now, differentiate u with respect to x: du/dx = 1 - sin(x).

Rearranging this equation, we get dx = du/(1 - sin(x)).

Substituting these values, the integral becomes:

∫(1/(u(1 - sin(x)))) du

Next, we simplify further by factoring out 1/(1 - sin(x)) from the integral:

∫(1/(u(1 - sin(x)))) du = ∫(1/u) du = ln|u| + C

Replacing u with its original expression, we have:

ln|x + cos(x)| + C

Therefore, the answer to the integral is ln|x + cos(x)| + C, where C represents the constant of integration.

For more questions on integral

https://brainly.com/question/30094386

#SPJ8