Solve the following equation for Ω over the interval [0, 2π), giving exact answers in radian units. If an equation has no solution, enter DNE. Multiple solutions should be entered as a comma-separated list.
cos(Ω) = - cos(2Ω).
Ω = _______

Answer:

[tex]\dfrac{\text{d}y}{\text{d}x}=4x-1[/tex]

Step-by-step explanation:

Differentiating from First Principles is a technique to find an algebraic expression for the gradient at a particular point on the curve.

[tex]\boxed{\begin{minipage}{5.6 cm}\underline{Differentiating from First Principles}\\\\\\$\text{f}\:'(x)=\displaystyle \lim_{h \to 0} \left[\dfrac{\text{f}(x+h)-\text{f}(x)}{(x+h)-x}\right]$\\\\\end{minipage}}[/tex]

The point (x + h, f(x + h)) is a small distance along the curve from (x, f(x)).

As h gets smaller, the distance between the two points gets smaller.

The closer the points, the closer the line joining them will be to the tangent line.

To differentiate y = 2x² - x + 3 using first principles, substitute f(x + h) and f(x) into the formula:

[tex]\implies \displaystyle \dfrac{\text{d}y}{\text{d}x}=\lim_{h \to 0} \left[\dfrac{2(x+h)^2-(x+h)+3-(2x^2-x+3)}{(x+h)-x}\right][/tex]

Simplify the numerator:

[tex]\implies \displaystyle \dfrac{\text{d}y}{\text{d}x}=\lim_{h \to 0} \left[\dfrac{2x^2+4xh+2h^2-x-h+3-2x^2+x-3)}{x+h-x}\right][/tex]

[tex]\implies \displaystyle \dfrac{\text{d}y}{\text{d}x}=\lim_{h \to 0} \left[\dfrac{2x^2-2x^2+x-x+3-3+4xh+2h^2-h)}{h}\right][/tex]

[tex]\implies \displaystyle \dfrac{\text{d}y}{\text{d}x}=\lim_{h \to 0} \left[\dfrac{4xh+2h^2-h)}{h}\right][/tex]

Separate into three fractions:

[tex]\implies \displaystyle \dfrac{\text{d}y}{\text{d}x}=\lim_{h \to 0} \left[\dfrac{4xh}{h}+\dfrac{2h^2}{h}-\dfrac{h}{h}\right][/tex]

Cancel the common factor, h:

[tex]\implies \displaystyle \dfrac{\text{d}y}{\text{d}x}=\lim_{h \to 0} \left[4x+2h-1\right][/tex]

As h → 0, the second term → 0:

[tex]\implies \displaystyle \dfrac{\text{d}y}{\text{d}x}=4x-1[/tex]

Answer:

3m-4

Step-by-step explanation:

marcie's age be x

her father age is four less than three times

the equation tht describes her father age is 3m-4=40

The value in the red box would be 19√7.

An algebraic expression is a made up of terms both constants and variables. For example, we can write -

2x + 3y + z

5x + y

x + 8y

Given is a pyramid as shown in the image.

We can write -

b{4} = 2√7 - 4√7 = - 2√7

b{4} = - 2√7

- 4√7 + b{9} = 3√28

b{9} = 3√28 + 4√7

b{9} = 6√7 + 4√7

b{9} = 10√7

b{6} = 10√7 - √7

b{6} = 9√7

b{2} =  - 2√7 + 6√7

b{2} = 4√7

b{3} = 3√28 + 9√7

b{3} = 6√7 + 9√7

b{3} = 15√7

b{1} = 4√7 + 15√7

b{1} = 19√7

Therefore, the value in the red box would be 19√7.

To solve more questions on expressions, visit the link-

brainly.com/question/29223887

#SPJ1

{QUESTION IN ENGLISH -

Look at the following pyramid, in which each box has a number that is formed by adding the two bottom boxes.

What is the number that occupies the red box?}

Answer:

[tex]27\pi[/tex]

Step-by-step explanation:

The area of a circle is given by the formula [tex]A = \pi r^2[/tex].

We are given the radius of this circle, so we can plug in.

[tex]A = \pi r^2\\A=6^2\pi \\A=36\pi[/tex]

Seeing that there is [tex]\frac{3}{4}[/tex] of the circle left, multiply [tex]36\pi[/tex] by [tex]\frac{3}{4}[/tex].

[tex]36\pi(\frac{3}{4})\\ 9\pi (3)\\27\pi[/tex]

The transformation of the points and shapes after being transformed are calculated below

The coordinates of B in the figure is

B = (5, 1)

A translation of (x-4, y-3) means

B' = (5 - 4, 1 - 3)

B' = (1, -2)

Here, we have the following corresponding points

Pre = (2, 1)

Image = (-1, 2)

This represents

(x, y) = (-y, x)

This represents (d) 270° clockwise rotation

Given that the smaller figure is gotten from a bigger figure

Then the dilation is a reduction and the scale factor could be 1/2 or 1/4

We have

P = (3, -2) and S = (4, -5)

For the first transformation, we have

(x - 2, y)

P' = (1, -2) and S' = (2, -5)

For the second, we have

P'' = (1, 2) and S'' = (2, 5)

Here, we have

A = (-2, -5)

This means that the new ordered pair of point A is

A' = (-2, -5) * 1/2

A' = (-1, -2.5)

Hence, the new ordered pair of point A is (-1, -2.5)

Read more about transformation at

https://brainly.com/question/27224272

#SPJ1

5. 24 hours over 7 days (Because 1 day = 4 hrs)

6. 16 limes over 2 bags (1 bag = 8 limes)

7. 54 cups over 9 boxes (6 cups = 1 box)

8. 27 meters (or minutes) over 3 seconds (9 meters over 1 second)

9. 36 lbs over $24 ($1 = 1.5lbs)

Answer:

a = 6

b = 5

c = -4

Step-by-step explanation:

(2x-1)(3x+4) = [tex]6x^{2}[/tex]+8x-3x-4 = [tex]6x^{2}[/tex]+5x-4

If the equation is [tex]ax^{2}[/tex]+bx+c, then the values of a, b, and c, are 6, 5, and -4 as it makes the equation true.

The required slope of the line shown in the graph is 4/3, and the lines representing the rise and run are shown in the graph.

The slope of a line is a measure of how steeply the line is inclined with respect to the horizontal axis.

Here,

To calculate the slope of a line from the rise and run values, we use the formula:

slope = rise/run

In this case, rise = 6 and run = 4.5. Substituting these values into the formula, we get:

slope = 6 / 4.5

Simplifying the fraction by dividing both the numerator and denominator by 1.5,

slope = 4/3

Therefore, the slope of the line is 4/3.

Learn more about slopes here:
https://brainly.com/question/3605446

#SPJ1

Answer:

Below

Step-by-step explanation:

12 000 * r = 9600

r = 9600  / 12000 = .8  

 So multiply each term by .8 to get the next term:

year 1     12 000

year 2    12 000 * .8

year 3    12 000 * .8  * .8

Year 4   12 000 * .8 * .8  * .8    = 12 000 * .8^3

.

.

year 7  12 000 * (.8)^6 = $ 3145.73

an = a1 r^(n-1)

an = 12 000 (.8)^n-1

Answer: 22

Step-by-step explanation:

Answer:

22

Step-by-step explanation:

(36 x8-204)

multiply first

36(8)=288

then subtract

288-204=84

8+84 ÷6

divide first

84 ÷6=14

8+14=22

Answer:

24

Step-by-step explanation:

The sum of the three angles in a triangle is always 180 degrees.

Let x be the measure of the third angle.

Then we have:

102 + 54 + x = 180

Simplifying the left side:

156 + x = 180

Subtracting 156 from both sides:

x = 180 - 156

x = 24

Therefore, the measure of the third angle is 24 degrees.

Answer:

C. 10 sandwiches

Step-by-step explanation:

Each section of a box plot makes up 25% of it. Since Q1 is marked by $18, that means 25% of 40 sandwiches can be bought with it. So, [tex]\frac{40}{4}[/tex] = 10.

The question involves a basic division operation in Mathematics. Without the cost of a sandwich, it's impossible to answer. If provided, just divide the total money by the price of a sandwich to find the number that can be purchased.

The student's question involves simple division, which is a topic under the subject of Mathematics. To determine how many sandwiches one can afford with $18, it is necessary to have the cost of one sandwich. Unfortunately, without the given price of a single sandwich as indicated in the boxplot, we cannot compute the answer.

But if we are provided the cost of a single sandwich, we would simply divide the total amount of money ($18) by the cost of a single sandwich. This would give us the total number of sandwiches affordable with the given amount of money.

Assuming a sandwich costs $2, here is how the computation would be: $18 ÷ $2 = 9 sandwiches. So, with $18, we could afford 9 sandwiches at $2 each.

https://brainly.com/question/31392500

#SPJ2

(a) For a line, the ratio of the change in y to the change in x is called the slope of the line.
(b) The point-slope form of the equation of a line with slope m passing through (x1, y1) is y - y1 = m(x - x1).

The slope of a line is a measure of its steepness and is calculated by finding the ratio of the change in y (the rise) to the change in x (the run) between two points on the line.

The point-slope form of the equation of a line is a way to write the equation of a line when you know its slope and one point on the line. It is written as y - y1 = m(x - x1), where m is the slope of the line and (x1, y1) is the point on the line.

Learn more about point -slope at https://brainly.com/question/17056695

#SPJ11

From the system of equations one apple pie costs $6 and one lemon meringue pie costs $7.

A group of equations that need to be solved concurrently is referred to as a system of equations. The values of the variables that satisfy each and every one of the system's equations are the solutions to the corresponding equations. Systems of equations can be solved using a variety of techniques, such as substitution, elimination, and graphing. Systems of equations can be used to simulate situations in business, science, and engineering when there are several variables at play. Systems of differential equations, linear equations, and quadratic equations are a few examples of systems of equations.

Let us suppose the cost of the apple pie = x.

Let us suppose the cost of the meringue pie = y.

Given that, Dan sold 14 apple pies and 9 lemon meringue pies for a total of $147.

14x + 9y = 147

For Jenny:

8x + 12y = 132

Using the elimination method we have:

Multiplying Dan's equation by 4 gives:

56x + 36y = 588

Multiplying Jenny's equation by 3 gives:

24x + 36y = 396

Subtracting the second equation from the first:

32x = 192

x = 6

Substitute the value of x in equation:

14(6) + 9y = 147

84 + 9y = 147

9y = 63

y = 7

Hence, from the system of equations one apple pie costs $6 and one lemon meringue pie costs $7.

Learn more about system of equation here:

https://brainly.com/question/10431413

#SPJ1

Answer:

1/  24 bottle of water for $3 is a better buy

2/ $0.045

Step-by-step explanation:

12 bottles of water for $2

2 / 12 =$0.17

So, it costs $0.17 for each bottle of water.

24 bottles of water for $3

3 / 24 = $0.125

So, it costs $0.125 for each bottle of water.

0.17 - 0.125 = $0.045

So, 24 bottles of water for $3 is a better buy by $0.045

The simplified expression is (8x-7) / ((3x-2)[tex]^{((2)/(3)))}[/tex].

To simplify the expression (3(3x-2)[tex]^{((1)/(3))}[/tex] - (x-1)(3x-2)[tex]^{(-(2)/(3)))/((3x-2)}[/tex][tex]^{((2)/(3)))}[/tex] first we need to perform the indicated operations.

1. Using the power rule, we can rewrite (3x-2)[tex]^{((1)/(3))}[/tex] as 3x-2 and (3x-2)^(-(2)/(3)) as 1/(3x-2).  

Therefore, the expression can be rewritten as (3(3x-2) - (x-1)/(3x-2)) / ((3x-2)[tex]^{((2)/(3)))}[/tex].

2.Now, using the distributive property, we can simplify the expression to (9x-6-(x-1)) / ((3x-2)[tex]^{((2)/(3)))}[/tex].

Finally, simplifying further, we get the expression (8x-7) / ((3x-2)[tex]^{((2)/(3)))}[/tex].

Learn more about simplified expression here:

https://brainly.com/question/403971#

#SPJ11

Answer:

6x + 3

Step-by-step explanation:

Answer:

6x + 3

Step-by-step explanation:

x = a number

6 times a number (x) can also be written as 6x.

Plus 3 is simply adding 3, therefore, it is written as 6x+3

The product that results in an irrational number is given as follows:

[tex]\sqrt{84} \times 21[/tex]

21 is a rational number, hence for the product to be irrational, we need an irrational number, which is the non-exact square root of 84.

More can be learned about rational and irrational numbers at brainly.com/question/5186493

#SPJ1

The solution of the given system of the equation will be (0, 1), and (4, 9).

Simultaneous equations, a system of equations Two or more equations in algebra must be solved jointly (i.e., the solution must satisfy all the equations in the system). The number of equations must match the number of unknowns for a system to have a singular solution.

There are four methods for solving systems of equations: graphing, substitution, elimination, and matrices.

Given a system of equations such that,

y = x² - 2x +1

y = 2x + 1

By subtracting both equations we will get,

x²-2x +1 - 2x -1 = 0

x² -4x = 0

x = 0, x = 4

at this value

y = 1, y = 9

therefore, the solution of the given system of the equation will be (0, 1), and (4, 9).

Learn more about the System of equations here:

https://brainly.com/question/12628931

#SPJ1

Answer:

a) The data would be discrete because it can only take on a finite number of values.

The teacher used a scale of integers from 0 to 10, which means that the data can only take on one of those 11 values. Continuous data, on the other hand, can take on an infinite number of values within a given range.

b) The data would be ordinal data because it can be ordered or ranked.

The scale of integers from 0 to 10 represents a ranking of how much homework was completed, with 0 being the lowest and 10 being the highest. Nominal data, on the other hand, cannot be ordered or ranked and is used to classify or categorize things.

To know more about discrete data, refer here:

https://brainly.com/question/13421250#

#SPJ11

Using probability distribution, we can find that P(x=9) = 0.13

To determine the chance of each potential value that a random variable might have, a function known as the probability distribution is used. A discrete probability distribution can be defined using a probability distribution function and a probability mass function.

Both a probability density function and a probability distribution function can be used to define a continuous probability distribution. The geometric, Bernoulli, binomial, and Bernoulli distributions are examples of probability distributions.

Now in the given question,

P(3) = .04

P(6) = .62

P(12) = .21

Now,

p (3) + p (6) + p (9) + p (12) = 1

0.04 + 0.62 + p(9) + 0.21 = 1

p(9) = 0.13

Therefore, the value of P (9) = 0.13

To know more about probability distribution, visit:

https://brainly.com/question/14210034

#SPJ1

Option A and C will be the correct answers based on the provided statement.

A right triangle's hypotenuse is its longest side, its "opposing" side is the one that faces a certain angle, and its "adjacent" side is the one that faces the angle in question. To define the side of right triangles, we utilize specific terminology.

Congruence of the SAS Triangle According to the theorem, two triangles are said to be congruent to one another if they have a single pair of corresponding sides and an incorporated angle that are equal to one another.

The image shows two triangles that are congruent by the SAS Congruence Theorem.

As a result, the following claims satisfy the requirements for two triangles to be regarded as congruent to one another by the SAS Congruity Theorem:

A. the corresponding two sides and the included angle in both triangles are congruent.

C. A pair of two sides that are congruent with the equivalent two sides and angle in the opposite triangle and are parallel to an angle's ray.

To know more about Triangle visit:

https://brainly.com/question/17335144

#SPJ9

The equation are: x = -1 radians (-57.3°) and x = 11 radians (626.9°).

To solve this equation, use the identity sin2x + cos2x = 1 and apply it to the left side of the equation.

2 sin2x + 20 cos x = 6

2 (1 - cos2x) + 20 cos x = 6

2 - 2 cos2x + 20 cos x = 6

2 cos2x - 20 cos x + 2 = 6

cos2x - 10 cos x + 1 = 0

Next, solve the resulting quadratic equation using the quadratic formula: x = [-b ± √(b2 - 4ac)]/2a. In this case:

x = [-(-10) ± √((-10)2 - 4(1)(1))]/2(1)

x = [10 ± √(100 - 4)]/2

x = [10 ± √(96)]/2

x = (10 ± 4√6)/2

x = (10 ± 12)/2

x = 5 ± 6

We then use the interval [0,2π) to calculate the exact radian values for x. The two solutions in this interval are:

x = 5 - 6 = -1

x = 5 + 6 = 11

For reference, the angle corresponding to -1 radians is -57.3° and the angle corresponding to 11 radians is 626.9°.
To check the solution, graph the two sides of the equation on Desmos, with the interval [0,2π). The graph will show the two points of intersection (marked with circles) which correspond to the two solutions.

In conclusion, the exact values of x which satisfy the equation are: x = -1 radians (-57.3°) and x = 11 radians (626.9°).

Learn more about Desmos Graph

brainly.com/question/23017727

#SPJ11

The degree of the given polynomial is 2 and the leading coefficient is 5. The given expression is 5a^(2)+2a+6. It is a polynomial expression.

The degree of a polynomial is the highest power of the variable in the polynomial. In this case, the highest power of the variable a is 2, so the degree of the polynomial is 2.

The leading coefficient of a polynomial is the coefficient of the term with the highest power of the variable. In this case, the term with the highest power of the variable a is 5a^(2), so the leading coefficient is 5.

Therefore, the degree of the given polynomial is 2 and the leading coefficient is 5.

For more about coefficient:

https://brainly.com/question/28975079

#SPJ11

Answer:

Let x be the number of additional miles Tammy needs to run this week to reach her goal of at least 10 miles per week.

To determine the inequality, we can start with the given information and use the inequality symbol for "greater than or equal to" (≥):

4.5 + x ≥ 10

This inequality states that the sum of the distance Tammy has already run this week (4.5 miles) and the additional distance she still needs to run (x miles) must be greater than or equal to 10 miles in total for her to reach her goal.

To solve for x, we can start by subtracting 4.5 from both sides of the inequality:

x ≥ 10 - 4.5

Simplifying, we get:

x ≥ 5.5

Therefore, Tammy must run at least 5.5 more miles this week to reach her goal of at least 10 miles per week.

Step-by-step explanation:

wag na mag delete pls lng ang bob0 nyo namn pag na delete nyo toh mga admin

Answer:

the answer in this is letter A

Kevin buys a motorcycle for $11,000 with an annual interest rate of 10.75% and a 108-month term, his monthly payments will be $200.39 if he makes a down payment of $2,300.

The monthly payment for a $11,000 loan with an annual interest rate of 10.75% and a 108-month term can be calculated using the formula for the present value of an annuity:

[tex]PV = PMT * (1 - (1 + r/n)^{-n*t}) / (r/n)[/tex]

where PV is the present value of the loan, PMT is the monthly payment, r is the annual interest rate, n is the number of compounding periods per year, and t is the loan term in years.

With a down payment of $2,300, the loan amount is reduced to $8,700 ($11,000 - $2,300). Plugging in the values, we get:

PV = $8,700

r = 0.1075

n = 12 (since payments are monthly)

t = 9 (108 months / 12)

PMT = $200.39 (rounded to the nearest cent)

Kevin needs to pay off a loan of $11,000, which he plans to do over a period of 108 months with an annual interest rate of 10.75%. However, if he makes a down payment of $2,300, his loan amount will be reduced to $8,700. Using the formula for the present value of an annuity, we can calculate his monthly payments, which come out to be $200.39. Therefore, his monthly payments will be $200.39 if he makes a down payment of $2,300.

For more questions like Interest Rate visit the link below:

https://brainly.com/question/28752405

#SPJ11

The point estimate for p(cap) and q(cap) as per defined condition of mainstream media is equal to 0.700 and 0.300 respectively.

Total number of adults in the country = 4393

Number of adults think mainstream media is more interested in making money = 3074

The point estimate for p, denoted as p(cap),

p(cap) represents proportion of individuals in the sample.

Individual who think mainstream media is more interested in making money than in telling the truth.

This implies,

p(cap)

= 3074/4393

≈ 0.700

The point estimate for q, denoted as q(cap), is the proportion of individuals in the sample.

Individuals who do not think mainstream media is more interested in making money than in telling the truth.

This implies,

q(cap)

= 1 - p(cap)

= 1 - 0.700

≈ 0.300

Therefore, the point estimate for p(cap) is approximately 0.700 and the point estimate for q(cap) is approximately 0.300.

Learn more about estimate here

brainly.com/question/18808345

#SPJ4

The above question is incomplete, the complete question is:

Let p be the population proportion for the following condition. Find the point estimates for p and q.

A study of 4393 adults from country A, 3074 think mainstream media is more interested in making money than in telling the truth.

The point estimate for p, p(cap), is (Round to three decimal places as needed.)

The point estimate for q, q(cap), is (Round to three decimal places as needed.)

You can write an equivalent fraction with a smaller numerator and denominator.

When we take a fraction with the ratio of two integers =

Let the odd numerator be 3, and

Let the odd denominator be 9

therefore, now that we have to determine if one can write an equivalent fraction with a smaller numerator and denominator, the ratio will be as follows:

3:9 or we can similarly say 3/9

when we further simplify it, we will be getting the value of 1:3 or 3/9

hence, this shows that you can write an equivalent fraction with a smaller numerator and denominator.

To learn more about fractions, click here:

brainly.com/question/10354322

#SPJ1

To solve this problem, we can use a system of equations. Let's call the number of main-floor seats x and the number of balcony seats y.
The first equation can be written as:
10x + 4y = 5800
The second equation can be written as:
0.3x + 0.5y = 1900

Now we can use the elimination method to solve for one of the variables. Let's multiply the second equation by -10 to eliminate the x variable:
-3x - 5y = -19000
Adding the two equations together gives us:
7x - y = 3900
Now we can use substitution to solve for one of the variables. Let's solve for y in the first equation:
y = (5800 - 10x)/4
And substitute this value into the second equation:
7x - (5800 - 10x)/4 = 3900
Multiplying both sides by 4 gives us:
28x - 5800 + 10x = 15600
Solving for x gives us:
38x = 21400
x = 563.16
And plugging this value back into the first equation to solve for y gives us:
y = (5800 - 10(563.16))/4
y = 609.21
So there are approximately 563 main-floor seats and 609 balcony seats.

To know more about equations refer here:

https://brainly.com/question/29538993

#SPJ11

Answer:

its nissa

Step-by-step explanation:

Ez