Find the linear approximation, L(x), of f(x) = sin(x) at x = pi/3.
L(x) =__________
Use the linear approximation to approximate sin(5pi/12) (Round your answer to four decimal places.)
L(5pi/12) = _______

The question is incomplete and the value or fraction of the amount of fraction of pizza eaten for dinner isnt Given. Assume the fraction of pizza eaten for dinner = p

Answer:

Kindly check explanation

Step-by-step explanation:

To solve the problem above;

Amount of pizza eaten for dinner = (fraction eaten * total size of pizza)

Amount of pizza eaten for dinner = 16 * p = 16p

Amount of pizza crust left :

(Total size of pizza crust - Amount of pizza eaten for dinner)

Amount of pizza crust left = 16 - 16p

Note that this is just an hypothetical solution because the value represented as p was omitted in the question.

Simply substitute p in the solution with it's exact value to obtain the exact amount of pizza crust left.

Answer:

8x-32

Step-by-step explanation:

multiply 8 with both terms

please mark this answer as brainlist

Answer:  \(\boldsymbol{\frac{5\text{x}-2}{\text{x}^2-\text{x}}}\)  (choice D)

You have the correct answer.

=====================================================

Work Shown:

\(\frac{2}{\text{x}} + \frac{3}{\text{x}-1}\\\\\frac{2(\text{x}-1)}{\text{x}(\text{x}-1)} + \frac{3\text{x}}{\text{x}(\text{x}-1)}\\\\\frac{2\text{x}-2}{\text{x}^2-\text{x}} + \frac{3\text{x}}{\text{x}^2-\text{x}}\\\\\frac{2\text{x}-2+3\text{x}}{\text{x}^2-\text{x}}\\\\ \boldsymbol{\frac{5\text{x}-2}{\text{x}^2-\text{x}}}\\\\\)

--------

Explanation:

The idea I used is that we cannot add the fractions unless the denominators are the same. The denominators x and (x-1) lead to the lowest common denominator, aka LCD, of \(\text{x}(\text{x}-1) = \text{x}^2 - \text{x}\). We multiply the denominators together to get the LCD.

The first original fraction \(\frac{2}{\text{x}}\) is missing (x-1) in the denominator. This is why I multiplied top and bottom by (x-1) in the 2nd step. Similarly, the fraction \(\frac{3}{\text{x}-1}\) is missing an x out front to get to x(x-1). This is why I multiplied top and bottom of that fraction by x.

After we get the denominators to be the same, we can then add the numerators like any other algebraic expression. The denominator stays the same the entire time.

It's similar to how \(\frac{2}{7} + \frac{3}{7} = \frac{2+3}{7} = \frac{5}{7}\) has the numerators add like you'd expect while the denominator stays at 7 the entire time.

You can think of it like this: "2 sevenths + 3 sevenths = 5 sevenths" or "2s+3s = 5s" for short. The term "sevenths" is effectively a unit such as cm or meters. We must have common units if we want to add them.

B) The left end of the cable is 15 m above the roadway. The y-intercept of the graph represents the height of the left end of the cable, which is 15 m above the roadway.

Intercept is the point where a line intersects with an axis on a graph. It is the point at which a line crosses the x-axis or y-axis. Intercepts are important when analyzing relationships between variables, and they can help to draw conclusions about how two variables are related. For example, if a line has a negative slope, the y-intercept will be a positive number, indicating that as the x-value increases, the y-value will decrease. In linear regression, the intercept is the average value of the dependent variable when the independent variable is equal to zero. It is also used to determine the value of a linear equation when given the value of one of its variables.

To learn more about intercept
https://brainly.com/question/24212383
#SPJ1

She needs to make about $ 17.2, so the correct option is the last one.

First, we need to add all the values in the table to see how much she needs, we will get:

A = 653 + 245 + 299 + 462 + 435 + 136 + 512 = 2,747

Now, we know that Dora works 40 hours per week, 4 weeks a month, so she works a total of.

40*4 hours = 160 hours.

Then the amount that she needs to make per hour is given by the quotient between the total amount she needs and the number of hours:

N =  2,747/160

N = 17.2

The only option that has that in the range is the last one.

Learn more about quotients at:

https://brainly.com/question/629998

#SPJ1

The Keynesian model is an economic theory that advocates for government intervention through fiscal policy to stabilize the economy and promote aggregate demand and employment.

Given model is,

\($v_{1}^{*}=g \cdot t+\epsilon_{t}^{y}\\r_{1}=r_{1}-\pi_{t}^{e}\\v_{1}=v_{i}^{*}-\beta\left(r_{t}-r^{*}\right)-\omega e_{i}+\epsilon_{t}^{d}\\\pi_{t}=\pi_{i}^{e}+\gamma\left(\pi_{t-1}-\pi_{i}^{e}\right)+\epsilon_{t}^{p}$\)

The explanation of the terms present in the model are:1. $v_{1}^{*}$ is the natural level of output.

2. \($\epsilon_{t}^{y}$\) is the unexpected shock to output.

3.\($r_{1}$\) is the nominal interest rate.

4. \(\pi_{t}^{e}\) is the expected inflation rate.

5. \($v_{1}$\) is the actual level of output.

6. \($v_{i}^{*}$\) is the natural level of output in the previous period.

7.\($\beta$\) is the responsiveness of the output to the difference between the actual and expected real interest rates.

8. \($r_{t}$\) is the real interest rate.

9. \($r^{*}$\) is the natural interest rate.

10. \($\omega e_{i}$\) is the unexpected shock to the output.

11. \($\epsilon_{t}^{d}$\) is the unexpected shock to the nominal interest rate.

12. \($\pi_{t}$\) is the inflation rate.

13. \($\gamma$\) is the speed of adjustment of the inflation rate to the expected inflation rate.

14. \($\pi_{i}^{e}$\) is the expected inflation rate in the previous period.

15. \($\epsilon_{t}^{p}$\) is the unexpected shock to the inflation rate.

The model is a new Keynesian model.

To know more about Keynesian model visit:

https://brainly.com/question/32242068

#SPJ11

An angle in a rectangular coordinate system is in standard position if its vertex is at the origin of the plane, the initial side of the angle is on the positive x-axis, and the terminal side of the angle is in one of the four quadrants. The angle is measured in a counterclockwise direction from the positive x-axis and is considered positive if it lies in the counterclockwise direction and negative if it lies in the clockwise direction.

The position of an angle is measured from the reference line called the initial side, which is the positive x-axis, and it ends at the terminal side, which is the side where the angle is located. An angle in a rectangular coordinate system is in a standard position if its vertex is at the origin of the plane. An angle is said to be in a standard position if its vertex is located at the origin of the coordinate system.

To summarize, an angle in a rectangular coordinate system is in standard position if its vertex is at the origin of the plane, the initial side of the angle is on the positive x-axis, and the terminal side of the angle is in one of the four quadrants. The position of an angle is measured from the reference line called the initial side, which is the positive x-axis, and it ends at the terminal side, which is the side where the angle is located.

Learn more about the rectangular coordinate system: https://brainly.com/question/4726772

#SPJ11

Answer:

The answer is that the ball was in the air for 0.56 seconds when it was 54 feet above the ground. This was determined by using the Quadratic Formula to solve the equation 54 = -16s^2 + 96s for the variable s.

Step-by-step explanation:

To solve this equation, we can use the Quadratic Formula, which states that for a quadratic equation in the form ax^2 + bx + c = 0, the solutions are given by:

x = (-b +/- sqrt(b^2 - 4ac)) / (2a)

In this case, a = -16, b = 96, and c = -54. Plugging these values into the Quadratic Formula, we get:

s = (-96 +/- sqrt(96^2 - 4 * -16 * -54)) / (2 * -16)

= (96 +/- sqrt(9216 + 4352)) / -32

= (96 +/- sqrt(13,568)) / -32

Since we want the time (in seconds) that the ball was in the air, we need to find the positive solution to this equation. Thus, we have:

s = (96 + sqrt(13,568)) / -32

= (96 + 120) / -32

= 0.5625 seconds

Rounding this value to the nearest hundredth of a second, we get 0.56 seconds. This means that the ball was in the air for 0.56 seconds when it was 54 feet above the ground.

To solve this equation, we used the Quadratic Formula. This method allowed us to find the time (in seconds) that the ball was in the air by solving for the value of the variable s in the given equation. This helped Vue answer his question by providing a numerical value for the amount of time that the ball was in the air when it was 54 feet above the ground.

Answer:

48ml

because its the correct answer!

Answer:

48 ml

Step-by-step explanation.  80, percentage decreased by 40% (percent) of its value = 48

Answer:

the answer is A: 6.10

Step-by-step explanation:

well, to find the total money you add the two amounts which are $2.85+$3.25 which will add up to $6.10.

Answer:

C=75.4

Step-by-step explanation:

Answer:

c = 75.36 mm

Step-by-step explanation:

r=D/2=24/2=12mm

\(c=2\pi r\)

\(c=2(3.14)(12)=75.36mm\)

Hope this helps

In 33 weeks, they will have sold 150 units.

What is sales of products?

Selling a good or service in exchange for cash, a benefit, or some other kind of payment is known as product sales. When a customer purchases a good or service that will meet their needs, the transaction is known as a product sale. The quantity of goods sold during a specific time period aids in calculating product sales.

Step by Step Explaination:

Equation that models the sales of the product

The equation that models the sales of the product after an initial release exists:

s = 12√4 + 10

where s denotes the total sales (in thousands)

t denotes the time in weeks

you want to replace the s with 150 in the equation and then just solve

for t.

150 = 12√4t + 10

Subtract 10 from both sides

150 - 10 = 12√4t + 10

140 = 12√4t

Divide both sides by 12      

11.66= √4t  

Taking square root on both sides of the equation.    

135.95 = 4t      

Now divide both sides by 4

33.98 = t (approximately).

so in 33 weeks, they will have sold 150 units.

Learn more about this question here:

https://brainly.com/question/10319230

#SPJ1

π/32 is the area enclosed by the curve r= sin(8θ)

The given curve is polar curve and hence the area of the polar curve is given by:

Let A be the area of the curve so,

A = \(\int\limits^a_b {\frac{1}{2} r^2 } \, d\theta\)

where a and b is the boundary at which r=0

so after equation r=0

sin(8θ) =0

=> sin(8θ) =0

=> 8θ = 0,π

=> θ = 0, π/8

so a=0 , b= π/8

now  

   A = \(\int\limits^a_b {\frac{1}{2} r^2 } \, d\theta\)    ------(i)

 so   \(r^2\) = (sin(8θ))^2

=>  \(sin^2\) ( 8θ )

ans we know that

cos(2α) = 1 -  2\(sin^2\) α

so   \(r^2\)  = (1- cos(16θ) )/2

putting the value of r in the equation (i) we get :-

A = \(\int\limits^a_b {\frac{1}{4} *(1-cos(16\alpha ) } \, d\alpha\)

=> 1/4* \(\int\limits^a_b {(1-cos(16\alpha ) } \, d\alpha\)

here a=0 and b=π/8

after putting the value and solving the integral

A = π/32

so A is the area enclosed by r=sin(8θ) is π/32

To know more about polar curve click on below link:

https://brainly.com/question/1094340#

#SPJ4

Answer:

cookie=0.5, popcorn=4

Step-by-step explanation:

1x+2y=5

1x+4y=6

cookie cost 0.5

popcorn cost 4

Answer:

A. 2(x-3)=14

The original price is $10

Step-by-step explanation:

We know

The scarf went on sale for 3$ off the original price.

Catherine bought two of them.

She paid a total of $14

Let x represent the original price; we have the equation

2(x - 3) = 14

2x - 6 = 14

2x = 20

x = $10

So, the equation the model represents this situation is A. 2(x-3)=14

The original price is $10

The subset construction method is used to convert an NFA to an equivalent DFA. It involves determining the epsilon closure of states, finding transitions for input symbols, identifying accepting states, and drawing the DFA diagram. The construction ensures that the resulting DFA recognizes the same language as the original NFA.

To construct an equivalent DFA for the given NFA using the subset construction method, follow these steps:

1. Start with the initial state of the DFA, which is the epsilon closure of the initial state of the NFA. In this case, the initial state of the NFA is state q0. The epsilon closure of q0 is {q0, q1}.

2. For each state in the DFA, determine the transitions for each input symbol. For example, for the DFA state {q0, q1}, we need to determine the transitions for the input symbol 'a'. To do this, find the epsilon closure of the set of NFA states reached from the current DFA state by following 'a' transitions. In this case, from {q0, q1}, following 'a' transitions leads to {q2}. The epsilon closure of {q2} is {q2} itself.

3. Repeat step 2 for all possible input symbols and for all DFA states until all transitions have been determined.

4. Identify the accepting states of the DFA. In this case, any DFA state that contains an accepting state of the NFA is also an accepting state. In the given NFA, q3 is an accepting state. Therefore, any DFA state that contains q3 is also an accepting state.

5. Finally, draw the DFA diagram using the determined transitions and accepting states.

Learn more about the subset construction method:

https://brainly.com/question/28705656

#SPJ11

Bert can pour concrete in a uniform width around his rectangular pool up to 4 meters wide.

To solve this problem, we need to find the area of the pool and the area of the pool with the walkway, and then subtract the two areas to find the area of the walkway. Let's call the width of the walkway "x".

The area of the pool is:

20m x 14m = 280m^(2)

To find the area of the pool with the walkway, we need to add twice the length of the pool plus twice the width of the pool (since there are two lengths and two widths) to the overall dimensions of the pool and walkway. This gives us:

(20 + 2x) x (14 + 2x) = 240m^(2) + 280m^(2)

Expanding this equation gives us:

4x^(2) + 68x - 160 = 0

We can solve for "x" using the quadratic formula:

x = (-b ± sqrt(b^(2) - 4ac)) / 2a

Where a = 4, b = 68, and c = -160.

Plugging in these values gives us:

x = (-68 ± sqrt(68^(2) - 4(4)(-160))) / (2 x 4)

x = (-68 ± sqrt(4624 + 2560)) / 8

x = (-68 ± sqrt(7184)) / 8

x ≈ -10 or x ≈ 4

Since we're looking for a positive value for "x", we can ignore the negative solution.

To know more about area of the pool refer here:

https://brainly.com/question/12484498#

#SPJ11

Therefore, $22.95 would be the best estimate for the cost of a vehicle to drive through the safari in 2011.

The estimated cost of a vehicle to drive through the safari in 2011, we need to substitute the value of x (number of years since it opened in 2005) as 6 into the regression equation y = 3.648 * 1.182x.

Plugging in x = 6, the equation becomes: y = 3.648 * 1.182 * 6

Calculating the expression: y = 25.849536

Rounding to two decimal places, the estimated cost is approximately $25.85.

Among the given options, the closest value to $25.85 is $22.95 (Option B). Therefore, $22.95 would be the best estimate for the cost of a vehicle to drive through the safari in 2011.

Learn more about cost here

https://brainly.com/question/31517591

#SPJ11

Answer:

image isn't loading for me :((( can you try replying to me w the question

Answer: 6300 grams

Why?

1 kilogram = 1000 grams

63 * 1000 = 63000 grams

Hope this helps

:D

Answer:

1 kilogram = 1000 Grams

1000 Grams + 63 Grams = 1063 Grams

Answer = {[1063 Grams]}

Option A i.e. the first and the third service will be provided by a full-service broker but not by a discount broker.

What is meant by a broker?

An impartial party whose services are often used in several businesses is a broker. The main duty of a broker is to connect buyers and sellers; as a result, the broker acts as a neutral intermediary between a buyer and a seller.

The services which will be provided by a full-service broker but not by a discount broker are

Option I. Research of potential investment opportunities

Option III. Recommendation of investments

For any form of investment, research and recommendations are key and important components. Before you make any investments, you should conduct adequate research.

Hence, option A i.e. the first and the third service will be provided by a full-service broker but not by a discount broker.

Learn more about broker from the given link

https://brainly.com/question/29057823

#SPJ1

Bro each ticket is 4$. You just divide the money she earned with how much a ticket costs;

284/4 = 71 tickets

Step-by-step explanation:

Rise over run is often referred to as the slope of the line or the gradient of the line. It is the measure obtained by dividing the y component of the line with the x component of the line. The rise over run ratio is an important characteristic to define the line, and is required to find the equation of the line.

Answer:

3446

Step-by-step explanation:

&&4%65444454585547

Hey there!

The answer for adjacent angles is BGC and CGD, CGD and DGE, and DGE and EGF.

The answer for vertical angles is AGB and EGD, DGC and AGF, and BGC and FGE.

Have a good day!

Answer:

mn(4m - 7n)

Step-by-step explanation:

➠ 4m^2n-7mn^2

➠ 2^2 x m^2n - 7mn^2

➠ mn(\((\frac{2^2*m^2n}{mn} -\frac{7mn^2}{mn} )\)

➠ mn(\(2^2*m^{2-1}-(7n^{2-1}))\)

➠ mn(4m - 7n)

3. is 10 add 5 or round 5 its 10  4. is 28 and i just added sorry if 4 is wrong