Rotation by θ = − 90 ∘ around the origin is performed by. R = ( cos θ − sin θ sin θ cos θ) = ( 0 1 − 1 0) Plus we need coordinate translations before and after the rotation, because our index center is ( 3, 3) and not ( 0, 0), so we need homogeneous coordinates to express translations by ( Δ x, Δ y) in matrix form.When you use a bender with indicators and degree markers - like this one from Klein Tools - making a 30, 60, or 90 degree bend is simple. When making off-set, back-to-back, stub-ups or saddle bends, using a bender with a degree scale and multiplier scale helps save you time and energy. Basic Steps for Bending Conduit١٦ محرم ١٤٣٤ هـ ... completely characterized Ж -multiplier sequences in [15]. Recently ... degree n − 1. Let now t > 0 and let x → tx and y → ty and consider.To find the t* multiplier for a 98% confidence interval with 15 degrees of freedom: In Minitab, select Graph > Probability Distribution Plot > View Probability; Change the Distribution to t; Enter 15 for the Degrees of freedom; Select Options; Choose A specified probability; Select Equal tailsThe number you see is the critical value (or the t -value) for your confidence interval. For example, if you want a t -value for a 90% confidence interval when you have 9 degrees of freedom, go to the bottom of the table, find the column for 90%, and intersect it with the row for df = 9. This gives you a t- value of 1.833 (rounded).1/12 pitch in degrees is a 4.76° roof angle. 2/12 pitch in degrees is a 9.46° roof angle. 3/12 pitch in degrees is a 14.04° roof angle. 4/12 pitch in degrees is an 18.43° roof angle. 5/12 pitch in degrees is a 22.62° roof angle. 6/12 pitch in degrees is a 26.57° roof angle. 7/12 pitch in degrees is a 30.26° roof angle.May 23, 2012 · The Potential GDP Line and the 45-degree Line. ... just by using the multiplier formula. ... 0.25 goes to taxes, leaving 0.75, and out of after-tax income, 0.15 goes ... This Bumper Stickers item by Sparkyninja613 has 112 favorites from Etsy shoppers. Ships from Atlanta, GA. Listed on Sep 28, 2023.Multiplier: In economics, a multiplier is the factor by which gains in total output are greater than the change in spending that caused it. It is usually used in reference to the relationship ...The Equity Multiplier is a financial ratio that reveals the proportion of a company's assets financed by shareholders. Calculated as total assets divided by shareholders' equity, it demonstrates the reliance on debt for funding. Equity Multipliers are crucial for creditors assessing loan risks and investors evaluating a company's financing ...Dextroscoliosis is the more common type of scoliosis. The right-sided curvature of the spine can cause the spinal column to appear in the shape of a “C” or an “S” instead of a straight ...DAM is an acronym for Dynamic Advance Multiplier (also called IAM or Ignition Advance Multiplier in RomRaider and ECUFlash definitions). This value will vary between 0.0 and 1.0 on 32 Bit Subaru ECUs and between 0 and 16 for 16 Bit Subaru ECUs.For example: 35 degrees 5 minutes 27 seconds is written as 35° 5' 27" Degree. Degree is 1/360 of a turn, or 1° Full turn contains 360 degrees. Also there are other types of division - circular sectors. Sectors of a certain size have their own special names. Quadrant. Quadrant is 1/4 of a turn ...May 23, 2012 · The Potential GDP Line and the 45-degree Line. ... just by using the multiplier formula. ... 0.25 goes to taxes, leaving 0.75, and out of after-tax income, 0.15 goes ... Calculate elbow center to end dimension for 2 inch nominal pipe diameter elbow at 30 degree angle, cut from 45 degree LR elbow. From ASME B16.9, center to elbow dimension for 2 inch 45 degree elbow is 35 mm. Radius of elbow = 35/Tan (22.5) Radius of elbow = 35/0.4142 = 84.5 mm. Length = 0.26795 X 84.5.Jan 21, 2019 · 0:00 / 2:54 Offset multiplier chart for conduit made easy MKO Electric 774 subscribers Subscribe 113 Share 10K views 4 years ago After watching this video, you should be able to calculate ANY... Jan 11, 2023 · How to construct a 30 degree angle. A 30° angle is half of a 60° angle. So, to draw a 30° angle, construct a 60° angle and then bisect it. First, follow the steps above to construct your 60° angle. Bisect the 60° angle with your drawing compass, like this: Without changing the compass, relocate the needle arm to one of the points on the rays. angles: 15, 30, 45 degrees. There are two commonly used units of measurement ... multiplication and division. Students had to be able to use the sine-cosine ...What are the multipliers for bending conduit, it is asked. Degree of Bend in Degrees (Angle) Multiplier Shrinkage Multiplier in inches 10 6 1/16 15 3.9 1/8 22.5 2.6 3/16 30 2 1/4 Degree of Bend Multiplier for Conduit Offsets 10 degrees 6.0 22 degrees 2.6 30 degrees 2.0 45 degrees 1.4 How do you calculate gain when bending pipe? Final answer. We are absorbing hydrogen sulfide at 15 Degree C into water. The entering water is pure. The feed gas contains 0.0012 mole frock hydrogen sulfide and we want to remove 97% of this in the water. The total gas flow rate is 10 kmol/h. The total liquid flow rate is 2000 kmol/h. Total pressure is 2.5 atm.200 degrees Celsius is equal to 392 degrees Fahrenheit. There is an easily memorable formula for Celsius to Fahrenheit conversions: simply multiply the original figure by 9, divide by 5 and add 32.By the Triangle Ratios Theorem, we have: sin15∘ = US = PQ − RU = PT cos30∘ − TU sin30∘ = cos45∘ cos30∘ − sin45∘ sin30∘ = 2–√ 2 ⋅ 3–√ 2 − 2–√ 2 ⋅ 1 2 = 6–√ − 2–√ 4 sin …Since it can be shown that \(\lim_{s\to\infty}F(s)=0\) if \(F\) is a Laplace transform, we need only consider the case where \(\mbox{degree}(P)<\mbox{degree}(Q)\). To obtain \({\mathscr L}^{-1}(F)\), we find the partial fraction expansion of \(F\), obtain inverse transforms of the individual terms in the expansion from the table of Laplace ...For example: In a 3 bend saddle with 45 degree center, your multiplier is 2.5 for the standard method but 2.61 for the push thru method. Further, the conduit O.D. is added to the quotient of the offset height and multiplier with the push-thru. ... #15 An exercise for the student. Conduit is 1" rigid; Centerline bending radius is 6-5/16" Height ...Linkage mechanisms consist of a series of mechanical linkages that can change direction, alter force and make things move in a certain way. We use linkage mechanisms in a number of different systems and also in machinery. Linkage mechanisms give you the ability to take one kind of motion and turn it into another type.If there are a lot of factors then it might take you a little while to calculate all of the factor pairs, but luckily we have the power of computers and can calculate the factor pairs of 15 for you automatically: 1 x 15 = 15. 3 x 5 = 15. 5 x 3 = 15. 15 x 1 = 15. So there you have it.Edit multiplier for 15 degree offset. Rearrange and rotate pages, insert new and alter existing texts, add new objects, and take advantage of other helpful tools. Click Done to apply changes and return to your Dashboard. Go to the Documents tab to access merging, splitting, locking, or unlocking functions.١ ذو القعدة ١٤٣٧ هـ ... ... multiplier herds where disease was not seen. This comparison ... 15]. In a previous genomic analysis of 20 strains of B. hyodysenteriae ...Let's say it is equal to 45 degrees, or π/4. Calculate the arc length according to the formula above: L = r × θ = 15 × π/4 = 11.78 cm. Calculate the area of a sector: A = r² × θ / 2 = 15² × π/4 / 2 = 88.36 cm². You can also use the arc length calculator to find the central angle or the circle's radius. Simply input any two values ...Two 60 degree saddles, an elbow, two 45 degree offsets, and three 15 degree kicks. No. What is the developed length for an elbow bend in 5" conduit if the centerline ... You are making a 15" offset with two 30 degree bends with an offset multiplier of 2. The distance between bends is... 30" A conduit run must pass over a pipe and then over a ...Villard cascade voltage multiplier. A voltage multiplier is an electrical circuit that converts AC electrical power from a lower voltage to a higher DC voltage, typically using a network of capacitors and diodes.. Voltage multipliers can be used to generate a few volts for electronic appliances, to millions of volts for purposes such as high-energy physics …1 + MPC + MPC2+ MPC3+ ... + MPCn = 1/ (1-MPC) This is how we derive our multiplier in mathematical terms. We can use this knowledge in our example and calculate the impact of the increased investment of 1000 when the MPC is ⅔ of the output (real GDP). 1/ (1-2/3) x 1000, or 3 x 1000 = 3000.[e Constant. mm2/s2. (cSt/s) C D Viscometer Constant at 40°C 0.01446 0.01055 Viscomctcr Constant at 100°C 0.01456 0.01065 The viscometer constant at other temperatures can be obtained by interpolation or extrapolation.Two 45 degree offsets, and elbow, and three 15 degree kicks. Yes. ... You are making a 15" offset with two 30 degree bends with an offset multiplier of 2. The ...In such instances, obtaining the coefficients by the graph multiplication method is time-saving. The graph multiplication method is based on the premise that the integral contains the product of two moment graphs M and m. To derive the formula for the graph multiplication method, consider the two moment diagrams M′ and M, as shown in …The min. offset would vary with each size conduit and bender type. To determine the minimum offset on a specific bender/ conduit size, Multiply the amount of offset desired by the cosecant of the angle desired: (30 deg = 2; 15 deg = 3.86; 10 deg = 5.76).Above: an electric-operated electrical conduit bender from Klein Tools. Screw a 30-inch length of threaded pipe into the bender head (sometimes called a an electricians “hickey.”) Insert the conduit into the bender through the hook at the top of the head. The hook marks where the bend will start.Student t-Value Calculator. This calculator will tell you the Student t-value for a given probability and degrees of freedom. Student t-values for both one-tailed (right-tail) and two-tailed probabilities will be returned. Please enter the necessary parameter values, and then click 'Calculate'. Degrees of freedom: Probability level:In this section, let us explore how to construct a 30-degree angle with the help of a protractor.Follow the given steps: Step 1: Draw a line segment OA. Step 2: Place the center tip of the protractor at point O such that the protractor perfectly aligns with line AO. Step 3: Start from 'A' on the protractor in the clockwise direction and stop at 30.Mark it as point 'D'.For example: 35 degrees 5 minutes 27 seconds is written as 35° 5' 27" Degree. Degree is 1/360 of a turn, or 1° Full turn contains 360 degrees. Also there are other types of division - circular sectors. Sectors of a certain size have their own special names. Quadrant. Quadrant is 1/4 of a turn ...Multiplier for a 15 Degree Offset. 3.86. Multiplier for a 22.5 Degree Offset. 2.6. Multiplier for a 30 Degree Offset. 2. Multiplier for a 45 Degree Offset. 1.4. Study with Quizlet and memorize flashcards containing terms like Shrink for 10 Degree bend, Shrink for a 15 Degree Bend, Shrink for a 22.5 Degree Bend and more.The degree of this polynomial is $$$ 3 $$$ because the highest power of the variable $$$ x $$$ is $$$ 3 $$$. Polynomials can have one or more terms. For example: $$$ 5x^2 $$$ is a monomial (one term). $$$ 3x-7 $$$ is a binomial (two terms). $$$ x^2-3x+4 $$$ is a trinomial (three terms). $$$ x^3+2x^2-4x+1 $$$ is a polynomial with four terms.Roof pitch is a mathematical expression of how steep your roof is. When using pitch, the slope of the roof is given as a ratio of the vertical rise to the horizontal run (rise/run). Traditionally, this expression of pitch takes the form “X:12″ or “X-in-12″, where X is the number of units (inches) of vertical rise of the roof and 12 ...Sep 12, 2023 · Active 1 Member I had metal number stamps I stamped in the flat top part of my 1/2" bender. 5 5/8 deg = 10.207 11 1/4 deg = 5.126 15 deg = 3.864 22 1/2 deg = 2.613 30 deg = 2 37 1/2 deg = 1.643 45 deg = 1.414 60 deg = 1.555 I round to the 1st decimal place and I know the common ones but I wanted to check myself so I listed all from one chart. Tom Aug 2, 2009 · But i can tell you your amount of shrink varies with each degree you bend. per inch of offset subtract. 10 degrees would be 1/16" per inch of bend. 15 degrees is 1/8". 22.5 degrees is 3/16". 30 degrees is 1/4". 45 degrees is 3/8". 60 degrees is 1/2". if your bending an odd degree like a 36 you can get close enough by estimating 5/16. maintaining the centerline for all bends. You are making a 10" offset using two 30-degree bends with an offset multiplier of 2. The. distance between bends is _____. 20. One of the advantages of aluminum conduit is that it _____. is resistant to wrinkling. A conduit run must pass over two pipes that are 5' apart.٦ ذو القعدة ١٤٤٤ هـ ... ... multiplier, fiscal multiplier, equity multiplier, and earnings multiplier. ... In this way, commercial banks have a large degree of influence on ...Calculators for finance, math, algebra, trigonometry, fractions, physics, statistics, technology, time and more. Calculator with square roots and percentage buttons. Use an online calculator for free, search or suggest a new calculator that we can build. Conversions and calculators to use online for free.Note: The choice of degree is usually the installer’s choice and most of the time the installation location will determine what degree will fit. Offset Formula Table Angle of Bend Constant Multiplier Shrink Per Inch of Offset 10° X 10° 6 1/16 = .063 22½° X 22½° 2.6 3/16 = .188 30° X 30° 2.0 1/4 = .250 45° X 45° 1.4 3/8 = .375Levoscoliosis is a type of spinal curvature where the spine curves to the left in a “C” shape. This curve usually starts in the lower back. Treatments, such as braces or surgery, can help ...The bending radius is expressed in relation to the pipe’s outer diameter. If the radius is equal to the pipes diameter then the radius is 1D. The radius is 2 times greater than the outer diameter then the pipes bends is 2D. There are also different standard pipe bend angles ranging from 15% degrees to 180 degrees.The direct answer involves using the tax multiplier. $16 billion x -3 = a $48 billion decrease in the GDP. It can also looked at in terms of the expenditure multiplier. A $16 billion increse in taxes will reduce C by $12 billion, which when multiplied by the expenditures multiplier of 4 reduces GDP by $48 billion.A temperature such as 15 °C is stated "fifteen degrees Celsius". On the Celsius scale the boiling point of water is 100 °C, the freezing point of water is 0 °C and absolute zero is −273.15 °C. Fahrenheit. Fahrenheit is a temperature scale and degrees Fahrenheit are units of temperature on that scale. The symbol for degree Fahrenheit is °F.Figure D1 The Expenditure-Output Diagram The aggregate expenditure-output model shows aggregate expenditures on the vertical axis and real GDP on the horizontal axis. A vertical line shows potential GDP where full employment occurs. The 45-degree line shows all points where aggregate expenditures and output are equal.By definition, the j-operator j ≡ √-1. Imaginary numbers can be added, subtracted, multiplied and divided the same as real numbers. The multiplication of ” j ” by ” j ” gives j2 = -1. In Rectangular Form a complex number is represented by a point in space on the complex plane. In Polar Form a complex number is represented by a line ...A multiplier is a value created by taking the reciprocal of the sine from theta and then multiply that value by the opposite. The multiplier is usually simplified by set degree marks that are common bends. Such as 10˚, 22.5˚, 30˚, 45˚, and 60˚. note 1/Sin (θ) • Opposite Shrink ConstantNote: The choice of degree is usually the installer’s choice and most of the time the installation location will determine what degree will fit. Offset Formula Table Angle of …Aug 2, 2009 · But i can tell you your amount of shrink varies with each degree you bend. per inch of offset subtract. 10 degrees would be 1/16" per inch of bend. 15 degrees is 1/8". 22.5 degrees is 3/16". 30 degrees is 1/4". 45 degrees is 3/8". 60 degrees is 1/2". if your bending an odd degree like a 36 you can get close enough by estimating 5/16. June 28, 2021. Roof Pitch Angle Chart lets you find out how steep or flat your roof slope is. The roof pitch is displayed or shown using a two-digit combination. The most frequent approaches for designating the pitch of a roof are (4/12 or 4:12).The min. offset would vary with each size conduit and bender type. To determine the minimum offset on a specific bender/ conduit size, Multiply the amount of offset desired by the cosecant of the angle desired: (30 deg = 2; 15 deg = 3.86; 10 deg = 5.76).There are loads of things you can do to increase knee range of movement. Gaining even just a few degrees of movement, particularly knee extension, can make a massive difference. Some of the most effective ways to increase knee range of motion include exercises, activity modification, joint mobilisations and making changes to your diet.She has a master's degree in mathematics from University of California, Santa Cruz and a bachelor's degree in mathematics from University of California, San Diego. ... the multiplier is {eq}1.15 ...For example: 35 degrees 5 minutes 27 seconds is written as 35° 5' 27" Degree. Degree is 1/360 of a turn, or 1° Full turn contains 360 degrees. Also there are other types of division - circular sectors. Sectors of a certain size have their own special names. Quadrant. Quadrant is 1/4 of a turn ...Edit multiplier for 15 degree offset. Rearrange and rotate pages, insert new and alter existing texts, add new objects, and take advantage of other helpful tools. Click Done to apply changes and return to your Dashboard. Go to the Documents tab to access merging, splitting, locking, or unlocking functions.The min. offset would vary with each size conduit and bender type. To determine the minimum offset on a specific bender/ conduit size, Multiply the amount of offset desired by the cosecant of the angle desired: (30 deg = 2; 15 deg = 3.86; 10 deg = 5.76).Degree of Bend Multiplier Degree of Bend Multiplier Degree of Bend Multiplier 1 .0000 31 .0136 61 .1134 2 .0000 32 .0150 62 .1196 3 .0000 33 .0165 63 .1260 4 .0000 34 .0181 64 .1327 5 .0000 35 .0197 65 .1397 6 .0001 36 .0215 66 .1469 7 .0001 ... 15 INCH OFFSET USING 25 DEGREE BENDS.Decorate and personalize laptops, windows, and more; Removable, kiss-cut vinyl stickers; Super durable and water-resistant; 1/8 inch (3.2mm) white border ...Degrees are offered both at Bachelor, Master of Science, and. PhD level. The ... 15. Multiplier events. CONCLUSION. We believe that all the partners have made ...True. Study with Quizlet and memorize flashcards containing terms like What is the distance multiplier for a 5 degree bend?, What is the distance multiplier for a 10 degree bend?, …Step 3: Find the p-value for the test statistic. To find the p-value by hand, we need to use the t-Distribution table with n-1 degrees of freedom. In our example, our sample size is n = 20, so n-1 = 19. In the t-Distribution table below, we need to look at the row that corresponds to “19” on the left-hand side and attempt to look for the ...CORRECTED MATHEMATICAL FORMULA FOR HYDRAULIC TUBE BENDING The following formula should be used to determine the start point for each required bend. The example will be for a Double Bevel Bend L1 = 26 L2 = 15 25 degree angle L3 = 39 65 degree angle L4 = 15 65 degree angle L5 = 26 25 degree angleA golf club with a loft of 45 degrees is suitable for advanced golfers. The standard lofts for golf clubs can vary depending on the manufacturer and the model, but here are some general guidelines: Driver: 8-12 degrees. 3-wood: 15-18 degrees. 5-wood: 20-22 degrees. 2-iron: 17-19 degrees.٢٥ ربيع الآخر ١٤٣٠ هـ ... ... degree of risk is created. But BECAUSE any Capitalist economy with Property Rights and Rules is managed by Govt, and because the widespread ...See full list on dengarden.com T-distribution and the standard normal distribution. As the degrees of freedom (total number of observations minus 1) increases, the t-distribution will get closer and closer to matching the standard normal distribution, a.k.a. the z-distribution, until they are almost identical.. Above 30 degrees of freedom, the t-distribution roughly matches …Amazon Prime Student 6 month Free Trial: https://amzn.to/2J4txZw Amazon Prime 30 Day Free Trial: https://amzn.to/3mqTcdq DEWALT DCF815S2 12-Volt Max 1/4-Inch...Microstepping control divides each full step into smaller steps to help smooth out the motor’s rotation, especially at slow speeds. For example, a 1.8 degree step can be divided up to 256 times, providing a step angle of 0.007 degrees (1.8 ÷ 256), or 51,200 microsteps per revolution. Microstepping is achieved by using pulse-width …To find the t* multiplier for a 98% confidence interval with 15 degrees of freedom: In Minitab, select Graph > Probability Distribution Plot > View Probability; Change the Distribution to t; Enter 15 for the Degrees of freedom; Select Options; Choose A specified probability; Select Equal tailsEighteen degrees Celsius equals 64 degrees Fahrenheit. It is possible to convert Celsius to Fahrenheit by multiplying the Celsius value by 9, dividing the result by 5 and adding 32.Free Polynomial Degree Calculator - Find the degree of a polynomial function step-by-stepLearn how to use the roof pitch multiplier and the roof's footprint to accurately figure out total roof area. Skip to content. ... (12:12). A roof that goes up at a 45-degree angle has a slope of 12:12. Expressing Roof Slope in Degrees. The rest of the English-speaking world uses degrees, which seems simpler, ... 15:12: 51.34° 1.601 ...1 + MPC + MPC2+ MPC3+ ... + MPCn = 1/ (1-MPC) This is how we derive our multiplier in mathematical terms. We can use this knowledge in our example and calculate the impact of the increased investment of 1000 when the MPC is ⅔ of the output (real GDP). 1/ (1-2/3) x 1000, or 3 x 1000 = 3000.Multiplier for a 15 Degree Offset. 3.86. Multiplier for a 22.5 Degree Offset. 2.6. Multiplier for a 30 Degree Offset. 2. Multiplier for a 45 Degree Offset. 1.4. Study with Quizlet and memorize flashcards containing terms like Shrink for 10 Degree bend, Shrink for a 15 Degree Bend, Shrink for a 22.5 Degree Bend and more.The multiplier for determining the distance between bends is_____when bending offsets using 30 bends. 2.0. The multiplier for determining the distance between bends is_____when bending offsets using 45 bends. 1.4. Upgrade to remove ads. Only $35.99/year. About us. About Quizlet; How Quizlet works;For example: In a 3 bend saddle with 45 degree center, your multiplier is 2.5 for the standard method but 2.61 for the push thru method. Further, the conduit O.D. is added to the quotient of the offset height and multiplier with the push-thru.The head-to-tail method is a graphical way to add vectors. The tail of the vector is the starting point of the vector, and the head (or tip) of a vector is the pointed end of the arrow. The following steps describe how to use the head-to-tail method for graphical vector addition. Let the x -axis represent the east-west direction.Sep 15, 2023 · Roof pitch is a mathematical expression of how steep your roof is. When using pitch, the slope of the roof is given as a ratio of the vertical rise to the horizontal run (rise/run). Traditionally, this expression of pitch takes the form “X:12″ or “X-in-12″, where X is the number of units (inches) of vertical rise of the roof and 12 ... a bend used to change direction in a conduit run. True or False: Parallel offsets can be made with conduit of different sizes by marking and bending at the center or each bend. True. Study with Quizlet and memorize flashcards containing terms like What is the distance multiplier for a 5 degree bend?, What is the distance multiplier for a 10 ...As a shortcut, the roof slope multiplier for any slope can be determined by finding the square root of ((rise/run)² + 1).Divide the rise by the run. Square the result. Add 1 to the result of that. Find the square root of that result. If you know the roof slope in degrees, simply find the secant using a scientific calculator. For example, if ...72 degree 60 degree 45 degree 30 degree 22.5 degree 11.25 degree 5.625 degr, B. the 45-degree line and the saving schedule intersect. C. Sa + X + G = Ig + T. D. Sa + Ig + X = G + T. A. Sa + M + , The height of the canopy depends on the degree of exposure to the prevail, Note: The choice of degree is usually the installer’s choice and most of the time the installation location , Degrees are offered both at Bachelor, Master of Science, and. PhD leve, a bend used to change direction in a conduit run. True or False: Parallel offsets can be made with conduit of different, DAM is an acronym for Dynamic Advance Multiplier (also called IAM or Ig, The procedure to use the find the value of x calculator is as fo, To draw a 30-degree angle using the protractor, follow these steps: , Rotation by θ = − 90 ∘ around the origin is performed b, To find the t* multiplier for a 98% confidence interval with 15 degr, 5 5/8 deg = 10.207. 11 1/4 deg = 5.126. 15 deg = 3.864. 2, 72 degree 60 degree 45 degree 30 degree 22.5 degree 11.25 , Example Converting 50° Celsius to Fahrenheit. , The degree of this polynomial is $$$ 3 $$$ because the highest powe, What is the multiplier for a 15-degree bend? What is the 10 Bend , ٦ ذو القعدة ١٤٤٤ هـ ... ... multiplier, fiscal multiplier, eq, The same method can be applied to those with inequality con.