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Then collect the common terms and adjust the signs. For one particular well, the splash is heard 14 seconds after the stone is released. Solution On solving quadratic equations see also the lessons - Introduction into Quadratic Equations - PROOF of quadratic formula by completing the square - HOW TO complete the square - Learning by examples - HOW TO solve quadratic equation by completing the square - Learning by examples - Solving quadratic equations without quadratic formula - Who is who in quadratic equations - Using Vieta's theorem to solve qudratic equations and related problems - Challenging word problems solved using quadratic equations - HOW TO solve the problem on quadratic equation mentally and avoid boring calculations - OVERVIEW of lessons on solving quadratic equations in this site.Use this file/link ALGEBRA-I - YOUR ONLINE TEXTBOOK to navigate over all topics and lessons of the online textbook ALGEBRA-I.
This is the value of our „X“ and the solution of our word problem.
Knowing how to mathematically express and solve word problems has genuine real world applications and you will use those skills very often during the course of your everyday life.
When motorboat moves downstream, its speed relative to the bank of the river is miles/hour, and the time spent moving downstream is hours. Andrew and Bill, working together, can cover the roof of a house in 6 days.
So, the total time up and back is , and it is equal to 7.5 hours, according to the problem input. To simplify the equation, multiply both sides by and collect the common terms. Andrew, working alone, can complete this job in 5 days faster than Bill. Solution Let be the number of days for Bill to cover the roof, working alone.
The frame will be cut out of a piece of steel, and to keep the weight down, the final area should be 28 cm when: x is about −9.3 or 0.8 The negative value of x make no sense, so the answer is: x = 0.8 cm (approx.) There are two speeds to think about: the speed the boat makes in the water, and the speed relative to the land: We can turn those speeds into times using: time = distance / speed (to travel 8 km at 4 km/h takes 8/4 = 2 hours, right?
) And we know the total time is 3 hours: total time = time upstream time downstream = 3 hours Put all that together: Two resistors are in parallel, like in this diagram: The total resistance has been measured at 2 Ohms, and one of the resistors is known to be 3 ohms more than the other. The formula to work out total resistance "R = 3 Ohms is the answer. Quadratic Equations are useful in many other areas: For a parabolic mirror, a reflecting telescope or a satellite dish, the shape is defined by a quadratic equation.Since two tubes working together fill the tank in 12 hours, this gives the equation . The second root does not fit the given conditions: if the smaller tube fills the reservoir in 6 hours, then the larger one should make it in 6-18=-12 hours, which has no sense. Of the two roots x= 12 and x= -10 only positive root x= 12 satisfies the condition.To simplify this equation, multiply both sides by and transfer all terms from the right side to the left with the opposite signs. Apply the quadratic formula (see the lesson Introduction into Quadratic Equations) to solve this equation. So, the potentially correct solution is : the smaller tube fills the reservoir in 36 hours. If the smaller tube fills the reservoir in 36 hours, then the larger one makes it in 36-18=18 hours, working separately. When a stone is dropped into a deep well, the number of seconds until the sound of a splash is heard is given by the formula t = , where x is the depth of the well in feet.The easiest way to explain this would be using an example. Let us imagine that you are working as a computer programmer in a company that makes computer games.You are getting paid 50$ per hour and at the end of the day, you earned 400$.We can do that by dividing the whole equation by 50.50 * X = 400 |: 50 X = 8 You can see now that the number of hours you have to work to earn 400$ if you are being paid 50$ per hour is 8.If Andrew works alone, he can complete this job in days.Thus, in one single day Andrew covers part of the roof area, while Bill covers part of the roof area. Two tubes, working together, can fill the reservoir with the liquid in 12 hours.One-step equations can also be communicated in the form of word problems.The only difference between mathematically expressed equations and word problems is that, in word problems, you have to recognize the variable and other elements of the equation yourself.