Now we use our algebra skills to solve for 'x'. Total time = time upstream + time downstream = 3 hours (to travel 8 km at 4 km/h takes 8/4 = 2 hours, right?) We can turn those speeds into times using: when going downstream, v = x+2 (its speed is increased by 2 km/h).when going upstream, v = x−2 (its speed is reduced by 2 km/h).Unit 8 Absolute value equations, functions, & inequalities. Unit 2 Solving basic equations & inequalities (one variable, linear) Unit 3 Linear equations, functions, & graphs. Let v = the speed relative to the land (km/h)īecause the river flows downstream at 2 km/h: Algebra (all content) 20 units 412 skills.Let x = the boat's speed in the water (km/h).There are two speeds to think about: the speed the boat makes in the water, and the speed relative to the land: What is the boat's speed and how long was the upstream journey? The negative value of x make no sense, so the answer is:Įxample: River Cruise A 3 hour river cruise goes 15 km upstream and then back again. The desired area of 28 is shown as a horizontal line. Let us solve this one by Completing the Square. How many you sell depends on price, so use 'P' for Price as the variable what is the best price? And how many should you make? at $350, you won't sell any bikes at all.$700,000 for manufacturing set-up costs, advertising, etcīased on similar bikes, you can expect sales to follow this 'Demand Curve':.Now you want to make lots of them and sell them for profit. You have designed a new style of sports bicycle! So the ball reaches the highest point of 12.8 meters after 1.4 seconds. Then find the height using that value (1.4) The method is explained in Graphing Quadratic Equations, and has two steps:įind where (along the horizontal axis) the top occurs using −b/2a:

Note: You can find exactly where the top point is! The factors of −15 are: −15, −5, −3, −1, 1, 3, 5, 15īy trying a few combinations we find that −15 and 1 work Multiply to give a×c, and add to give b' method in Factoring Quadratics:

There are many ways to solve it, here we will factor it using the 'Find two numbers that It looks even better when we multiply all terms by −1: (Note for the enthusiastic: the -5t 2 is simplified from -(½)at 2 with a=9.8 m/s 2)Īdd them up and the height h at any time t is:Īnd the ball will hit the ground when the height is zero: Gravity pulls it down, changing its position by about 5 m per second squared: It travels upwards at 14 meters per second (14 m/s): (Note: t is time in seconds) The height starts at 3 m: Ignoring air resistance, we can work out its height by adding up these three things:

Solve for quadratic equation