Suppose that we use Euler's method to approximate the solution to the differential equation dy y(0.5) = 9. dx Let f(x, y) = a³/y. We let xo 0.5 and yo = 9 and pick a step size h = 0.2. Euler's method is the the following algorithm. From x, and yn, our approximations to the solution of the differential equation at the nth stage, we find the next stage by computing Сn+1 — ӕ, +h, Yn+1 = Yn + h · f(xm, Yn). Complete the following table: Сп Yn 0.5 5 The exact solution can also be found using separation of variables. It is y(x) = Thus the actual value of the function at the point x = 1.5 y(1.5) =
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
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