Learn vocabulary, terms, and more with flashcards, games, and other study tools. Answer to: Assume that the profit generated by a product is given by P(x) = 5*sqrt(x), where x is the number of units sold. A manufacturer has found that when m employees are working, the number of units of product produced per day is q = 10 &Sqrt… (b) Find the marginal revenue function. Assume x ge 0 and y ge 0. x2y3 + 2 x3y4+xy y Which of the following is a like radical to 3 7x? 2(4 16x)-2(4 2y)+3(4 81x)-4(4 32y) What is the following sum? Suppose p = 100 − √ q 2 + 20 is a demand equation for a manufacturer’s product. The first rule we will look at is the product rule for simplifying square roots, which allows us to separate the square root of a product of two numbers into the product of two separate rational expressions. For instance, we can rewrite [latex]\sqrt{15}[/latex] as [latex]\sqrt{3}\cdot \sqrt{5}[/latex]. Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor. Assume x ge 0 and y ge 0. For the steps below assume \(y\) is a function of \(x\). (a) Find the rate of change of p with respect to q. When evaluating square roots we ALWAYS take the positive answer. \[ - \sqrt {16} = - 4\] This may not seem to be all that important, but in later topics this can be very important. Start studying Algebra II Q3 Unit 1: Radical Operations and Equations. Start studying Algebra 2 part 2 exam. The first rule we will look at is the product rule for simplifying square roots, which allows us to separate the square root of a product of two numbers into the product of two separate rational expressions. Get more help from Chegg. This calculator simplifies ANY radical expressions. Example 1: to simplify $(\sqrt{2}-1)(\sqrt{2}+1)$ type (r2 - 1)(r2 + 1). The 4 in the first radical is a square, so I'll be able to take its square root, 2, out front; I'll be stuck with the 5 inside the radical. For instance, we can rewrite [latex]\sqrt{15}[/latex] as [latex]\sqrt{3}\cdot \sqrt{5}[/latex]. Following this convention means that we will always get predictable values when evaluating roots. If we want the negative answer we will do the following. This suggests a general method for implicit differentiation. Get 1:1 help now from expert Algebra tutors Solve it with our algebra problem solver and calculator Learn vocabulary, terms, and more with flashcards, games, and other study tools. The graph of [math]x^2+(y-\sqrt[3]{x^2})^2=1[/math] is very interesting and is show below using desmos. By multiplying the variable parts of the two radicals together, I'll get x 4, which is the square of x 2, so I'll be able to take x 2 out front, too. 8. Figure 2.20: The function \(\sin y +y^3=6-x^2\) and its tangent line at the point \((\sqrt[3]{6},0)\). 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