If Y varies inversely as the cube root of x. If y = 4 when x ... - Socratic
May 17, 2017 · y = 6 when x = 8 If y varies inversely as the cube root of x then we can express this algebraically thus y = k*1/x^(1/3) Using the values y = 4 when x = 27 We get 4 = k / 27^(1/3 ) 4 = k /3 Therefore k = 12 The relationship can now be fully expressed as y = 12/x^(1/3 ) Using this rule when x = 8 y = 12 / 8^(1/3) = 12/2 = 6
What is the cube root of x^8? - Socratic
Oct 13, 2015 · root(3)(x^8) = x^2 root(3)(x^2) or if you prefer: root(3)(x^8) = x^(8/3) For any a, b in RR, root(3)(ab) = root(3)(a)root(3)(b) and root(3)(a^3) = a So: root(3)(x^8 ...
How do you write x^(2/3) in radical form? - Socratic
Aug 9, 2017 · Explanation: First, we can rewrite the term as: x2× 1 3. Next, we can use this rule of exponents to rewrite the term again: xa×b = (xa)b. x2× 1 3 ⇒ (x2)1 3. Now, we can use this rule to write the term as an radical: x1 n = n√x. (x2)1 3 = 3√(x2)
How do you use Newton's Method to approximate the value of …
Aug 22, 2014. The Newton-Raphson method approximates the roots of a function. So, we need a function whose root is the cube root we're trying to calculate. Let's say we're trying to find the cube root of 3. And let's say that x is the cube root of 3. Therefore, x3 = 3. For the Newton-Raphson method to be able to work its magic, we need to set ...
How do you find the domain of #g(x) = root3(x+3)#? - Socratic
Jun 23, 2017 · Therefore whether x +3 is positive or negative, we can find its cube root. Hence, domain of g(x) = 3√x +3 is x:x ∈ R and x ∈ (− ∞,∞) Answer link. The domain is RR. See explanation. To find the domain of a function you have to think of all real values of x for which the function's value can be calculated. In the given function there ...
Simplification of Radical Expressions - Algebra - Socratic
There are two common ways to simplify radical expressions, depending on the denominator. Using the identities \sqrt {a}^2=a and (a-b) (a+b)=a^2-b^2, in fact, you can get rid of the roots at the denominator. Case 1: the denominator consists of a single root. For example, let's say that our fraction is {3x}/ {\sqrt {x+3}}.
If y varies inversely as the cube root of x, and y = 12 when
Jul 3, 2016 · 24 Write the english as maths: y prop1/root(3)x Change the variation to an equation by multiplying by a constant. y = k/root(3)x" we need to find a value for "k k = root(3)x xx y = root(3)8 xx 12 = 2 xx 12 = 24 Replace k with 24 to obtain the equation y = 24/root(3)x Now we can calculate y for any given x. y = 24/root(3)1 =24/1 =24
Find cube root of 15 by using iteration method? - Socratic
Feb 17, 2018 · cube root of 15 correct to three decimal places is x=2.466 Let the cube root of 15 be x Then, cubing both sides and interchanging x^3=15 x^3-15=0 Let f(x)=x^3-15 We need to investigate for the roots of the polynomial x^3-15 Consider any perfect cube close to the number 15 1^3=1,,,,,,,2^3=8,,,,,,,,,,, 3^3=27 15 lies between 8 and 27 Hence cube root of 15 lies …
Find the cube roots of 8? - Socratic
Feb 18, 2018 · We can form the graph of #f^(-1)(x) = root(3)(x)# by reflecting about the line #y=x# (effectively swapping #x# and #y#) to get: graph{(y^3-x) = 0 [-10, 10, -5, 5]} Now #2^3 = 8#, so #2# is a cube root of #8#, and since #f(x) = x^3# is one to one, it is the only real cube root of #8#. In other words it is the only real zero of the polynomial: #x ...
How do you get the complex cube root of 8? - Socratic
Jan 3, 2016 · The cube roots of 8 are 2, 2omega and 2omega^2 where omega=-1/2+sqrt(3)/2 i is the primitive Complex cube root of 1. Here are the cube roots of 8 plotted in the Complex plane on the circle of radius 2: graph{(x^2+y^2-4)((x-2)^2+y^2-0.01)((x+1)^2+(y-sqrt(3))^2-0.01)((x+1)^2+(y+sqrt(3))^2-0.01) = 0 [-5, 5, -2.5, 2.5]} They can be written as: 2(cos(0)+i …