Use the determinant of the coefficient matrix to determine which of the following linear systems have unique solutions.
2 answers:
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The answer is 1.) 6^1/6
The third root of something is the same as an exponent to the 1/3 power.
(When an exponent is a fraction, the numerator is powers and the denominator finds the root. For example: 3 to the power of 4/2 is multiplied by itself 4 times (81) then the denominator, 2, means we find the square root of it (9). 4/2=2, and 3 to the 2nd power is also 9.)
So that would be 6 to the 1/3 power, then you find the square root of that, so it's (6 to the 1/3 power) to the 1/2 power, and according to the Power Rule (a power on top of a power means you multiply the two powers), that would end up being 1/6.
![\sqrt{ \sqrt[3]{6} } = \sqrt{ {6}^{ \frac{1}{3} } } = (6 { \frac{1}{3} })^{ \frac{1}{2} } = {6}^{ \frac{1}{3} \times \frac{1}{2} } = {6}^{ \frac{1}{6} }](https://tex.z-dn.net/?f=%5Csqrt%7B%20%20%5Csqrt%5B3%5D%7B6%7D%20%20%7D%20%20%3D%20%20%5Csqrt%7B%20%7B6%7D%5E%7B%20%5Cfrac%7B1%7D%7B3%7D%20%7D%20%7D%20%20%3D%20%286%20%7B%20%5Cfrac%7B1%7D%7B3%7D%20%7D%29%5E%7B%20%5Cfrac%7B1%7D%7B2%7D%20%7D%20%20%3D%20%20%7B6%7D%5E%7B%20%5Cfrac%7B1%7D%7B3%7D%20%20%5Ctimes%20%20%5Cfrac%7B1%7D%7B2%7D%20%7D%20%20%3D%20%20%7B6%7D%5E%7B%20%5Cfrac%7B1%7D%7B6%7D%20%7D%20)
The third root of something is the same as an exponent to the 1/3 power.
(When an exponent is a fraction, the numerator is powers and the denominator finds the root. For example: 3 to the power of 4/2 is multiplied by itself 4 times (81) then the denominator, 2, means we find the square root of it (9). 4/2=2, and 3 to the 2nd power is also 9.)
So that would be 6 to the 1/3 power, then you find the square root of that, so it's (6 to the 1/3 power) to the 1/2 power, and according to the Power Rule (a power on top of a power means you multiply the two powers), that would end up being 1/6.
<em>Note: you did not add the answer options, so I am solving this question generally to solve your query, which anyways would clear your concept.</em>
Answer:
Please check the explanation.
Step-by-step explanation:
Given the equation
All we need is to find any random value of 'x' and then solve for 'y'.
For example, putting x=2
Thus, (2, 17) is one of the many ordered pairs solutions of the equation.
Similarly, putting x=3
Thus, (3, 21) is one of the many ordered pairs solutions of the equation.
Hello there! I can help you! So in this question, we are talking about an elephant eating 400 pounds each day. Knowing this can help us solve these questions:
a. So v represents number of pounds and d represents the number of days. We would write the equation as v = 400d, because you multiply the amount of days and pounds eaten per day to find the total amount of vegetation the animal has ate.
b. So given the equation, all we have to do is plug in a number for d and multiply to find v. Let's find the value for 3 days, starting with day 1. 400 * 1 is 400. 400 pounds eaten in day 1. 2 * 400 is 800. 800 total pounds eaten on day 2. 3 * 400 is 1,200. 1,200 total pounds eaten on day 3. With those numbers, your table should look like the one below if you do it correctly.
c. With that, your points should be placed at (1, 200), (2, 800), (3, 1,200). You can see that the line is constant, and that when you connect the dots, the line is straight. It is a linear equation, where the line is straight and the value is constant.
a. So v represents number of pounds and d represents the number of days. We would write the equation as v = 400d, because you multiply the amount of days and pounds eaten per day to find the total amount of vegetation the animal has ate.
b. So given the equation, all we have to do is plug in a number for d and multiply to find v. Let's find the value for 3 days, starting with day 1. 400 * 1 is 400. 400 pounds eaten in day 1. 2 * 400 is 800. 800 total pounds eaten on day 2. 3 * 400 is 1,200. 1,200 total pounds eaten on day 3. With those numbers, your table should look like the one below if you do it correctly.
c. With that, your points should be placed at (1, 200), (2, 800), (3, 1,200). You can see that the line is constant, and that when you connect the dots, the line is straight. It is a linear equation, where the line is straight and the value is constant.