The concept of radicals and radical exponents is tricky at first, but makes sense when we look into the logic behind it.
When we write a radical in exponential form, like writing √x as x^(1/2), we are simply putting the power of the radical in the denominator (bottom number) of the exponent, and the numerator is the power we raise the exponent to, or the power that would be inside the radical.
In our example, √x is really ²√(x¹), or the square root of x to the first power. For this reason, we write it as x^(1/2).
Let's say we wanted to write the cubed root of x squared, in exponential form.
In radical form, it would look like this:
³√(x²) . This means we square x, and then take the cubed root.
In exponential form, remember that we take the power of the radical (3), and make that the denominator of the exponent, and keep the numerator as the power that x is raised to (2).
Therefore, it would be x^(2/3), or x to the 2 thirds power.
Just like when multiplying by a fraction, you multiply by the numerator and divide by the denominator, in exponential form, you raise your base number to the power of the numerator, and take the root of the denominator.
A way to remember what you have learned is creating notes or doing practice problems
Answer:
X=58 degrees
Step-by-step explanation:
So We can start by finding the angle thats supplementary to 109.
Well 109 and another unknown angle (which will be Y for this scenario) would form a straight line which is 180 degrees.
109+y=180
Solve that by isolating the y and you would get 71 as the missing side.
Now we have 2 sides, 71 and 51. We’re trying to find x or the angle vertical to the thrid interior angle of the triangle.
Vertical is basically equal so we really just gotta find the third side. A triangle is equal to 180 degrees and if you add em up.
71+51+x=180
Combine like terms
122+x=180
Isolate the X
x=58
So x is 58 degrees.
Hello!
2.5 litres = 1,000 * 2.5 = 2,500 cubic cm
volume = π * radius2 * height
2,500 = π * r2 * 20
2,500 / 20π = r^2
(Square Root of) 2,500 / 20π = r^2
6.307 <span>centimeters </span>= r (Radius)
Hope this Helps! Have A Wonderful Day! :)
Answer:
![Interval = [666.78, 781.62]](https://tex.z-dn.net/?f=Interval%20%3D%20%5B666.78%2C%20781.62%5D)
Step-by-step explanation:
Given
The data for 25 undergraduates
Solving (a): Range and Standard deviation
The range is:
From the dataset:
So:
The standard deviation is:
First, calculate the mean
So, the standard deviation is:
Solving (b): The interval of the 95% of the observation.
Using the emperical rule, we have:
![Interval = [\bar x - 2*\sigma, \bar x+ 2*\sigma]](https://tex.z-dn.net/?f=Interval%20%3D%20%5B%5Cbar%20x%20-%202%2A%5Csigma%2C%20%5Cbar%20x%2B%202%2A%5Csigma%5D)
![Interval = [724.2 - 2*28.71, 724.2 + 2*28.71]](https://tex.z-dn.net/?f=Interval%20%3D%20%5B724.2%20-%202%2A28.71%2C%20724.2%20%2B%202%2A28.71%5D)
