For this case we must simplify the following expression:![7 (\sqrt [3] {2x}) - 3 (\sqrt [3] {16x}) - 3 (\sqrt [3] {8x})](https://tex.z-dn.net/?f=7%20%28%5Csqrt%20%5B3%5D%20%7B2x%7D%29%20-%203%20%28%5Csqrt%20%5B3%5D%20%7B16x%7D%29%20-%203%20%28%5Csqrt%20%5B3%5D%20%7B8x%7D%29)
We rewrite:
We rewrite the expression:
![7 (\sqrt [3] {2x}) - 3 (\sqrt [3] {2 ^ 3 * 2x}) - 3 (\sqrt [3] {2 ^ 3 * x}) =](https://tex.z-dn.net/?f=7%20%28%5Csqrt%20%5B3%5D%20%7B2x%7D%29%20-%203%20%28%5Csqrt%20%5B3%5D%20%7B2%20%5E%203%20%2A%202x%7D%29%20-%203%20%28%5Csqrt%20%5B3%5D%20%7B2%20%5E%203%20%2A%20x%7D%29%20%3D)
By definition of properties of powers and roots we have:
![\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}](https://tex.z-dn.net/?f=%5Csqrt%20%5Bn%5D%20%7Ba%20%5E%20m%7D%20%3D%20a%20%5E%20%7B%5Cfrac%20%7Bm%7D%20%7Bn%7D%7D)
Then, taking the terms of the radical:
![7 (\sqrt [3] {2x}) - 3 (2 \sqrt [3] {2x}) - 3 (2 \sqrt [3] {x}) =\\7 \sqrt [3] {2x} -6 \sqrt [3] {2x} -6 \sqrt [3] {x} =](https://tex.z-dn.net/?f=7%20%28%5Csqrt%20%5B3%5D%20%7B2x%7D%29%20-%203%20%282%20%5Csqrt%20%5B3%5D%20%7B2x%7D%29%20-%203%20%282%20%5Csqrt%20%5B3%5D%20%7Bx%7D%29%20%3D%5C%5C7%20%5Csqrt%20%5B3%5D%20%7B2x%7D%20-6%20%5Csqrt%20%5B3%5D%20%7B2x%7D%20-6%20%5Csqrt%20%5B3%5D%20%7Bx%7D%20%3D)
We add similar terms:
![\sqrt [3] {2x} -6 \sqrt [3] {x}](https://tex.z-dn.net/?f=%5Csqrt%20%5B3%5D%20%7B2x%7D%20-6%20%5Csqrt%20%5B3%5D%20%7Bx%7D)
Answer:
Option C
The equation stems from the principle concept of Hooke's Law. After derivation, the general equation for finding the work of a stretch spring is written below:
W = k[(x₂ - x₁) + (x₁ - xn)]
where
k is the spring constant
xn is the natural length of the spring
x₁ is the length after stretching
x₂ is the length after stretching even further
Suppose the spring was only stretched once, then x₁ = x₂. The equation is simplified to:
<em>W = k(x₁ - xn)</em>
Answer:
width = 18.97 inches
Step-by-step explanation:
To find the smallest width of the box to fit the bat, we need to put the bat in the diagonal of the box.
The diagonal of the box is given by:
diagonal^2 = length^2 + width^2 + height^2
Then, using the diagonal = 36 inches, length = 30 inches and height = 6 inches, we have:
36^2 = 30^2 + width^2 + 6^2
1296 = 900 + width^2 + 36
width^2 = 360
width = 18.97 inches
Answer:
5 Bags
Step-by-step explanation:
There are 75 carrots and 40 celery sticks.
If we want each bag to have the same combination, the greatest number of bags we can make is determined by the Greatest common divisor of the two numbers.
To find the Greatest common divisor of 70 and 40
<u>Step 1:</u> Express each number as a product of its prime factors
- 40=2 X 2 X 2 X 5
- 75=3 X 5 X 5
<u>Step 2:</u> Pick each pair of common factors.
- 40=2 X 2 X 2 X 5
- 75=3 X 5 X 5
The only factor common to both pairs is 5.
Therefore, the Greatest common divisor of 70 and 40 is 5.
The greatest number of bags that can be made is 5.
<span>What number must you add to complete the square x^2 + 12x = -3?</span>
Make sure to always check your answers, by the way!
The answer is: (x + 6)² - 33
Hope I helped!
Let me know if you need anything else!
~ Zoe
