<em>Answer:</em>
<em />
<em>x³ + x² - 6x = 0</em>
<em>x(x² + x - 6) = 0</em>
<em>x(x² + 3x - 2x - 6) = 0</em>
<em>x[x(x + 3) - 2(x + 3)] = 0</em>
<em>x(x - 2)(x + 3) = 0</em>
<em>x₁ = 0</em>
<em>x - 2 = 0 => x₂ = 2</em>
<em>x + 3 = 0 => x₃ = - 3</em>
Answer:
The unit vector u is (-5/√29) i - (2/√29) j
Step-by-step explanation:
* Lets revise the meaning of unit vector
- The unit vector is the vector ÷ the magnitude of the vector
- If the vector w = xi + yj
- Its magnitude IwI = √(x² + y²) ⇒ the length of the vector w
- The unit vector u in the direction of w is u = w/IwI
- The unit vector u = (xi + yj)/√(x² + y²)
- The unit vector u = [x/√(x² + y²)] i + [y/√(x² + y²)] j
* Now lets solve the problem
∵ v = -5i - 2j
∴ IvI = √[(-5)² +(-2)²] = √[25 + 4] = √29
- The unit vector u = v/IvI
∴ u = (-5i - 2j)/√29 ⇒ spilt the terms
∴ u = (-5/√29) i - (2/√29) j
* The unit vector u is (-5/√29) i - (2/√29) j
Answer:
A
Step-by-step explanation:
The volume of a prism can be found by multiplying the area of the base by the height. It is the formula V = B*h. Here B = 108. Substitute and solve.
V = 108*8 = 864
This is answer A.
Answer:
9
Step-by-step explanation:
For this problem, you would use the GCF
Find the GCF of 45, 81, 63
GCF(45, 81, 63) = 9
45 = 9 * 5
81 = 9 *9
63= 9 * 7
Since 5, 9, 7 have no common factors, the GCF has to be 9.
This means that the greatest number of plants he can put in each row is 9.
The number of rows he uses for each plant will (obviously) vary.
