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:
For company A, y = 24x + 42
For company B, y = 28x + 25
Step-by-step explanation:
x is the number of containers
y is the total cost
For company A, y = 24x + 42
For company B, y = 28x + 25
For the cost of both companies to be the same, then
24x + 42 = 28x + 25
28x - 24x = 42 - 25
4x = 17
x = 4.25
Mr Lycan would have to order about 4 containers so the cost would be the same from each company
1/4 or 4/8 or 5/10
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Answer:
Step-by-step explanation:
The equation for solving for density is:
Density = mass / volume
Then plug in the values:
Density = 6 g / 12 mL
Divide and don't forget the units!
Density = 0.5 g/mL
Answer:
y = 1/3x + 4 1/3
Step-by-step explanation:
2x - 6y = 12
First find the slope
Solve for y
Subtract 2x
2x - 6y -2x= 12-2x
-6y = -2x+12
Divide by -6
-6y/-6 =-2x/-6 +12/-6
y = 1/3 x -2
The slope is 1/3
Parallel lines have the same slope
Using the slope intercept form y = mx+b where m is the slope and b is the y intercept
y = 1/3x +b
And substituting in the point
4 = 1/3 (-1) +b
4 = -1/3 +b
Add 1/3 to each side
4 + 1/3 = b
y = 1/3x + 4 1/3
