The magnitude of each vector is the Pythagorean sum of its components.
a. |v1| = √(2² + (-6)²) = √40 = 2√10
|v2| = √((-4)² + 7²) = √65
b. To make each vector into a unit vector, divide each component by the vector's magnitude.
u1 = v1/|v1| = (2/(2√10), -6/(2√10))
u1 = (√10/10, -3√10/10)
u2 = v2/|v2| = (-4/√65, 7/√65)
u2 = (-4√65/65, 7√65/65)
Answer: OPTION C
Step-by-step explanation:
There are some transformations for a function f(x). Some of them are shown below:
1. If 
, the function is shifted up "k" units.
2. If 
, the function is shifted down "k" units.
3. If 
, the function is shifted left "k" units.
4. If 
, the function is shifted right "k" units.
In this case you know that the function "g" is the transformation of the function "f".
Observe that the function "f" intersects the y-axis at:
And the function "g" intersects the y-axis at:
Therefore, since both functions are 4 units apart, you can conclude that the function "f" was shifted down 4 units to get the function "g".
Then, the rule that shows that transformation is:
Answer: 240
Step-by-step explanation:
Distribute all numbers
24 - 6(-21)
24 - (-126)
24+216
240
Answer:
40 inches
Step-by-step explanation:
Volume, V of hemisphere = 2/3 π r^3
Radius, r = 24 inches ;
V = 2/3 π 24^3
V = 28952.917 in³
Volume of cylinder = π r^2 * h
h = height ; r = Radius = 32 /2 = 16 inches
Volume of hemisphere = volume of cylindrical tank
28952.917 = π (16)^2 * h
28952.917 = 804.24771h
h = 28952.917 / 804.24771
h = 35.9999
h = 40 inches
Molten stell rise is 40 inches
Answer:
The hint in this problem is the word "about" or approximately how many pounds. So we could find the solution by estimation through rounding off. We know that almonds cost about 3.50 per pound and a bag costs about $7.00. Dividing 7 by 3.50 per pound, will give us $7 ÷ $3.50 = 2 pounds.
The answer is 2 pounds.
