Answer:
No, it is not possible to obtain zero by adding two vectors of unequal magnitudes.
Explanation:
The Sum of two vectors can only be zero if they are equal in magnitude and opposite in direction. So no two vectors of unequal magnitude cannot be added to give a null vector. Three vectors of equal magnitude and making an angle 120 degrees with each other gives a zero resultant.
Answer:
<em>Functions evaluated at x = -1</em>
A. a(-1) = -2(-1) + 3 = 5
B. b(-1) = 0 (as per graph)
C. <u>Find the equation first:</u>
- m = 4/8 = 1/2
- c(x) = 1/2x - 4
- c(-1) = -1/2 - 4 = -4.5
D. d(-1) = (-1)² - 4 = -3
E. e(-1) = 2 (as per table)
F. f(-1) = 5/2 = 2.5 (as per graph)
G. g(-1) = 2(3)⁻¹ - 2 = 2/3 - 2 = - 1 1/3
H. h(-1) = 2 (as per table)
<u>The order:</u>
- C >> D >> G >> B >> E and H >> F >> A
Since f(x) is a polynomial function and g(x) is an exponential function, we know that both the value and the rate of change of g(x) will exceed those of f(x) when x gets large.
The rate of change of g(x) is less than that of f(x) for x < 3.4. The value of g(x) is less than that of f(x) for x < 4.39. Of the statements offered, the only one that is true is ...
... As x increases, the rate of change of g exceeds the rate of change of f.
_____
In the attached graph, the functions are graphed as solid lines; their rates of change are graphed as dashed lines of the same color.
Answer:
i think it is 180 dollars
Step-by-step explanation:
Answer: No her plates will not fit in the box
Step-by-step explanation: Each plate is 0.5 inches tall; therefore, the stack of 8 plates will have a height of .
Also, the diameter of the largest plate is 10 inches or has a radius of 5 inches, which matches the radius of the cylindrical box; therefore, we know that the stack of plates can fit into the base area of the cylindrical box.
What we want to figure out now is the height of the cylindrical box to see if it is greater than or equal to 4 inches—the height of the stack of plates.
The volume of a cylinder is , and since for our cylindrical box the volume is 150 cubic inches; therefore,
putting in and solving for height we get
,
which is not greater than 4 inches, which means the plates will not fit into the box since the height of the stack is greater than the height of the box.
