Answer:
The square roots of 49·i in ascending order are;
1) -7·(cos(45°) + i·sin(45°))
2) 7·(cos(45°) + i·sin(45°))
Step-by-step explanation:
The square root of complex numbers 49·i is found as follows;
x + y·i = r·(cosθ + i·sinθ)
Where;
r = √(x² + y²)
θ = arctan(y/x)
Therefore;
49·i = 0 + 49·i
Therefore, we have;
r = √(0² + 49²) = 49
θ = arctan(49/0) → 90°
Therefore, we have;
49·i = 49·(cos(90°) + i·sin(90°)
By De Moivre's formula, we have;
Therefore;
√(49·i) = √(49·(cos(90°) + i·sin(90°)) = ± √49·(cos(90°/2) + i·sin(90°/2))
∴ √(49·i) = ± √49·(cos(90°/2) + i·sin(90°/2)) = ± 7·(cos(45°) + i·sin(45°))
√(49·i) = ± 7·(cos(45°) + i·sin(45°))
The square roots of 49·i in ascending order are;
√(49·i) = - 7·(cos(45°) + i·sin(45°)) and 7·(cos(45°) + i·sin(45°))
Answer:
D
Step-by-step explanation:
I just did this lol
As you progress in math, it will become increasingly important that you know how to express exponentiation properly.
y = 2x3 – x2 – 4x + 5 should be written <span>y = 2^x3 – x^2 – 4^x + 5. The
" ^ " symbol denotes exponentiation.
I see you're apparently in middle school. Is that so? If so, are you taking calculus already? If so, nice!
Case 1: You do not yet know calculus and have not differentiated or found critical values. Sketch the function </span>y = 2x^3 – x^2 – 4^x + 5, including the y-intercept at (0,5). Can you identify the intervals on which the graph appears to be increasing and those on which it appears to be decreasing?
Case 2: You do know differentiation, critical values and the first derivative test. Differentiate y = 2x^3 – x^2 – 4^x + 5 and set the derivative = to 0:
dy/dx = 6x^2 - 2x - 4 = 0. Reduce this by dividing all terms by 2:
dy/dx = 3x^2 - x - 2 = 0 I used synthetic div. to determine that one root is x = 2/3. Try it yourself. This leaves the coefficients of the other factor, (3x+3); this other factor is x = 3/(-3) = -1. Again, you should check this.
Now we have 2 roots: -1 and 2/3
Draw a number line. Locate the origin (0,0). Plot the points (-1, 0) and (2/3, 0). This subdivides the number line into 3 subintervals:
(-infinity, -1), (-1, 2/3) and (2/3, infinity).
Choose a test number from each interval and subst. it for x in the derivative formula above. If the derivative comes out +, the function is increasing on that interval; if -, the function is decreasing.
Ask all the questions you want, if this explanation is not sufficiently clear.
Answer:
5/2
Step-by-step explanation:
divide both sides by 4
Formula:
V = 1/3 * b^2 * h
Plug in what we know:
V = 1/3 * 7^2 * 16
Simplify the exponent:
V = 1/3 * 49 * 16
Multiply all 3 numbers together:
V = 261.3cm^3
