Answer:
240, 241, 242
Step-by-step explanation:
Use x, x+1, and x+2 to express the three consecutive numbers.
Set up an equation: x + x+1 + x+2 = 723.
Solve for x.
<em>z</em> = 3<em>i</em> / (-1 - <em>i</em> )
<em>z</em> = 3<em>i</em> / (-1 - <em>i</em> ) × (-1 + <em>i</em> ) / (-1 + <em>i</em> )
<em>z</em> = (3<em>i</em> × (-1 + <em>i</em> )) / ((-1)² - <em>i</em> ²)
<em>z</em> = (-3<em>i</em> + 3<em>i</em> ²) / ((-1)² - <em>i</em> ²)
<em>z</em> = (-3 - 3<em>i </em>) / (1 - (-1))
<em>z</em> = (-3 - 3<em>i </em>) / 2
Note that this number lies in the third quadrant of the complex plane, where both Re(<em>z</em>) and Im(<em>z</em>) are negative. But arctan only returns angles between -<em>π</em>/2 and <em>π</em>/2. So we have
arg(<em>z</em>) = arctan((-3/2)/(-3/2)) - <em>π</em>
arg(<em>z</em>) = arctan(1) - <em>π</em>
arg(<em>z</em>) = <em>π</em>/4 - <em>π</em>
arg(<em>z</em>) = -3<em>π</em>/4
where I'm taking arg(<em>z</em>) to have a range of -<em>π</em> < arg(<em>z</em>) ≤ <em>π</em>.
You are given Maggie's planning on going to Penn State University. You are also given that she could live there if she has more than $2,000 if she already bought a laptop at $450.
For part A, the inequality that we can form is x ≥ 2,450 because she needs more than $2,000 to survive after buying a $450 dollar worth laptop. Adding the two makes it 2,450.
For part B, if she has to withdraw $30 per week, then the inequality that we can form is x ≥ 2,450 - 30
For part C,
30x ≥ 2,000
x ≥ 66.67
For part D, the answer 66.67 means that Maggie can have 66 times to withdraw $30 per week worth of food from her balance $2000.
Answer:
4.5 square units
Step-by-step explanation:
A = a + b/2 = 4 + 5/2 times 1 = 4.5
Impedance is a vector sum using the formula Z = square root (XL2
+ R2); where Z = impedance, XL = inductive reactance, and R =
resistance. Therefor the formula for a circuit where XL = 64ohm's
and R = 36ohm's is Z = square root(642 + 322); Z = 71.6ohms.
