Answer:
74800 is the amount of $1700 at the rate of 5.5 for 8 yrs
Actual length of the pole and the length of the shadow cast by the pole follow the proportional relationship.
Following this rule, 20 feet tall flagpole will cast 3.33 feet shadow.
If the length of the shadow = x feet
Proportional relationship will be defined by the expression,
feet
Therefore, length of the shadow cast by flagpole will be 3.33 feet.
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Answer:
Step-by-step explanation:
z₁ = 2 − 2i
z₂ = (1 − i) + √3(1 + i) = (1 + √3) + (√3 - 1) i
a) We get the modulus of z₁ as follows
║z₁║ = √((2)²+(-2)²) = 2
now we find the argument
α = Arctan (-2/2) = Arctan (-1) = -45º ⇒ α = 360º + (-45º) = 315º
b) z₁ = 2 Cis 315º
Although the complex number is in binomic or polar form, its representation must be the same, since the complex number is the same, only that it is expressed in two different forms. The modulus represents the distance from the origin to the point. The degree of rotation is the angle from the x-axis. When the polar form is expanded, the result is the rectangular form of a complex number.
c) If z₀*z₁ = z₂ and z₀ = a + b i
we have
(a + b i)*(2 − 2i) = (1 + √3) + (√3 - 1) i
⇒ 2a + 2bi - 2ai - 2bi² = (1 + √3) + (√3 - 1) i
⇒ 2a + 2bi - 2ai - 2b(-1) = (1 + √3) + (√3 - 1) i
⇒ 2a + 2b + 2bi - 2ai = (1 + √3) + (√3 - 1) i
⇒ 2 (a + b) + 2 (b - a) i = (1 + √3) + (√3 - 1) i
Now we can apply
2 (a + b) = 1 + √3
2 (b - a) = √3 - 1
Solving the system we get
a = 1/2
b = √3 / 2
Finally
z₀ = (1/2) + (√3 / 2) i
d) ║z₀║ = √((1/2)²+(√3 / 2)²) = 1
α = Arctan ((√3 / 2)/(1/2)) = 60º
e) z₀ = Cis 60º
f) Since z₂ = z₀*z₁, then z₂ is the transformation of z₁ rotated counterclockwise by arg(w) which is 60º
Answer:
A=.2
to isolate the variable you would have to do the opposite of squaring a number which means you would have to square root the number on the other side of the equal sign
SQRT-1/25
.2
Answer:
6.7
Step-by-step explanation:
or 6.666666666666666666
