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AysviL [449]
2 years ago
9

123 Savings and Loan charges a monthly fee of $8 on checking accounts and an overdraft protection fee of $33. Neela's check regi

sti
he had a balance of $456
when she wrote a check for $312. Three days later she realized her check register had an error and she actually only had $256, so she transferred $250 into her checking
account. The next day, her monthly account statement was sent to her. What was the balance on her statement?
Mathematics
1 answer:
Stells [14]2 years ago
8 0

Based on the calculation below, the balance on Neela's statement is $153.

<h3>How do we calculate the balance on a bank statement?</h3>

The balance on Neela's statement can be calculated using the following formula:

Balance on statement = Actual amount in the account - Monthly fee - Overdraft protection fee - Check written + Amount transferred ............ (1)

Substituting all the relevant values into equation (1), we have:

Balance on statement = $256 - $8 - $33 - $312 + $250

Balance on statement = $153

Learn more about bank statement balance here: brainly.com/question/13837329.

#SPJ1

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Step-by-step explanation:

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Find the value of angle y?
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What is (2-2i√3)4 equivalent to?
maxonik [38]

a. (2 - 2i√3)⁴ in polar form is 256(cos(-4π/3) + isin(-4π/3)) = 256cis(-4π/3)

b. (2 - 2i√3)⁴ in rectangular form is -128 + 128√3

To answer the question, we need to know what complex numbers are

<h3>What are complex numbers?</h3>

Complex numbers are numbers of the form z = x + iy

<h3>a. Complex numbers in polar form</h3>

Complex numbers in polar form z = r(cosθ + isinθ) where

  • r = √(x² + y²) and
  • θ = tan⁻¹(y/x)

Given that z = (2 - 2i√3)⁴ =

So,

  • x = 2 and
  • y = -2√3

So, converting to polar form

r = √(x² + y²)

= √[2² + (-2√3)²]

= √[4 + 4(3)]

= √[4 + 12]

= √16

= 4

θ = tan⁻¹(y/x)

θ = tan⁻¹(-2√3/2)

θ = tan⁻¹(-√3)

θ = -π/3

So, z = r(cosθ + isinθ)

= 4(cos(-π/3) + isin(-π/3))

<h3>Powers of complex numbers</h3>

A complex number z raised to power n is zⁿ = rⁿ(cosnθ + isin(nθ)]

z⁴ = (2 - 2i√3)⁴

= r⁴(cos4θ + isin4θ)

= 4⁴(cos(4 × -π/3) + isin(4 × -π/3))

= 256(cos(-4π/3) + isin(-4π/3))

= 256cis(-4π/3)

(2 - 2i√3)⁴ in polar form is 256(cos(-4π/3) + isin(-4π/3)) = 256cis(-4π/3)

<h3>b. Complex numbers in rectangular form</h3>

The complex number z =  r(cosθ + isinθ) in rectangular form is z = x + iy where

  • x =  rcosθ and
  • y =  rsinθ

Given that z⁴ = 256(cos(-4π/3) + isin(-4π/3)) in rectangular form,

x = rcosθ

= 256(cos(-4π/3)

= 256cos(-4 × 60°)

= 256cos(-240)

= 256cos(240)

= 256 × -1/2

= -128

y =  rsinθ

= 256sin(-4π/3)

= 256sin(-4 × 60°)

= 256sin(-240)

= -256sin240

= -256 × -√3/2

= 128√3

So, z⁴ = x + iy

= -128 + 128√3

So, (2 - 2i√3)⁴ in rectangular form is -128 + 128√3

Learn more about complex numbers in polar form here:

brainly.com/question/9678010

#SPJ1

7 0
2 years ago
What is the measure of the highlighted angle
IgorLugansk [536]
Angle on a straight line sums up to 180
so
72+x + x+130 = 180
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2x =-22
x= -11

so Angle on the LHS is 61°
while angle on the RHS is 119°
7 0
3 years ago
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