Answer:
He pays to the cab driver for 25 miles.
Step-by-step explanation:
Consider the provided information.
Let us consider he walks x miles at the rate of 4 miles per hour.
As we know 
Therefore, time taken is: 
He get a taxi for (31-x) miles at the rate of 50 miles per hour.
Therefore, time taken is: 
It took 2 hours after he started.
That means the sum of time take is 2 hours.





Hence he walk 6 miles and he get a taxi for 31-6=25 miles.
He pays to the cab driver for 25 miles.
We will evaluate both expressions step by step.
Sylvia's espression:
h + 0.05h
h: Original hat price.
0.05h: Increase of 5% due to sales tax.
Jin's expressions:
1.05h
h: Original hat price.
1.05: Factor for which you must multiply the original price to add 5% due to sales tax.
Answer:
B - Her monthly average would have increased by $19.57. ... Katie works as a waitress and records her monthly tips in the table shown below. If Katie decided not to work the month of November, how would her five month average compare to her six month ... Lisa is currently taking physics as one of her electives in school.
Step-by-step explanation:
For this case we must pose a verbal problem equivalent to the following expression:

So, we have:
The sum of double a number plus five.
We propose the expression:
A number subtracted from the sum of double the same number plus five equals twenty-six.
Answer:
A number subtracted from the sum of double the same number plus five equals twenty-six.
The given complex number is
z = 1 + cos(2θ) + i sin(2θ), for -1/2π < θ < 1/2π
Part (i)
Let V = the modulus of z.
Then
V² = [1 + cos(2θ)]² + sin²(2θ)
= 1 + 2 cos(2θ) + cos²2θ + sin²2θ
Because sin²x + cos²x = 1, therefore
V² = 2(1 + cos2θ)
Because cos(2x) = 2 cos²x - 1, therefore
V² = 2(1 + 2cos²θ - 1) = 4 cos²θ
Because -1/2π < θ < 1/2π,
V = 2 cosθ PROVEN
Part ii.
1/z = 1/[1 + cos2θ + i sin 2θ]

The denominator is

Therefore

The real part of 1/ = 1/ (constant).