Cos^(2)x=(cscxcosx)/(tanx+cotx)

1 answer:

6 0

$\cos^2 x = \dfrac{\csc x \cos x}{\tan x + \cot x}$

$\cos^2 x = \dfrac{\csc x \cos x}{\dfrac{\sin x}{\cos x} + \dfrac{\cos x}{\sin x}}$

$\cos^2 x = \dfrac{\csc x \cos x}{\frac{\sin x}{\cos x} \times 
\frac{\sin x}{\sin x} + \frac{\cos x}{\sin x} \times \frac{\cos x}{\cos 
x}}$

$\cos^2 x = \dfrac{\csc x \cos x}{\frac{\sin^2 x}{\sin x \cos x} + \frac{\cos^2 x}{\sin x \cos x}}$

$\cos^2 x = \dfrac{\csc x \cos x}{\frac{1}{\sin x \cos x}}$

$\cos^2 x = \csc x \cos x \sin x \cos x$

$\cos^2 x = \dfrac{1}{\sin x} \cos x \sin x \cos x$

$\cos^2 x = \cos^2 x$

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two high school students are hired to rake leaves. They will work a couple hours each afternoon until the job is completed. They

Schach [20]

Answer:

x = 14 days

Step-by-step explanation:

To answer the question, find a function that represents the payment mode of plan A and an equation that represents the mode of payment of plan B.

For Plan B the payment is constant every afternoon, $ 11.5 (or 1150 cents) so the equation to represent this form of payment is as follows:

A = 1150x (with units in cents)

This equation represents the line of a line of slope 1150, which passes through point (0,0). Where x is the number of days {1, 2, 3 ....}

In form of payment B, the amount of payment is doubled each day. And the first payment is 2 cents. Therefore this model is represented by an exponential base 2 equation of the form:

$B = (2) ^ x$

Where x represents the number of days, which is always greater than 0 {1, 2, 3, 4 ...}

To know in which day the salary will be approximately the same we equate both equations and we clear x.

A = B

$1150x = (2) ^ x\\1150x- (2) ^ x = 0$

It is a somewhat difficult equation to solve, so I recommend iterating to get a value where the function approaches 0 (when this difference is zero it means that the A and B salaries are the same).

Suppose

x = 13 days

$1150(13) - (2) ^ {13} = 6758$ cents

It is not equal to 0.

Let's try with x = 15

$1150(15) - (2) ^ {15} = -15518$ cents

Then the value that makes the function zero is between x = 13 and x = 15

Let's try with x = 14

$1150(14) - (2) ^ {14} = -284$ cents = 2.84 $ difference. X = 14 is the whole number where functions A and B are closer together (the salary is approximately the same). Therefore the answer is