The rectangular coordinates of a point are (5.00, y) and the polar coordinates of this point are ( r, 67.4°). what is the value of the polar coordinate r in this case?

  r ≈ 13.01

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you that ...

  Cos = Adjacent/Hypotenuse

  cos(67.4°) = 5.00/r . . . . . . filling in the given values

Solving for r gives ...

  r = 5.00/cos(67.4°) ≈ 13.01

Check your requirements for rounding. We rounded to 2 decimal places because the x-coordinate, 5.00, was expressed using 2 decimal places.

r = 13.01

Step-by-step explanation:

The formula to find r is  

We know x = 5.00, we need to find y in order to find r.  Use the tangent formula with the given angle to solve for y:

so

and

5.00 tan(67.4) = y so

y = 12.01

Now use that in your formula to find r:

and

so

r = 13.01

answer: the value should be used for i in the formula of calculation the monthly payment , the interest rate per period is 0.85.

step-by-step explanation:

the given rate of interest i= 85%

in calculating the monthly payment for a loan with an interest rate compounded monthly, the value of the interest rate per period we use in the formula must be in decimal form.

to convert it in decimal, we divide it by 100, we get

hence, the value should be used for i in the formula of calculation the monthly payment , the interest rate per period is 0.85.

  y= -3x is the required function.

step-by-step explanation:

we have been given a table:

x             y

0             0

1             -3

3             -9

-2             6

we can see that the values of y is -3 times the value of x

hence, the function would be: y= -3x.

put the values of x will give the same y as in the table that means function is satisfying the given table.