Answer:
See below in bold.
Step-by-step explanation:
(1) cosec ( x + 10) = 3
Now cosec x = 1/sin x so
1 / sin (x + 10) = 3
3 sin (x + 10) = 1
sin (x + 10) = 1/3
x + 10 = 19.47 , 160.53 degrees
x = 9.47, 150.53 degrees.
(ii) cot (x - 30) =0.45
cot (x - 30)= 1 /tan (x- 30) so we have
tan (x - 30) = 1 / 0.45 = 2.2222
x - 30 = 65.77 degrees
x = 95.77 degrees.
Answer:
slope= -3
y-intercept= 6
Step-by-step explanation:
1. Approach
To solve this problem, one needs the slope and the y-intercept. First, one will solve for the slope, using the given points, then input it into the equation of a line in slope-intercept form. The one can solve for the y-intercept.
2.Solve for the slope
The formula to find the slope of a line is;

Where (m) is the variable used to represent the slope.
Use the first two given points, and solve;
(1, 3), (2, 0)
Substitute in,

Simplify;

3. Put equation into slope-intercept form
The equation of a line in slope-intercept form is;

Where (m) is the slope, and (b) is the y-intercept.
Since one solved for the slope, substitute that in, then substitute in another point, and solve for the parameter (b).

Substitute in point (3, -3)

Move the shape down by one quadrant and flip it so where “U” was at, “W” is in its place and Vice versa
5. The 5th figure will have 30 tiles.
6. The 6th figure will have 42 tiles.
7. The pattern is non-linear (quadratic).
8. The 20th figure can be made with 420 tiles.
_____
The Nth figure is made with n*(n+1) tiles. To answer question 8, you must solve
.. n(n +1) = 420
.. n^2 +n -420 = 0
.. (n +21)(n -20) = 0
.. n = 20 or -21 . . . . the negative solution is extraneous
1,995,000
The number after the thousands place is 2, which is less than 5 so the thousands place is rounded to 5,000 instead of 6,000.