The height of a saw tooth in inches after time in seconds is represented by the function y = 0.3sin (30x + 1.5) - 0.1 for t > 0. without graphing the function, determine the range that the saw tooth covers.

Range is from -0.4 till 0.2, inclusive

Step-by-step explanation:

y = 0.3sin (30x + 1.5) - 0.1

-1 < sin(x) < 1

-1 < sin(30x + 1.5) < 1

Because this is a change in domain, not in range

-0.3 < 0.3sin(30x + 1.5) < 0.3

-0.3-0.1 < 0.3sin(30x + 1.5) - 0.1 < 0.3-0.1

-0.4 < 0.3sin(30x + 1.5) - 0.1 < 0.2

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1

where is the gragh

step-by-step explanation: