bearing in mind that there are 60 minutes in 1 degree, and 60 seconds in 1 minute.
60°19'39"
so 39 seconds is really 39/60 minutes, or 0.65 minutes
so 19'39" is really 19.65'.
since there are 60 minutes in 1 degree, then 19.65' is really 19.65/60 degrees, or 0.3275°.
60°19'39" is then 60.3275°.
<u>Answer</u>
-5 and 5
<u>Explanation</u>
Absolute value generally means the considering the magnitude only but not the sign. -5 and 5 have the same magnitude.
/-5/ = 5
/+5/ = 5
Answer:
(a) y = -3/5 x + 13/5
(b) y = 5/3 x + 1/3
Step-by-step explanation:
(a) The slope of the tangent line is dy/dx. Use implicit differentiation:
x² + y² + 4x + 6y − 21 = 0
2x + 2y dy/dx + 4 + 6 dy/x = 0
2x + 4 + (2y + 6) dy/dx = 0
x + 2 + (y + 3) dy/dx = 0
(y + 3) dy/dx = -(x + 2)
dy/dx = -(x + 2) / (y + 3)
At the point (1, 2), the slope is:
dy/dx = -(1 + 2) / (2 + 3)
dy/dx = -3/5
Using point-slope form of a line:
y − 2 = -3/5 (x − 1)
Simplifying to slope-intercept form:
y − 2 = -3/5 x + 3/5
y = -3/5 x + 13/5
(b) The normal line is perpendicular to the tangent line, so its slope is 5/3. It also passes through the point (1, 2), so point-slope form of the line is:
y − 2 = 5/3 (x − 1)
Simplifying to slope-intercept form:
y − 2 = 5/3 x − 5/3
y = 5/3 x + 1/3
16:6 is an equivalent ratio
