Find the eqn. of the tangent line to the curve of f(x) = x^2 + 5x -5 at (0,-5).
Differentiate f(x) to obtain an expression for the derivative (slope of the tangent line):
f '(x) = 2x + 5
Subst. 0 for x here: f '(0) = 2(0) + 5 = 5 (at the point (0, -5))
Use the point-slope equation of a str. line to find the eqn of the tan. line:
y-k = m(x-h), where (h,k) is a point on the line and m is the slope:
y - [-5] = 5(x-0), or y+5 = 5x. Then y = 5x - 5 is the eqn. of the TL to the given curve at (0,-5).
Answer:
y= 1/2x+0
Step-by-step explanation:
Area of a circle can be calculated using the following formula
Area = πr²
where π = 3.14 and r - radius of circle
Area of the whole circle is for a central angle of 360°.
We are asked to find the area of a sector. Sector is when 2 arms enclose a central angle by which one arm has rotated.
1 radian = 57.3°
2.4 radian = 57.3 x 2 = 137.52°
Area for 360° = πr²
area for 137.52° = πr² / 360° x 137.52 = π x 6 cm x 6 cm x 0.382 = 13.752 cm²
