Answer:
and
Step-by-step explanation:
The equation of curve is
We need to find the equation of the tangent line to the curve at the point (-3, 1).
Differentiate with respect to x.
The point of tangency is (-3,1). It means the slope of tangent is .
Substitute x=-3 and y=1 in the above equation.
Divide both sides by 130.
If a line passes through a points with slope m, then the point slope form of the line is
The slope of tangent line is and it passes through the point (-3,1). So, the equation of tangent is
Add 1 on both sides.
Therefore, and .
Changing a fraction to its decimal form can be done by long division method. Dividing the denominator by its numerator will change the fraction into decimal form. Alternatively, you can use a calculator to do that for you. Below are the fractions with their decimal forms listed:
1.) 2/5 = 0.4 (D)
2.) 7/20 = 0.35 (A)
3.) 3/25 = 0.12 (C)
4.) 7/10 = 0.7 (B)
By giving just the radius and asking for the arc length of that circle your answer will be without math is 22
π
feet
But;
Let’s do same math!
Arc length = (()/360)⋅2⋅⋅
(
(
a
n
g
l
e
o
f
a
r
c
)
/
360
)
⋅
2
⋅
π
⋅
r
In this case angle of arc was not specified so: 360∘
∘
was used.
Arc length = ((360)/360)⋅2⋅⋅11
(
(
360
)
/
360
)
⋅
2
⋅
π
⋅
11
Arc length = 22
π
feet