Answer:
![b=-\frac{31}{6}](https://tex.z-dn.net/?f=b%3D-%5Cfrac%7B31%7D%7B6%7D)
Step-by-step explanation:
We are given the equation of the curve:
(1)
And the equation of the line that is normal (perpendicular to that curve) in the point
:
(2)
Note this equation has the form
, where
is the slope of the line that es normal to the curve and
the intersection of that line with the y-axis.
Well, let’s begin by finding the slope of the line that is tangent to the curve by differentiating the equation (1):
(3)
Then, we have to evaluate that when
(remember we are given the point
):
(4) This is the slope of the line that is tangent to the curve
And the slope of the line that is perpendicular to that tangent line is its negative reciprocal. Hence:
(5) This is the slope of the line normal to the curve
Then:
(6)
Rewritting (2):
(7)
Evaluating in the point
:
(8)
Finding
:
(9) This is the value of
Substituting (9) in (6):
(10)
(11) This is the value of ![a](https://tex.z-dn.net/?f=a)
Answer:
Answers: (to the nearest hundredth)
Between two cars,
Central angle = 0.39 radians (or 71.4°)
Arc length = 7.85 ft
Area of a sector = 78.54 ft²
Step-by-step explanation:
7. 56
8. 68
9. 5.5 and 22
10. 8.35
11. 88
12. 4.93
Lets see!
We need to use the pythagorean theorem (a^2+b^2=c^2) to check.
So..
15^2+ 17^2 = 19^2
225+ 289= 361
Hm 225 and 289 do NOT equal 361 therefore it is NOT a right triangle.
Answer:
64
Step-by-step explanation:
Its practically just 8 times 8