Answer:
Step-by-step explanation:
77; The formula to calculating the area of a trapezoid is (a+b)/2 * c. a+b are the 2 parallel lines, and c is the height or the altitude. So, it is (10+12)/2 * 7, which is 22/2 * 7 = 11*7=77 :)
You just add them all together
9+11+5+7= 32
Y = 2.2x
to check let’s plug in numbers
6.6 = 2.2(3)
6.6 = 6.6
since it’s true it’s most likely the right answer :)
Answer:
30
Step-by-step explanation:
Answer:
a) d(x)=![\sqrt{17x^{2} -12x+5}](https://tex.z-dn.net/?f=%5Csqrt%7B17x%5E%7B2%7D%20-12x%2B5%7D)
b)d'(x)=![\frac{17x-6}{\sqrt{17x^{2} -12x+5} }](https://tex.z-dn.net/?f=%5Cfrac%7B17x-6%7D%7B%5Csqrt%7B17x%5E%7B2%7D%20-12x%2B5%7D%20%7D)
c)The critical point is x=![\frac{6}{17}](https://tex.z-dn.net/?f=%5Cfrac%7B6%7D%7B17%7D)
d)Closest point is (
,![\frac{7}{17}](https://tex.z-dn.net/?f=%5Cfrac%7B7%7D%7B17%7D)
Step-by-step explanation:
We are given the line
![y=4x-1](https://tex.z-dn.net/?f=y%3D4x-1)
Let a point Q(
) lie on the line.
Point P is given as P(2,0)
By distance formula, we have the distance D between any two points
A(
) and B(
) as
D=![\sqrt{(x_{1}-x_{2})^2 + (y_{1}-y_2)^2}](https://tex.z-dn.net/?f=%5Csqrt%7B%28x_%7B1%7D-x_%7B2%7D%29%5E2%20%2B%20%28y_%7B1%7D-y_2%29%5E2%7D)
Thus,
d(x)=![\sqrt{(x-2)^2+(y-0)^2}](https://tex.z-dn.net/?f=%5Csqrt%7B%28x-2%29%5E2%2B%28y-0%29%5E2%7D)
But we have, ![y=4x-1](https://tex.z-dn.net/?f=y%3D4x-1)
So,
d(x)=![\sqrt{(x-2)^2+(4x-1)^2}](https://tex.z-dn.net/?f=%5Csqrt%7B%28x-2%29%5E2%2B%284x-1%29%5E2%7D)
Expanding,
d(x)=
- - - (a)
Now,
d'(x)= ![\frac{\frac{d}{dx} (17x^2-12x+5)}{2(\sqrt{17x^2-12x+5}) }](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cfrac%7Bd%7D%7Bdx%7D%20%2817x%5E2-12x%2B5%29%7D%7B2%28%5Csqrt%7B17x%5E2-12x%2B5%7D%29%20%7D)
i.e.
d'(x)=
- - - (b)
Now, the critical point is where d'(x)=0
⇒
=0
⇒
- - - (c)
Now,
The closest point on the given line to point P is the one for which d(x) is minimum i.e. d'(x)=0
⇒![x=\frac{6}{17}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B6%7D%7B17%7D)
as ![y=4x-1](https://tex.z-dn.net/?f=y%3D4x-1)
⇒y=![\frac{7}{17}](https://tex.z-dn.net/?f=%5Cfrac%7B7%7D%7B17%7D)
So, closest point is (
) - - -(d)