Answer:
.
Step-by-step explanation:
The equation of a circle of radius
centered at
is:
.
.
Differentiate implicitly with respect to
to find the slope of tangents to this circle.
![\displaystyle \frac{d}{dx}[x^{2} + y^{2}] = \frac{d}{dx}[25]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%5Bx%5E%7B2%7D%20%2B%20y%5E%7B2%7D%5D%20%3D%20%5Cfrac%7Bd%7D%7Bdx%7D%5B25%5D)
.
Apply the power rule and the chain rule. Treat
as a function of
,
.
.
.
That is:
.
Solve this equation for
:
.
The slope of the tangent to this circle at point
will thus equal
.
Apply the slope-point of a line in a cartesian plane:
, where
is the gradient of this line, and
are the coordinates of a point on that line.
For the tangent line in this question:
,
.
The equation of this tangent line will thus be:
.
That simplifies to
.
To answer this item, we let x be the time in which Tyler and Sophia will be able to cover the same distance along the circular track. Since Sophia runs faster, she will be able to finish the track and y meters more while Tyler will be able to finish y meters only.
5(x) = 400 + y
4(x) = y
The values of x and y are 400 and 1600. Thus, it will take 400 seconds for then to meet again.
Answer:
Step-by-step explanation:
2/16
4/14
20/18
1 gal to 7 qt
17 in to 2 ft
2 min to 45 seconds
yes
no
yes
Answer:
Step-by-step explanation:
Please check out the attachments for the solution :)