Answer:
=
, so the model car is moving away from the fixed point at a rate of approximately 1.7 feet per second.
Step-by-step explanation:
The functions x and y satisfy (x−20)^2+y^2=25 and differentiating gives 2(x−20)dx/dt+2y dy/dt=0. Substituting the three known values and solving for dy/dt yields dy/dt=−32. Since Z=x^2+y^2−−−−−−√, dZ/dt=(2x ^ dx/dt+2y^dy/dt) / 2x2+y2√. Substituting Since Substituting for x, y, , and
gives
=
,
Answer: 125.80 ft
Step-by-step explanation:
Asuming the described situation is as shown in the figure below, we need to find the distance between the kite and Jacks house, but first we need to find the
,
and then
.
How?
We will use trigonometry, especifically the trigonometric functions sine and cosine:
For :
(1)
Where is the opposite side to the angle and
the hypotenuse.
Isolating :
(2)
For :
(3)
Where is the adjacent side to the angle.
Isolating :
(4)
Finding :
(5)
(6)
Now that we have found these values, we have to work with a bigger triangle, where the hypotenuse is the distance between the kite and Jack's house and the sides are the values calculated in (4) and (6).
So, in this case we will use the <u>Pithagorean theorem</u>:
(7)
Isolating and writing with the known values:
(8)
(9)
This is the distance between the kite and the house
