If P is a point in the x axis therefore this means that
the y must be zero. Hence the coordinate of p is (x, 0).
We can use the distance formula to solve for the value of
x:
d^2 = (x – x1)^2 + (y – y1)^2
13^2 = (x + 3)^2 + (0 – 5)^2
169 = (x + 3)^2 + 25
(x + 3)^2 = 144
x + 3 = ± 12
x = -15, 9
Hence P has two possible coordinates:
<span>(-15, 0) and (9, 0)</span>
Answer:
D(L)/dt = 407,6 m/s
Step-by-step explanation:
Let call A the intersection point.
As the cars are driving from perpendicular directions, they form with a coordinates x and y, a right triangle, and distance between them is the hypotenuse (L), then
L² = x² + y²
Taking derivatives with respect to time we have:
2*L* D(L)/dt = 2*x *D(x)/dt + 2*y* D(y)/dt (1)
In this equation we know: At a certain time
x = 444 m and D(x)/dt = 10 m/s
y = 333 m and D(y)/dt = 666 m/s
And L = √(x)² + (y)² ⇒ L = √ (444)² +( 333)² ⇒ L = √197136 + 110889
L = √308025
L = 555 m
Thn plugin these values in euatn (1) we get
2* 555 * D(L)/dt (m) = 2* 444* 10 + 2*333*666 (m*m/s)
D(L)/dt = ( 4440 + 221778)/555 (m/s)
D(L)/dt = 407,6 m/s
His current quiz score would be 60
