Answer:
we have (a,b,c)=(4,-2,0) and R=4 (radius)
Step-by-step explanation:
since
x²+y²+z²−8x+4y=−4
we have to complete the squares to finish with a equation of the form
(x-a)²+(y-b)²+(z-c)²=R²
that is the equation of a sphere of radius R and centre in (a,b,c)
thus
x²+y²+z²−8x+4y=−4
x²+y²+z²−8x+4y +4 = 0
x²+y²+z²−8x+4y +4 +16-16 =0
(x²−8x + 16) + (y² + 4y + 4 ) + (z²) -16 = 0
(x-4)² + (y+2)² + z² = 16
(x-4)² + (y-(-2))² + (z-0)² = 4²
thus we have a=4 , b= -2 , c= 0 and R=4
remember that local minimuns are points in which the function was decreasing and starts increasing.
you can try two ways of doing it, graphing the functions or using derivatives.
since this are twelve functios the easier way is to graph them.
start by function y=x
in this case this function is continously increasing as x increases, which means that it does not have any local maxima or minima.
now do the same for
this graph has a local minima on th
Answer:
25.6 km/h
Step-by-step explanation:
Omani:
First, 1.5 hours = 1 hour and 30 minutes
and 66 miles = 105.6 km (66 x 1.6 = 105.6)
105.6 / 1.5 = 70.4 km/h
Omani's speed is 70.4 km/h
Adedi:
1 hour and 15 minutes is 1.25 hours
she drives 56 km in 1.25 hours
So 56 / 1.25 = 44.8 km/h
Adedi's speed is 44.8 km/h
Difference:
70.4 - 44.8 = 25.6 km/h
Omani is faster than Adedi with 25.6 km/h
