9/-1.........................
Dy/dx = y/x^2
1/y dy = 1/x^2 dx
int(1/y dy) = int(1/x^2 dx)
ln y + c1 = -x + c2
ln y = -x + c ; c= c2-c1
y = e^(-x+c) = e^c e^-x
y = Ce^-x ; C=e^c
X = 36/5
Or x = 7.2
21 + x = 6x - 15
21 = 6x - 15 - x
21 = 5x - 15
21 + 15 = 5x
36 = 5x
36/5 = x
He uses 15 gallons. Because 270/6 = 45. Meaning he drives 45 miles per gallon. So 675/45=15. 15 gallons he will need to use to drive 675 miles.
The <u>correct answers</u> are:
A) constant
B) straight line
C) linear
Explanation:
The equation y=0.25x+10 is in slope-intercept form, y=mx+b where m is the slope and b is the y-intercept. The slope is the rate of change. The number in our equation that is in place of m is 0.25. This means for every change in x, the graph will go up 0.25. The rate of change is the same throughout the entire function, so this is a constant rate of change.
Since the rate of change is constant, the graph will be a straight line. A constant rate of change means there is the same distance between every two points on the graph; this is only true of a straight line.
Since the graph is a straight line, the function is linear by definition.
