Let D be the distance of the bug from the origin.
D = √(x² + y²)
dD/dx = x/√(x² + y²)
dD/dy = y/√(x² + y²)
dD/dt = 7 cm/s
We need dx/dt and dy/dt. We will use the chain rule
dx/dt = dx/dD * dD/dt
= √(x² + y²)/x * 7 = [7√(x² + y²)]/x
Applying the same method for y,
dy/dt = [7√(x² + y²)]/y
Now, we substitute the values of x and y to get the rates.
dx/dt = [7√(x² + y²)]/x = (7√90)/3 = 22.1
dx/dy = [7√(x² + y²)]/y] = (7√90)/9 = 7.38
Answer:
equation of line is:
y = -2x - 6
Explanation:
The general form of the line is:
y = mx + c
where:
m is the slope of the line
c is the y-intercept
(a) getting the slope of the line:
slope of the line is calculated using the following rule:
slope of line (m) = (y2-y1) / (x2-x1) = (-24--12) / (9-3) = -2
The equation now becomes:
y = -2x + c
(b) getting the y-intercept:
The two given points belong to the line. Therefore, to get the y-intercept, we will use one of the points and substitute in the equation and solve for c.
I will use the point (3,-12)
y = mx + c
-12 = -2(3) + c
-12 = -6 + c
c = -12 + 6
c = -6
Based on the above, the equation of the line is:
y = -2x - 6
Hope this helps :)
Like:
f(x)=(1/3)*(3√24)*2x
If so:
f(x)=(2x/3)*3√24
f(x)=2x√24
f(x)=2x√(2*2*2*3)
f(x)=4x√6
df/dx=4√6
to show the graph is going up not down