Answer:
y = -1/3x + 2
Step-by-step explanation:
The gradient of the given line is 3 because (y = mx +c where m is the gradient)
Therefore, to find the gradient of the perpendicular line (at 90 degrees), you need to find the negative reciprocal.
The negative reciprocal of 3 is -1/3 because imagine if 3 = 3/1, to get the reciprocal, you flip it, and to get the negative, you just flip the sign.
Now we know that Line M is y = -1/3x + c, we need to find the y-intercept.
To do this, just input the point (3,1) into y = -1/3x + c, to get c. This is because we know (3,1) is on the line from the question.
So it would be 1 = (-1/3 x 3) +c
Which would be 1 = -1 +c
And so c = 2
Put everything together and you get y = -1/3x + 2
The answer is A, look at the difference between 0 and 15 (15) and the difference between 5 and 10 (5) then divide them 5/15.
Use y = mx + b to determine the equation of the graph, then decided the inequality symbol.
m = +5/+6 = 
b = 5
y = x + 5
6y = 5x + 30
-30 = 5x - 6y ⇒ 5x - 6y = -30
Now let's look at the inequality symbol: The shaded area is below so it will be a less than symbol and it is a solid line so the equal sign is included.
Answer: 5x - 6y ≤ -30
Yay, implicit differnentiation
when you take the derivitive of y, you multiply it by dy/dx
example
dy/dx y^2=2y dy/dx
for x, the dy/dx dissapears
ok
so differnetiate and solve for dy/dx
3y² dy/dx-(y+x dy/dx)=0
expand
3y² dy/dx-y-x dy/dx=0
3y² dy/dx-x dy/dx=y
dy/dx (3y²-x)=y
dy/dx=y/(3y²-x)
so at (7,2)
x=7 and y=2
dy/dx=2/(3(2)²-7)
dy/dx=2/(3(4)-7)
dy/dx=2/(12-7)
dy/dx=2/5
answer is 2/5
Answer:
-1, 0, 0.1, 1
Step-by-step explanation:
-1 is a negative value, which makes it before 0
0.1 is less than 1 but more than 0
