Find the y-intercept of the function 3x + 4y = 12
2 answers:
Answer:
( 0 , 3 )
Step-by-step explanation:
1. Way one of solving this problem
This equation is in standard form, one must get it to slope-intercept form to find the answer. In other words, one must solve for "y"
3x + 4y = 12
Manipulate the literal equation with inverse operations;
3x + 4y = 12
4y = 12 - 3x
/4 /4
y = - x + 4
2. Way two of solving this equation
The y-intercept is when this line intercepts the y-axis, so "x" is zero. Substitute "0" in for "x", and solve to find the y-intercept
3x + 4y = 12
x = 0
3 (0) + 4y = 12
0 + 4y = 12
Inverse operations;
4y = 12
/4 /4
y = 3
You might be interested in
Answer:
The area is growing at a rate of
Step-by-step explanation:
<em>Notice that this problem requires the use of implicit differentiation in related rates (some some calculus concepts to be understood), and not all middle school students cover such.</em>
We identify that the info given on the increasing rate of the circle's radius is 3 and we identify such as the following differential rate:
Our unknown is the rate at which the area (A) of the circle is growing under these circumstances,that is, we need to find .
So we look into a formula for the area (A) of a circle in terms of its radius (r), so as to have a way of connecting both quantities (A and r):
We now apply the derivative operator with respect to time () to this equation, and use chain rule as we find the quadratic form of the radius:
Now we replace the known values of the rate at which the radius is growing ( ), and also the value of the radius (r = 12 cm) at which we need to find he specific rate of change for the area :
which we can round to one decimal place as: