course MTh 271 10/04, 1515 assignment #007007. `query 7
......!!!!!!!!...................................
23:24:08 **** Query class notes #07 **** Explain how we obtain the tangent line to a y = k x^3 function at a point on its graph, and explain why this tangent line gives a good approximation to the function near that point.
......!!!!!!!!...................................
RESPONSE --> After selecting a point on the graph, a line is drawn through this point, tangential to the curve. This line stays close to the curve for a while. So, by finding the slope of this line, we can find a decent approximation of the values close to this point. confidence rating: 2 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ `questionNumber 70000 Query class notes #08 **** What equation do we get from the statement 'the rate of temperature change is proportional to the difference between the temperature and the 20 degree room temperature'? What sort of graph do we get from this equation and why?
......!!!!!!!!...................................
RESPONSE --> 'dT/'dt=k(T -Troom) 'dT/'dt=k(T -20) The graph should be linear. confidence rating: 1 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
.................................................
......!!!!!!!!...................................
22:44:57 `questionNumber 70000 1.2.10 (was 1.2.08 graph matching y = `sqrt(9-x^2) Describe the graph that matches this function and explain how you know this is the graph
......!!!!!!!!...................................
RESPONSE --> The graph matching this equation is F. We know that this is the appropriate graph because if both sides of the equation are squared, the resulting equation is that found of a graphed circle. confidence rating: 1 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
.................................................
......!!!!!!!!...................................
22:45:39 `questionNumber 70000 Extra problem: (was problem 1.2.10) If air freshener initially contains 30 grams, what is the formula for the number of grams present if 12% of the amount present evaporate per day?
......!!!!!!!!...................................
RESPONSE --> P(t)=30(.88)^t confidence rating: 2 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
.................................................
......!!!!!!!!...................................
23:06:38 `questionNumber 70000 1.2.32 (was 1.2.28 graph of y=`sqrt(x+1) Describe your graph, including coordinates of intercepts, whether increasing or decreasing (if both, where it does each), and concavity.
......!!!!!!!!...................................
RESPONSE --> y=sqrt(x+1) x-intercept (-1,0) Other points: (0,sqrt(1)), (1, sqrt(2)), (2, sqrt(3)), (3,2), (4, sqrt(5))... Graph begins a (-1,0) and is a curving line with concavity facing the x-axis. The graph increases at a decreasing rate. confidence rating: 2 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
.................................................
......!!!!!!!!...................................
23:16:10 `questionNumber 70000 1.2.56 (was 1.2.52 pts of intersection of x+y=7 and 3x-2y=11 What are the point(s) of intersection?
......!!!!!!!!...................................
RESPONSE --> x + y=7 y=7 - x 3x -2y =11 -2y=-3x + 11 y=(3/2)x - (11/2) 7-x = (3/2)x - (11/2) -x=(3/2)x - (11/2) - (14/2) -x=(3/2)x -(25/2) 0=(5/2)x - (25/2) (25/2)=(5/2)x (25/2)*(2/5)=x 5=x y=7 - 5 y=2 (5,2) y=(3/2)(5) - (11/2) y=(15/2) - (11/2) y=4/2 y=2 (5,2) One point of intersection at (5,2). confidence rating: 2 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
.................................................
......!!!!!!!!...................................
23:17:41 `questionNumber 70000 **** Query Add comments on any surprises or insights you experienced as a result of this assignment.
......!!!!!!!!...................................
RESPONSE --> I was surprised to learn that the equation for graphing a circle was so simple. Somehow, I imagined that it would be much more complex to get a single line to connect in such a manner. ------------------------------------------------ Self-critique Rating:ent: 2
................................................."