Combine like terms:
<span>
So you would choose A confidently
</span>
<span>
So you would choose A confidently
</span>
a tank holds 5000 gallons of water, which drains from the bottom of the tank in half an hour. The values in the table show the v
olume V of water remaining in the tank (in gallon) after t minutes.a) If P is the point (15,1275) on the graph of V, find the slopes of hte secant lines PQ when Q is the point on the graph with the following values.(5, 3410) -427/2(10, 2210) -187(20, 550) -145(25, 145) -113(30, 0) -85B) estimate the slope of hte tangent line at P by averaging the slopes of two adjacent secant lines. (Round your answer to one decimal places).
1 answer:
Answer:
- secant slopes: -213.5, -187, -145, -113, -85
- tangent slope: -166
Step-by-step explanation:
A) the slope values you have put in your problem statement are correct. As you know, they are computed from ...
(change in gallons)/(change in time)
where the reference point for changes is P. Using the first listed point Q as an example, the secant slope is ...
(3410 -1275)/(5 -15) = 2135/-10 = -213.5 . . . . gallons per minute
__
B) The average of the secant slopes for points Q adjacent to P is ...
(-187 +(-145))/2 = -332/2 = -166 . . . . gallons per minute
The tangent slope at point P is estimated at -166 gpm.
You might be interested in
The specified function's vertex form is
If a quadratic equation is written in the form
then it is called to be in vertex form. It is called so because when you plot this equation's graph, you will see vertex point(peak point) is on (h,k)
<h3>What is a perfect square polynomial?</h3>If a polynomial p(x) can be written as:
where f(x) is also a polynomial, then p(x) is called as perfect square polynomial
For the considered case, the polynomial specified is;
- Case 1: Converting to vertex form
Thus, the vertex form of the considered polynomial is
- Case 2: Converting to standard form
Standard form of a quadratic polynomial is
Thus, we get: the considered polynomial in standard form as:
- Case 3: Factoring the first two terms of polynomial
- Case 4: Forming a perfect square trinomial
The considered polynomial has only two terms, therefore, its not a trinomial.
Thus, the specified function's vertex form is
Learn more about vertex form of a quadratic equation here: