<p>Hey there! I am really stumped on page 424 #16 could any one help? </p>
<p>n(t)=t^2/2-20t+k </p>
<p>There was a 100-day period when the number of bees in a certain hive could be modeled by the function n above. In the function, k is a constant and n(t) represents the number of bees on day number t for 0<=t<=99. On what number day was the number of bees in the hive the same as it was on day number 10?</p>
<p>(a) 20
(b) 30
(c) 40
(d) 50
(e) 60</p>
<p>Now I plugged in the numbers and followed the function but this is the last question of a sequence and I don't know if it is supposed to be harder than that... ? Really appreciate any help! Thanks! ^^</p>
<p>n(t) is a quadratic, so it will be symmetric about the vertical line containing the vertex. The x-coordinate of the vertex is -b/2a = -(-20)/(2*1/2) = 20, so n(t) is symmetric about the line x = 20.</p>
<p>Therefore, by symmetry, n(10) = n(30), so the answer is B) 30.</p>
<hr>
<p>An alternative solution would be to simply solve n(t) = n(10).</p>
<p>Thank you so much! I will work this out! ^^ do you also happen to know this one? </p>
<p>Pp.519 #20</p>
<p>At a beach, a rectangular swimming area with dimensions x and y meters and a total area of 4,000 square meters is marked off on three sides with rope, as shown above (no pic sry), and bounded on the fourth side by the beach. Additionally, rope is used to divide the area into three smaller rectangular sections. In terms of y, what is the total length, in meters, of the rope that is needed both to bound the three sides of the area and to divide it into sections?</p>
<p>(a) y+4,000/y
(b) y+16,000/y
(c) y+16,000/3y
(d) 3y+8,000/3y
(e) 3y+16,000/3y</p>
<p>Sorry, I’ll need a pic or some description of the diagram…I don’t have the blue book.</p>
<p>xy=4000
x= (4000/y)</p>
<p>L = 4x + y
= 4(4000/y) + y
= (16000/y) + y</p>
<p>(Actually one of rspence’s second way) Alternatively for #16–</p>
<ol>
<li>Plug in the numbers and simplify.
(10^2/2)-20(10)+k=-150+k</li>
<li>The answer x must also equal -150+k because that’s the number of bees in the hive and the number of bees in the hive in days 10 and x must be equal.
((t^2)/2)-20t+k=-150+k</li>
<li>Subtract k from both sides.
((t^2)/2)-20t=-150</li>
<li>Multiply through by 2.
t^2-40t+300=0</li>
<li>Factor.
(t-10)(t-30)=0</li>
<li>The roots are:
t=10, t=30</li>
<li>Therefore, the answer is:
(b) 30.</li>
</ol>
<p>Celesterobert is correct. I can’t really describe it any other way.</p>