3. f(-6) = 12+1 =13
f(-2) = 4+1 = 5
f(0) =1
Range {1,5,13}
4. f(-2) = (-2)^3+1 =-7
f(-1) = (-1)^2 +1 =0
f(3) = (3)^3 +1 = 28
Range = {-7,0,28}
5.the sequence is arithmetic
d= -11+19 = 8
an = a1 + d(n-1)
an = -19 +8(n-1)
6.l =w+5
a =l*w
a(w) =(w+5) * w
a(w)= w^2 +5w
f(w) = w^2 +5w
f(8) = 8^2 +5(8)
f(8) = 64 +40
f(8) =104 in^2
<h2>Solution:.</h2>
Let the ceilings be <em>a</em><em> </em><em>&</em><em> </em><em>b</em>
and the distance from one corner of the ceiling to the opposite be <em>c</em>
<em>then </em><em>using</em><em> </em><em>Pythagoras</em><em> theorem</em>
hence ,c .°. the distance from one corner of the ceiling to the opposite is<em> </em><em>2</em><em>0</em>
The points you found are the vertices of the feasible region. I agree with the first three points you got. However, the last point should be (25/11, 35/11). This point is at the of the intersection of the two lines 8x-y = 15 and 3x+y = 10
So the four vertex points are:
(1,9)
(1,7)
(3,9)
(25/11, 35/11)
Plug each of those points, one at a time, into the objective function z = 7x+2y. The goal is to find the largest value of z
------------------
Plug in (x,y) = (1,9)
z = 7x+2y
z = 7(1)+2(9)
z = 7+18
z = 25
We'll use this value later.
So let's call it A. Let A = 25
Plug in (x,y) = (1,7)
z = 7x+2y
z = 7(1)+2(7)
z = 7+14
z = 21
Call this value B = 21 so we can refer to it later
Plug in (x,y) = (3,9)
z = 7x+2y
z = 7(3)+2(9)
z = 21+18
z = 39
Let C = 39 so we can use it later
Finally, plug in (x,y) = (25/11, 35/11)
z = 7x+2y
z = 7(25/11)+2(35/11)
z = 175/11 + 70/11
z = 245/11
z = 22.2727 which is approximate
Let D = 22.2727
------------------
In summary, we found
A = 25
B = 21
C = 39
D = 22.2727
The value C = 39 is the largest of the four results. This value corresponded to (x,y) = (3,9)
Therefore the max value of z is z = 39 and it happens when (x,y) = (3,9)
------------------
Final Answer: 39
Known :
f(x) = -3x - 5
g(x) = 4x - 2
Asked :
(f+g)(x) = ...?
Answer :
(f+g)(x) = (-3x - 5) + (4x - 2)
= (-3x + 4x) + (-5 - 2)
= x + (-7)
= <u>x </u><u>-</u><u> </u><u>7</u>
So, the value of (f+g)(x) is x - 7
<em>Hope </em><em>it </em><em>helpful </em><em>and </em><em>useful </em><em>:</em><em>)</em>
