Add three to both sides: 4|8n+10|=56
divide by 4: |8n+10|=14
so 8n+10 could be 14 or -14
if it's 14, n=0.5
if it's -14, n=-3.5
Your picture has several issues.
- x is not defined. It appears to be the number of apartments rented.
- R(x) is defined two different ways. The first way, it looks like it is the revenue from a single apartment. The second way, it looks like it is the revenue from the entire apartment complex.
- The derivative is in error. It should be -20x +2000. In any event, this is not the derivative you want. You're not trying to maximize revenue; you're trying to maximize profit.
- It might be useful to write an equation for profit: P(x) = R(x) -200x = -10x² +1800x. Then when you go to maximize it, your derivative will be P'(x) = 0 = -20x +1800 ⇒ x = 90.
Your answer is correct, but the path you followed to get there has a few potholes.
5 - 17
x is adding multiples of 3 to get y
example: 2+3=5, 3+6=9 4+9=13, 5+12=17 and so on.
Answer: 72
Plan A = 30 +0.15x
Plan B = 16 +0.20x
30+0.15x = 16+0.20x
subtract 16 from each side
14 +0.15x = 0.20x
subtract 0.15x from each side
14=0.05x
x = 14/0.05 = 280 minutes
280*0.15 = 42 +30 = $72
280 * 0.20 = 56 +16 = 72
280 minutes and cost $72 each
Step-by-step explanation:
Answer:
Step-by-step explanation:
A) From the order of the exercise we already know that the intersection points lies on the Y-axis, so its coordinates are P(0;y;0). In order to find it, we only need to substitute the equation 4x+4z=0 into the equation 4x+3y+4z=1. Then,
1=4x+3y+4z = 3y + (4x+4z)= 3y+0.
From the expression above it is easy to obtain that y=1/3, and the intersection point is P(0;1/3;0).
B) To obtain the parallel vector to both planes we use the cross product of the normal vector of the planes.
![\left[\begin{array}{ccc}i&j&k\\4&3&4\\4&0&4\end{array}\right] = 12i-0j+12k](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Di%26j%26k%5C%5C4%263%264%5C%5C4%260%264%5Cend%7Barray%7D%5Cright%5D%20%3D%2012i-0j%2B12k)
As we want a unit vector, we must calculate the modulus of u:
.
Thus, the wanted vector is 
. Therefore,
.
C) In order to obtain the vector equation of the intersection line of both planes, we just need to put together the above results.
where 
is a real number.
