Answer:
8.5
Step-by-step explanation:
Answer:

Step-by-step explanation:
We need at least two points to write the equation of a straight line.
The recursive formula that Elijah wrote is:


When we substitute n=0, we get:



The points (0,30) and (1,37) lies on this line.
The equation of this line is of the form:

where b =30 is the y-intercept and m=7 is the slope.
We plug in these values to get:

Note that the slope of the line is equal to the common difference of the Arithmetic Sequence.
You could also use the two points to find the slope:

Answer:
Hello
Step-by-step explanation:
There's a catch here, and I don't really want to go into full detail. Because of
this catch, I think it would be unusually tough to write a simple equation for this
situation. If you wouldn't mind, let's just list it instead:
<u>After</u> . . <u>water added</u> . . <u>total in pool</u>
7 min . . . 14 gallons . . . 14 gallons
1 more . . 1 gallon . . . . . 15 gallons
7 more . . 14 gallons . . . 29 gallons
1 more . . 1 gallon . . . . . 30 gallons
5 more . . 10 gallons . . . 40 gallons, the pool is full
Add up all the minutes: <u>21 minutes</u>
Answer:
a)∇f = 2y + 2x + 18z
b)
=108
Step-by-step explanation:
Given:
f (x,y,z ) = 
The curve C :

where 0 ≤ t ≤ 1
Required:
(a) F = ∇f =? (F is a vector here)
(b)
=?
Solution
First we will find the directional derivative F = ∇f
for that , we will use the formula :
∇f = 
Fx= δf/δx = δ/δx
= 2z i
Fy= δf/δy=δ/δy (2xy)j = 2x j
Fz= δf/δz=δ/δz
= 18z k
∇f = (2z) i .i + (2x) j.j + (18z) k.k
∇f = 2z + 2x + 18z
<em>For part b):</em>
<em>we will use line integral formula:</em>
to calculate dr, we will need the curve C:
r = x(t)+y(t)+z(t)
r=




= 
= 
put values of y, x and z
= 
=
=
(Note : f(1)-f(0))
=2(1)+162(1)+2(0)+162(0)-56
= 2+162 -56
=108