Answer:
a) e-0.03x(0.3-0.009x)
b) 33 hrs 20 min
c) 17.182
Step-by-step explanation:
Taking derivative of the above equation would give us the rate for change in donations :
hence
f'(x) = d/dx (0.3xe-0.03x)
using product rule of derivation where (uv)' = u'v +v'u
hence
f'(x) = (e-0.03x)d/dx(0.3x) + 0.3x*d/dx(e-0.03x)
= 0.3e-0.03x + 0.3x(-0.03)(e-0.03x)
f'(x) =0.3e-0.03x -0.009xe-0.03x
hence
a) rate of change in donations = e-0.03x(0.3-0.009x) taking exponent common
b) f'(x) = 0 according to statement
hence 0 = e-0.03x(0.3-0.009x)
0 = 0.3 - 0.009 x
which gives x = 33.33 hrs i.e after 33 hrs and 20 minutes rate of change of donations is 0.
c) donation level at the time is given by
f(x) = 0.3xe-0.03x
f(33.33) = 0.3 (33.33)e-0.03(33.33)
= 17.182
That is 17.182 thousand donations were made at that time.
Following numbers are greater than or equal to -12:
-12
-11
-10
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
And so on..................
(Brainiest please!!!!!)
Perpendicular means that it has a slope that is the reciprocal of the original, and parallel means that the slopes are the same.
Given:
The base is a rectangle of dimension 7 cm×6 cm.
The length of each diagonal side = 10 cm
To find the height of MT.
Formula
By Pythagoras theorem we get,
where, h be the hypotenuse
b be the base and
l be the height.
Now, in this diagram,
The perpendicular distance of M from BC = 3 cm
Slant height = 10 cm
Taking, b = 3 and h = 10 we get,
or, 
or, 
or, 
Hence,
The height of MT is 9.5 cm.
