Answer:
f(t) = 4 - 3t + 2t^2
Step-by-step explanation:
Given:
f(t) = a + bt + ct^2
Differentiate w.r.t. "t"
f'(t) = b + 2ct
1) f(1) = 3
a + b +c = 3...........1)
2) f(2) = 6
a + 2b + 4c = 6.........2)
3) f'(1) = 1
b + 2c = 1 ...............3)
Solving above three simultaneous equations:
a = 4
b = -3
c = 2
Therefore equation becomes:
f(t) = 4 + (-3)t + (2)t^2
Answer: There are 20 goats and 18 chikens.
Step-by-step explanation:
Hi, to answer this question we have to write a system of equations:
If the number of chickens is represented by C, and the number of goats is G.
Total of Animals equation:
a)C+ G = 38
Total of legs equation (since chickens have 2 legs and goats have 4 ):
b)2C + 4 G =116
If we multiply a) by 2 and subtract a) from b).
<em>2C + 4 G =116
</em>
<em>-
</em>
<em>2C + 2 G =76
</em>
<em>_________
</em>
<em>2G = 40
</em>
G = 40/2
G= 20
Replacing the value of G on any equation:
a) C+ (20) =38
C =38-20
C=18
There are 20 goats and 18 chickens.
Answer:
Alrighty! So this is what we know:
Slope (m) = (-4)
Co-ordinate (0,3)
Co-ordinate 2 (6,t)
t = ?
Let's find our equation...
y=mx+b <-- just plug what we know in...
3=(-4)0+b
3=0+b
b=3
We just found b! woohoo
Now what is t? t is a value we need to know WHICH IS the y value of a co-ordinate that corresponds to when x is 6, as we know a co-ordinate is expressed as --> (x value, y value).
SO-
t=y
plug it in our equation...
y=mx+b
t=(-4)x+3
t=(-4)(6)+3
t=(-24)+3
t=(-21)
SOOOOOOOO WE HAVE OUR T!! just write a therefore statement like "therefore the value of t is -21." and you're set! hope this helped, any questions? ask in the comment section. :)
Step-by-step explanation:
