Answer:
The proof is detailed below.
Step-by-step explanation:
We will first prove that if H(x) is a differentiable function in [a,b] such that H'(x)=0 for all x∈[a, b] then H is constant. For this, take, x,y∈[a, b] with x<y. By the Mean Value Theorem, there exists some c∈(x,y) such that H(y)-H(x)=H'(c)(x-y). But H'(c)=0, thus H(y)-H(x)=0, that is, H(x)=H(y). Then H is a constant function, as it takes the same value in any two different points x,y.
Now for this exercise, consider H(x)=F(x)-G(x). Using differentiation rules, we have that H'(x)=(F-G)(x)'=F'(x)-G'(x)=0. Applying the previous result, F-G is a constant function, that is, there exists some constant C such that (F-G)(x)=C.
If c=12, then c=2*pi*r has to equal 12 as well
Simply set 2*pi*r=12 and solve for R
pi*r=6
r= approximately 1.91
<span>7,434 is divisible by 6 so this is true
</span>
Answer:
Y=4x+4
Step-by-step explanation:
if it grows 4 inches each year that means it's the slope
and 4 feet tall model is the y intercept cuz its what you begin with
Answer:
41.04 g/L
Step-by-step explanation:
The relationship is modeled by the following function:
S(t) = 500*e^(-0.25*t)
where t is time elapsed after the dilution begins (in hours) and S(t) the concentration of salt in the tank (in g/L)
Replacing with t = 10
S(t) = 500*e^(-0.25*10)
S(t) = 41.04 g/L
