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.
Answer:
402.12 + 804.24 = 1206.36
Answer:
The second option
Step-by-step explanation:
To solve this, you should convert both rates to equations, with y being the total fare, and x being the number of miles. The rates of both use the format y=mx+b (where m is the amount per mile and b is the flat rate, or original rate).
By subbing in the values for m and b, you get y=2x+4 for A and y=3x+5 for B. This is the second option.
**This question involves writing linear equations, which you may wish to revise. I'm always happy to help!
0.08 is 10 times greater than 0.008, becase 0.008 · 10 = 0.08
