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.
3.625 as a fraction would be 3 5/8 or 29/8.
You would get that by converting 3.625 to 3 625/1000. You do that because there is a 3 before the decimal- (that is a whole #) and three digits after the decimal (that means it goes into the thousandths place, so the denominator is 1000), Then you take the numbers after the decimal and place it over the 1000. Then you would simply the 3 625/1000 by 125. and get 3 5/8 or as a mixed # 29/8. (Multiply the 8 and 3 to get 24 and add the numerator (5) to get 29. The denominator stays the same.
Hope this helps!
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4 fractions that are equal to 1/3
1*2/3*2 = 2/6
2/6
1*3/1*3 = 3/9
3/9
1*4/3*4 = 4/12
4/12
1*5/3*5 = 5/15
5/15
Answer:
3/7
Step-by-step explanation:
total cards 3+4 = 7
Not green = 7-4 = 3 cards
P ( not green )= not green cards / total = 3/7
The effective annual interest rate is:
i = (1 + 0.064/12)^12 - 1 = 0.066
In year 1: the interest is $613.80 (multiple $9300 by 0.066)
In year 2: the interest is $654.31 (add interest from year 1 to $9300 and multiply by 0.066)
In year 3: the interest is $656.98 (do the same as year 2)
In year 4: the interest is $657.16
The total interest is: $2582.25
The present worth of this amount is:
P = 2582.23 / (1 + 0.066)^4 = $1999.72
The answer is $1999.72.
