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:
9/4
Step-by-step explanation:
First multiply denominator by the whole
That is: 4 x 2 = 8
Secondly, whatever answer you got add it to the numerator
That is: 8 + 1 = 9
Lastly, whatever answer you got, take that as the numerator and the denominator remains the same
That is: 9/4
Finally, this is your improper fraction of the number provided!
Hope it helps!!!
the answer is D the last one,
the reason is just that any negative number is automatically smaller than a positive number. so -2.8 is smaller than even the smallest decimal possible as long as that decimal is positive. 1.4 is actually about 3 time more that -2.8
(both are still freezing cold)
First you need to figure out the cost of the skateboard after the discount but before the sales tax. By doing 100%-12% you figure out how much of the original cost you are paying 88%. Then you multiply 79.99(original cost) and 88%(how much you pay) which gets you 70.39. Then you figure out the sales tax by multiplying 70.39 by 6.75% which gives you 4.75(the sales tax). And the last thing you need to do is add the cost before tax(70.39) and the tax(4.75).
The skateboard costs $75.14
Answer:
N is M reflected across the x-axis; only the signs of the x-coordinates of M and N are different.
Step-by-step explanation:
The y-axis is vertical, and the x-axis is horizontal. If a point, or image, is reflected over the x-axis, in this case M and N, then the signs of the y-coordinates do not change, and instead the coordinates of the x-axis change.
