First plug in -4 for g to get 3(-4)-1. 3(-4) equals -12, and -12-1 equals -13.
Answer:
31
Step-by-step explanation:
Increases by 7 each time
Answer:
The distance between (-3, 2) and (0,3) is √10.
Step-by-step explanation:
As we go from (-3,2) to (0,3), x increases by 3 and y increases by 1.
Think of a triangle with base 3 and height 1. Use the Pythagorean Theorem to find the length of the hypotenuse, which represents the distance between the points (-3, 2) and (0, 3):
distance = √(3² + 1²) = √10
The distance between (-3, 2) and (0,3) is √10.
Answer:
True, see proof below.
Step-by-step explanation:
Remember two theorems about continuity:
- If f is differentiable at the point p, then f is continuous at p. This also applies to intervals instead of points.
- (Bolzano) If f is continuous in an interval [a,b] and there exists x,y∈[a,b] such that f(x)<0<f(y), then there exists some c∈[a,b] such that f(c)=0.
If f is differentiable in [0,4], then f is continuous in [0,4] (by 1). Now, f(0)=-1<0 and f(4)=3>0. Thus, we have the inequality f(0)<0<f(4). By Bolzano's theorem, there exists some c∈[0,4] such that f(c)=0.
