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.
Answer:
h = 4.5 inches
Step-by-step explanation:
The area of a trapezoid is given by
A = 1/2 (b1+b2) h
We know A b1 and b2
20.25 = 1/2 (5+4)*h
20.25 = 9/2 h
Multiply each side by 2/9 to isolate h
2/9 * 20.25 = 2/9 *9/2 h
4.5 =h
Answer:
4.8 in
Step-by-step explanation:
feet to inch conversion is *12
2 * 12 = 24
then divide the scale (for every 1 in on the model there is 5 in on the actual, so divide the actual value by 5)
24/5 = 4.8
your answer is 4.8 in
hope this helps:)
To complete a square for ax²+bx+c, you first make a=1.
in this case, a is already 1
move c to the right side: x²+14x=-47
next, add (1/2 of b)² to both sides, in this case, b=14, half of 14 is 7, so x²+14x+ 7²=-47+7²
the left side is now a perfect square: (x+7)²=2
x+7=√2 or x+7=-√2
x=√2-7, or x=-2-√7
Answer: check out MATHPORTAL.com
Step-by-step explanation:
