We know that, as per a corollary of intermediate value theorem, if a function f(x) is continuous on a closed interval [a,b], and values of f(a) and f(b) have opposite signs, then the function f(x) is guaranteed to have a zero on the interval (a,b).
So, basically, we need to figure out two values of x, at which the values of the given cubic function have opposite signs.
Let us consider the interval [-2,1].
We have 
. Upon substituting the values x=-2 and x=1 one by one, we get:
We can see that signs of values of the function at x=-2 and x=1 are opposite, therefore, as per intermediate value theorem, the function is guaranteed to have a zero on the interval [-2,1]
D would be the correct answer
Answer:
I’m so sorry, I just had help on this problem earlier, I forgot how to do it, but the answer is 32
Step-by-step explanation:
Answer:
88m^2
Step-by-step explanation:
In order to find the lateral surface area of a cylinder, you must use this formula: 2πrh. In this problem we are given the diameter and height. Divide the diameter by 2 to get the radius and plug the radius and height into the formula. With our equation that we just created, we get the answer 87.96. 87.96 rounded to the nearest tenth is 88.
Let the speed of first car be x mph
the speed of the second one is (x+3) mph
Relative speed=x+x+3=(2x+3) mph
but
time=distance/speed
thus
3=(261)/(2x+3)
solving for x we get:
3(2x+3)=261
6x+9=261
6x=261-9
6x=252
hence:
x=42 mph
Thus the average speed of first car is 42 mph
Average speed of the second car is (42+3)=45 mph
