To find the maximum or minimum value of a function, we can find the derivative of the function, set it equal to 0, and solve for the critical points.
H'(t) = -32t + 64
Now find the critical numbers:
-32t + 64 = 0
-32t = -64
t = 2 seconds
Since H(t) has a negative leading coefficient, we know that it opens downward. This means that the critical point is a maximum value rather than a minimum. If we weren't sure, we could check by plugging in a value for t slightly less and slighter greater than t=2 into H'(t):
H'(1) = 32
H'(3) = -32
As you can see, the rate of change of the object's height goes from increasing to decreasing, meaning the critical point at t=2 is a maximum.
To find the height, plug t=2 into H(t):
H(2) = -16(2)^2 +64(2) + 30 = 94
The answer is 94 ft at 2 sec.
Answer:
x=√2, x=-√2, x= 3 and x=-3
Step-by-step explanation:
We need to solve the equation x^4 - 11x^2+18=0
We can replace x^4 = u^2 and x^2 = u
So, the equation will become
u^2 -11u+18 = 0
Factorizing the above equation:
u^2 -9u-2u+18 =0
u(u-9)-2(u-9)=0
(u-2)(u-9)=0
u=2, u=9
As, u = x^2, Putting back the value:
x^2 =2 , x^2 =9
taking square roots:
√x^2 =√2 ,√x^2=√9
x=±√2 , x = ±3
so, x=√2, x=-√2, x= 3 and x=-3
Answer:
40/3; 13.3333333333333
Step-by-step explanation:
The volume of the cone is:
(1/3)(pi)(r^2)(h) =
(1/3)(pi)(10^2)(10) =
1000pi/3
The volume of the cylinder is:
(pi)(r^2)(h) =
(pi)(5^2)(h) =
25pi(h) = 1000pi/3 -->
pi(h) = 40pi/3 -->
h = 40/3
Answer:
Step-by-step explanation:
so i think if you land on heads it is more like a 70% chance of getting heads but then again it could be a 30% chance that you land on tails so if you land on head you get the Alsatian and tails you get a bulldog i hope you get the correct answer good luck
