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.
You have to start with the left triangle and find the side lengths. Since it is a 45-45-90, both sides are the same. Rule for this is hyp= sqrt2 * leg
Since hyp = 6sqrt2, the leg is 6.
The leg is also the hypotenuse of the triangle on the right side.
x is the side across from the hypotenuse and it is the short leg so x = (1/2)6
x = 3
Answer:
0.6 liters
Step-by-step explanation:
3 liters divided amongst 5 people comes to 0.6 liters per person. there are approximately 33.8 ounces in a liter so in ounces, everyone would get approximately 56.35 ounces of soda.
for a picture you could draw a cup with soda in it and label it to show the amount
Answer:
6 km
Step-by-step explanation:
1000 meters equals 1 kilometer
4 sqrt (32) + 6 sqrt (50)
4 sqrt (16*2) + 6 sqrt (2*25)
4 sqrt (16)*sqrt(2) + 6 sqrt (2)*sqrt(25)
4 *4*sqrt(2)+6sqrt(2)*5
16sqrt(2)+30sqrt(2)
46sqrt(2)
