Answer:
hmax = 194 ft
The maximum height is 194 ft
Step-by-step explanation:
According to the given equation for the model of the vertical motion. The height at any point in time can be written as;
h(t) = -16t^2 + v0t + h0 .......1
Where;
h(t) = height at time t
t = time
v0 = initial velocity = 96 ft/s
h0 = initial height = 50 ft
To determine the maximum height we need to differentiate the equation 1 to find the time at which it reaches maximum height;
At the highest point/height h' = dh/dt = 0
h'(t) = -32t +v0 = 0
-32t + v0 = 0
t = v0/32
t = 96/32
t = 3 s
At t=3 it is at maximum height.
The maximum height can be derived from equation 1;
Substituting the values of t,v0,h0 into equation 1;
h(t) = -16t^2 + v0t + h0 .......1
hmax = -16(3)^2 + 96(3) + 50 = 194 ft
hmax = 194 ft
The maximum height is 194 ft
<h3>
Answer: C) 6</h3>
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Explanation:
The weird looking E symbol is the greek uppercase letter sigma. It refers to a sum.
It tells us to add up terms in the form (-1)^n*(3n+2) where n is an integer ranging from n = 1 to n = 4.
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If n = 1, then we have
(-1)^n*(3n+2) = (-1)^1*(3*1+2) = -5
Let A = -5 as we'll use it later.
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If n = 2, then
(-1)^n*(3n+2) = (-1)^2*(3*2+2) = 8
Let B = 8 since we'll use this later as well
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If n = 3, then
(-1)^n*(3n+2) = (-1)^3*(3*3+2) = -11
Let C = -11
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If n = 4, then
(-1)^n*(3n+2) = (-1)^4*(3*4+2) = 14
Let D = 14.
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We'll add up the values of A,B,C,D to get the final answer
A+B+C+D = -5+8+(-11)+14 = 6
This means that

Answer: -16
Step-by-step explanation:
49 would be the result of -7 squared. Due to the fact it is negative, it would cancel out to be positive.
For the numerator, 49-1 is equivalent to 48.
48/x+4
-7+4 = -3
48/-3
= -16
It is given in the question that
A rectangular box has a square base with an edge length of x cm and a height of h cm. The volume of the box is given by

And the edge length of the base is 12 cm, the edge length of the base is decreasing at a rate of 2 cm/min, the height of the box is 6 cm, and the height is increasing at a rate of 1 cm/min.
Here we differentiate V with respect to t, and we use product rule, that is

Substituting the given values , we will get
[/tex]

So at that moment, the volume is decreasing at the rate of
