Answer:
1/5
Step-by-step explanation:
first write the formula of average speed
- 2) then equate the values of given question
- 3) you will find the solution
<span> first, write the equation of the parabola in the required form: </span>
<span>(y - k) = a·(x - h)² </span>
<span>Here, (h, k) is given as (-1, -16). </span>
<span>So you have: </span>
<span>(y + 16) = a · (x + 1)² </span>
<span>Unfortunately, a is not given. However, you do know one additional point on the parabola: (0, -15): </span>
<span>-15 + 16 = a· (0 + 1)² </span>
<span>.·. a = 1 </span>
<span>.·. the equation of the parabola in vertex form is </span>
<span>y + 16 = (x + 1)² </span>
<span>The x-intercepts are the values of x that make y = 0. So, let y = 0: </span>
<span>0 + 16 = (x + 1)² </span>
<span>16 = (x + 1)² </span>
<span>We are trying to solve for x, so take the square root of both sides - but be CAREFUL! </span>
<span>± 4 = x + 1 ...... remember both the positive and negative roots of 16...... </span>
<span>Solving for x: </span>
<span>x = -1 + 4, x = -1 - 4 </span>
<span>x = 3, x = -5. </span>
<span>Or, if you prefer, (3, 0), (-5, 0). </span>
(5,41)
(-5,23)
(-10,14)
(-15,5)
Answer: dr/dt = 9/(24pi) cm per minute
9/(24pi) is approximately equal to 0.119366
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Work Shown:
Given info
dS/dt = 18 cm^2/min is the rate of change of the surface area
r = 6 cm is the radius, from the fact that the diameter is 12 cm
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Use the surface area equation given, apply the derivative, plug in the given values and then isolate dr/dt which represents the rate of change for the radius
S = 4*pi*r^2
dS/dt = 2*4*pi*r*dr/dt
dS/dt = 8*pi*r*dr/dt
18 = 8*pi*6*dr/dt
18 = 48*pi*dr/dt
48pi*dr/dt = 18
dr/dt = 18/(48pi)
dr/dt = (9*2)/(24*2pi)
dr/dt = 9/(24pi)
The units are cm per minute, which can be written as cm/min.
You have to know how long it takes them both to solve the puzzles. ;)
