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Anna007 [38]
3 years ago
6

I need details please

Mathematics
1 answer:
m_a_m_a [10]3 years ago
3 0
Ok, first you need to read a - g and mark down the information you know. Also, this continuous function can look pretty much like anything long as it has the a - g constraints/rule. 

A) We know the domain(x values) is between -10 to infinity
(-10,-9,-8,-7,-6,-5,-4,-3-,2,-1,0,1,2,3,4,5,6,7,8,9,10, to ---------> infinity)
B) We know the range(y values) is between -6 to infinity
(-6,-5,-4,-3-,2,-1,01,2,3,4,5,6,7,8,9,10, to ---------> infinity) 

C) Next we know f(0) = f(4) = 0
So we know when x = 0  that f(0) = 0 or we can say  y = 0. We also know when f(4) = 0 so when x = 4 y = 0. So we have two points (0,0) and (4,0) that our function will be on so plot the two points (0,0) (4,0)

D) It tells us that f(x) (y) is increasing between the x values (-10,-6)  or (-2,2) or (4, to infinity)

E) It tells us that f(x) (y) is decreasing between the x values (-6,-2) or between (2,4)

F) Tells us that f(x) (y) is greater than or equal to between the x values of [-8,-4] or between the x values [0, to infinity) so this lets us know our drawing is going to be above or equal to 0 when we are in the values [-8,-4] or [0, to infinity)

G) Tells us that f(x) (y) is less than 0 when the function / drawing is between the x values of (-10, -8) or (-4,0)  

The picture is what the function could look like. It can be different but needs to following the rules that are given 




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Answer:

  49 cm²/s

Step-by-step explanation:

The problem statement tells you what to do.

Write an equation relating A, b, h:

  A = bh . . . . . . the equation for the area of a rectangle

Differentiate with respect to t:

  dA/dt = (db/dt)h + b(dh/dt) . . . . . . . product rule

To find the rate of change after 18 seconds, you need to know the dimensions b and h after 18 seconds. Since each dimension was increasing at the rate of 1 cm/s, it is 18 cm more than it was at the beginning:

At 18 seconds,

  b = 6 cm + 18 cm = 24 cm;

  h = 7 cm + 18 cm = 25 cm.

Of course, db/dt = dh/dt = 1 cm/s. Then the rate of change of area is ...

  dA/dt = (1 cm/s)(25 cm) + (24 cm)(1 cm/s)

  dA/dt = 49 cm²/s

_____

You could write a formula for the area as a function of time and differentiate that:

  A = (6 +t)(7 +t) = 42 + 13t + t²

Then the derivative is ...

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7 0
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