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Nitella [24]
3 years ago
11

7x + 9 = 6x - 5 x = -14 x = -4 x = 4 x = 14

Mathematics
1 answer:
TiliK225 [7]3 years ago
6 0

Answer:  x = -14


Step-by-step explanation:

7x + 9 = 6x - 5

-7x        - 7x

_____________

9 = -x -5

+5      +5

______________

14 = -x

__   ___

-1       -1


-14 = x

hope this helps! ❤ from peachimin

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Step-by-step explanation:

Though Process:

  • The punch glass (call it bowl to have a shape in mind) is in the shape of a hemisphere
  • the radius r=5cm
  • Punch is being poured into the bowl
  • The height at which the punch is increasing in the bowl is \frac{dh}{dt} = 1.5
  • the exposed area is a circle, (since the bowl is a hemisphere)
  • the radius of this circle can be written as 'a'
  • what is being asked is the rate of change of the exposed area when the height h = 2 cm
  • the rate of change of exposed area can be written as \frac{dA}{dt}.
  • since the exposed area is changing with respect to the height of punch. We can use the chain rule: \frac{dA}{dt} = \frac{dA}{dh} . \frac{dh}{dt}
  • and since A = \pi a^2 the chain rule above can simplified to \frac{da}{dt} = \frac{da}{dh} . \frac{dh}{dt} -- we can call this Eq(1)

Solution:

the area of the exposed circle is

A =\pi a^2

the rate of change of this area can be, (using chain rule)

\frac{dA}{dt} = 2 \pi a \frac{da}{dt} we can call this Eq(2)

what we are really concerned about is how a changes as the punch is being poured into the bowl i.e \frac{da}{dh}

So we need another formula: Using the property of hemispheres and pythagoras theorem, we can use:

r = \frac{a^2 + h^2}{2h}

and rearrage the formula so that a is the subject:

a^2 = 2rh - h^2

now we can derivate a with respect to h to get \frac{da}{dh}

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simplify

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we can put this in Eq(1) in place of \frac{da}{dh}

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and since we know \frac{dh}{dt} = 1.5

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and now we use substitute this \frac{da}{dt}. in Eq(2)

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simplify,

\frac{dA}{dt} = 3 \pi (r-h)

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r = 5cm

h = 2cm from the question

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