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natulia [17]
3 years ago
15

Given g(x) = 2x + 4, solve for x when g(x) = -8

Mathematics
1 answer:
Mnenie [13.5K]3 years ago
4 0

Answer:

The value of  x = -6

Step-by-step explanation:

<u><em>Step(i):-</em></u>

Given that g(x) = 2 x + 4  and g (x ) = -8

⇒    Equating  

               2 x +4 = - 8

  Subtracting '4' on both sides, we get

              2 x + 4 - 4 = -8 -4

        ⇒  2 x + 0 = -12

       ⇒   2 x  = -12

<u><em>Step(ii):-</em></u>

Dividing '2' on both sides, we get

             x = -6

The value of  x = -6

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a spherical balloon is deflated at a rate of 256pi/3 cm^3/sec. at what rate is the radius of the balloon changing when the radiu
Hunter-Best [27]
What you need to look for is \frac { dr }{ dt } when r=8.

Now:

Volume\quad of\quad a\quad sphere:\\ \\ V=\frac { 4 }{ 3 } \pi { r }^{ 3 }

\therefore \quad \frac { dV }{ dr } =\frac { 4 }{ 3 } \pi \cdot 3{ r }^{ 2 }=4\pi { r }^{ 2 }\\ \\ \therefore \quad \frac { dr }{ dV } =\frac { 1 }{ \frac { dV }{ dr }  } =\frac { 1 }{ 4\pi { r }^{ 2 } }

And:\\ \\ \frac { dV }{ dt } =-\frac { 256\pi  }{ 3 } \\ \\ Therefore:\\ \\ \frac { dr }{ dt } =\frac { dr }{ dV } \cdot \frac { dV }{ dt }

\\ \\ =\frac { 1 }{ 4\pi { r }^{ 2 } } \cdot -\frac { 256\pi  }{ 3 } \\ \\ =-\frac { 256 }{ 12 } \cdot \frac { \pi  }{ \pi  } \cdot \frac { 1 }{ { r }^{ 2 } }

\\ \\ =-\frac { 64 }{ 3{ r }^{ 2 } } \\ \\ When\quad r=8,\\ \\ \frac { dr }{ dt } =-\frac { 64 }{ 3\cdot { 8 }^{ 2 } } =-\frac { 1 }{ 3 } \\ \\ Answer:\quad -\frac { 1 }{ 3 } \quad cm/sec
3 0
3 years ago
A bacteria colony increases in size at a rate of 4.0581e1.6t bacteria per hour. If the initial population is 36 bacteria, find t
Harrizon [31]

Answer:

1560

Step-by-step explanation:

The rate of Increase of the population (P) of the bacteria is given as:

\frac{dP}{dt} =4.058e^{1.6t}

dP =4.058e^{1.6t}}dt\\Taking\: Integrals\\\int dP =4.058 \int e^{1.6t}dt\\P(t)=\frac{4.058}{1.6} (e^{1.6t} +K)\\P(t)=2.53625 (e^{1.6t} +K)

Where k is a constant of Integration.

At t=0, P(t)=36

36=2.53625 (e^{1.6*0} +K)\\36=2.53625 (e^{0} +K)\\36=2.53625 (1 +K)\\36=2.53625 +2.53625K\\K=13.19

Therefore:

P(t)=2.53625 (e^{1.6t} +13.19)\\At \: t=4\\P(4)=2.53625 (e^{1.6*4} +13.19)\\=1559.88\\P(4)=1560

3 0
3 years ago
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Answer:

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Step-by-step explanation:

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Step-by-step explanation:

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