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Oxana [17]
3 years ago
6

Exponential Growth problem.

Mathematics
1 answer:
xxMikexx [17]3 years ago
8 0
It will be understood that population 6,000 billion (6*10^12) in 2017.
If this is not the case, follow the logic and the final number can be adjusted easily.

Mathematical answer:
In 2017: 6,000 billion=6000*10^9 =6*10^12
rate of increase = 1.3% per year (assumed constant)
final year = 2100
Population estimate in 2100
=6*10^12*(1.013^(2100-2017))
=6*10^12*(1.013^(83)
=6*10^12*(2.921352509198383)
=17.528*10^12
=17,528 billion.


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Divide 2 and 1/5 by 1/10. Simplify your answer
laila [671]

Answer:

10

Step-by-step explanation:

2 divided by 1/10 equal 20.

1/5 divided by 1/10 equals 2.

20 divided by 2 equal 10.

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3 years ago
Find the critical points of the surface f(x, y) = x3 - 6xy + y3 and determine their nature.​
Vedmedyk [2.9K]

Compute the gradient of f.

\nabla f(x,y) = \left\langle 3x^2 - 6y, -6x + 3y^2\right\rangle

Set this equal to the zero vector and solve for the critical points.

3x^2-6y = 0 \implies x^2 = 2y

-6x+3y^2=0 \implies y^2 = 2x \implies y = \pm\sqrt{2x}

\implies x^2 = \pm2\sqrt{2x}

\implies x^4 = 8x

\implies x^4 - 8x = 0

\implies x (x-2) (x^2 + 2x + 4) = 0

\implies x = 0 \text{ or } x-2 = 0 \text{ or } x^2 + 2x + 4 = 0

\implies x = 0 \text{ or } x = 2 \text{ or } (x+1)^2 + 3 = 0

The last case has no real solution, so we can ignore it.

Now,

x=0 \implies 0^2 = 2y \implies y=0

x=2 \implies 2^2 = 2y \implies y=2

so we have two critical points (0, 0) and (2, 2).

Compute the Hessian matrix (i.e. Jacobian of the gradient).

H(x,y) = \begin{bmatrix} 6x & -6 \\ -6 & 6y \end{bmatrix}

Check the sign of the determinant of the Hessian at each of the critical points.

\det H(0,0) = \begin{vmatrix} 0 & -6 \\ -6 & 0 \end{vmatrix} = -36 < 0

which indicates a saddle point at (0, 0);

\det H(2,2) = \begin{vmatrix} 12 & -6 \\ -6 & 12 \end{vmatrix} = 108 > 0

We also have f_{xx}(2,2) = 12 > 0, which together indicate a local minimum at (2, 2).

3 0
2 years ago
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Units are simplified first when measurements are multiplied because the units can sometime be very large or small and do not have to be exact when measurements are precise.
8 0
4 years ago
Farhan cycles the first part of a 150km journey at an average speed of 35km/h and walks the remaining distance at an average spe
Gnoma [55]

Answer:

man ion know

Step-by-step explanation:

5 0
3 years ago
Gail gave her friend 7/18 of her stickers on Monday. She gave another friend 5/18 of her stickers on Wednesday. What fraction of
alukav5142 [94]

Answer:

she has 1/3 of her stickers left.

7/18+5/18= 12/18, which dicided by 6 equals 2/3, therefore she only has 1/3 left.

Step-by-step explanation:

i divided by 6 because it is the biggest whole number that both 12 and 18 go into.

7 0
3 years ago
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