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natita [175]
3 years ago
7

Using geometry, calculate the volume of the solid under z=64−x2−y2and over the circular disk x2+y2≤64

Mathematics
1 answer:
Anarel [89]3 years ago
3 0
Perhaps you mean to find the volume under z=\sqrt{64-x^2-y^2}? It seems like you have to rely on calculus otherwise (in the case that you indeed mean z=64-x^2-y^2).

Assuming this, note that z=\sqrt{64-x^2-y^2} describes the top half of a sphere with radius 8, which means the volume below this surface over the disk x^2+y^2\le64 is simply half the volume of the sphere. Thus the volume is

\dfrac43\pi8^3=\dfrac{2048}3\pi
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The population of a town increases by 4 % every year . In the last year the population of the town was 110000.
TEA [102]

Answer:

114,400 and 118,976.

Step-by-step explanation:

Let's represent this using a function. Let's let:

P(y) represent the total population, and y represent the total number of years since last year.

We know that the population grows by 4% every year or 0.04 every year. This is exponential growth. We can write this as:

P(y)=110000(1.04)^y

Note that the coefficient is 110000 because that is the year we are starting with. Also, note that it is 1.04 because we are essentially adding .04 to the original population.

Anyways, to find the present population, set y equal to 1 (because 1 year after last year is the present year)

P(1)=110000(1.04)^1=114400

The present population is 114,400 people.

For next year, set y equal to 2 (2 years after last year is next year)>

P(2)=110000(1.04)^2=118976

The population next year will be 118,976 people.

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Step-by-step explanation:

If you substitute x = 1 in the equation you get that y = 10 at that point which is the maximum point at which graph reaches in the y direction. As you can see, the slope of the derivative is increasing, which means that the slope of the tangent line is increasing before that point.

Hope this helps

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Serhud [2]
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