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levacccp [35]
3 years ago
6

The gravitational force exerted by the planet Earth on a unit mass at a distance r from the center of the planet is F(r) = GMr R

3 if r < R GM r2 if r ≥ R where M is the mass of Earth, R is its radius, and G is the gravitational constant. Is F a continuous function of r? Why/why not?
Mathematics
1 answer:
bagirrra123 [75]3 years ago
8 0

Answer:

Yes the function is continuous.

Step-by-step explanation:

Given

F(r)=\frac{GMr}{R^{3}}(r< R) and F(r)=\frac{GM}{r^{2}}(r\geq R)

For a function to be continuous we should have

\lim_{r\rightarrow R^{-}}F(r)=\lim_{r\rightarrow R^{+}}F(r)

Thus

\lim_{r\rightarrow R^{-}}F(r)=\frac{GMR}{R^{3}}=\frac{GM}{R^{2}}

Similarly we have

\lim_{r\rightarrow R^{+}}F(r)=\frac{GM}{R^{2}}

thus we can see that

\lim_{r\rightarrow R^{-}}F(r)=\lim_{r\rightarrow R^{+}}F(r)

Hence the function is continuous.

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Thehhe hey!!! You guys think u guys can help me on this? :)))
Tamiku [17]

Answer:

I got 4 3/8

Step-by-step explanation:

2 1/4=2 2/8

2 2/8 + 2 1/8 =4 3/8

6 0
3 years ago
Please help me cause I am not very good at math
Katarina [22]

Answer:

m=-2

General Formulas and Concepts:

<u>Pre-Algebra</u>

  • Order of Operations: BPEMDAS

<u>Algebra I</u>

  • Slope Formula (Rate of Change): m=\frac{y_2-y_1}{x_2-x_1}

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Find points from graph.</em>

Point (0, 5)

Point (2, 1)

<u>Step 2: Find slope </u><em><u>m</u></em>

  1. Substitute:                    m=\frac{1-5}{2-0}
  2. Subtract:                       m=\frac{-4}{2}
  3. Divide:                          m=-2
5 0
3 years ago
Read 2 more answers
Help me please asap thank you
Korolek [52]

Answer:

3/5

Step-by-step explanation:

The line is going up so it is positive and it is over 3 and up 5 so it would be 3/5.

Hope this helps! Sry if i get it wrong!

3 0
2 years ago
I need help on 1-6 and If you can, can you explain how to do these? I'm not entirely sure how to.
gayaneshka [121]
1. Using c=2pi(r), plug in 7 for r and solve. Then using a=pi(r)^2, plug in 7 for r once again and solve.

2. First, the diameter (d) is 12 so to get the radius (r), divide 12 by 2 and you should get 6. Then use c=2pi(r) for circumference and a=pi(r)^2 for area to solve.

3. To get the area of the semicircle, divide 16 by 2 to get the radius (r), plug it into a=pi(r)^2, and divide the answer you get for a by 2. To get the area of the triangle, use a=1/2bh, plugging in 16 for b and 10 for h. Finally, add your two answers (the a's from the semicircle and triangle problems).

4. Multiply 20 by 5.5 to get the area of the triangle. Then multiply 4.5 by 20 to get the area of the parallelogram and add your two quotients.

5. Use a=1/2bh and plug in 4 for b and 3 for h and solve. Then multiply the quotient by 10 and there's your volume. To find the surface area, solve SA=(10×4)+(10×3)+(10×5)+12. All I did there was find the area of all the sides and added them together.

6. To find the triangle's volume, use a=1/2bh (b=4, h=1.5) and then multiply the quotient of that by 2.5. To find the rectangle's volume, use v=lwh (l=4, w=2.5, h=2) and solve. Finally, add the triangle's volume and the rectangle's volume to get the total volume. To get its surface area, start with the rectangle. Find the areas of all the sides and add them together but then subtract the 2.5×4 rectangle as it is not on the surface. It should look like this: SA=2(4×2)+2(2.5×2)+10. Again, all I did was find the areas of all the rectangle's sides on the surface and added them. Next, find the triangle's areas on the surface and it should look like this: SA=2(1.5×4)+2(2.5×2.5). Finally, add both values of SA from the triangle and rectangle and there's your surface area.
7 0
3 years ago
Which expression can be written as k square root 3 where k is an integer
Damm [24]

Answer:

A simple expression is \sqrt{48} = 4\sqrt{3}

Step-by-step explanation:

Surds are irrational numbers expressed with respect to a square root. There are some basic rules required when dealing with surd.

Integers are numbers that do not have a decimal or fractional part i.e whole numbers. So, a simple expression that can be written as k square root 3 where k is an integer is \sqrt{48}.

So that,

                            \sqrt{48} = \sqrt{16 * 3}

                                   = 4\sqrt{3}

8 0
3 years ago
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