I dont understand how to answer this question, help please?

The gravitational force exerted by the planet Earth on a unit mass at a distance r from the center of the planet is:

jolli1 [7]

Answer:

Yes, F is a continuous function of r

Step-by-step explanation:

We are given that

When r<R

$F(r)=\frac{GMr}{R^3}$

$r\geq R$

$F(r)=\frac{GM}{r^2}$

Where M=Mass of the earth

R=Radius of earth

G=Gravitational constant

We have to find the function is continuous of r or not.

LHL

$\lim_{r\rightarrow R-}\frac{GMr}{R^3}=\frac{GMR}{R^3}=\frac{GM}{R^2}$

RHL

$\lim_{r\rightarrow R+}\frac{GM}{R^2}=\frac{GM}{R^2}$

$F(R)=\frac{GM}{R^2}$

When a function is continuous at x=a

Then, LHL=RHL=f(a)

RHL==LHL=F(R)

Hence, the function is continuous of r.

8 0

3 years ago

Select the graph that represents the solution to the following inequality: Ix-3I<3

Dominik [7]

The correct answer is: Answer choice: [C]:_________________________________________________→ {the number line/ graph provided for choice: [C] ; as follows}:_________________________________________________

4 0

3 years ago

2 different companies offer online subscriptions. Company A charges $75 upfront and $20 per month. Company B does not charge the

ki77a [65]

Answer:

$15$ months

Step-by-step explanation:

Given that company $A$ charges $\$75$ upfront and $\$20$ per month and company B does not charge the upfront fee but charges $\$35$ per month.

Let after $n$ months both the company charges the same amount.

Total charges by the company $A=\$ (75+n\times 20)$ and total charges by the company $B=\$ (n\times 35)$ .

Now, from the given condition both the charges are equal, so

$75+n\times 20=n\times 35 \\\Rightarrow 75= 35 n - 20 n\\\Rightarrow 75= 15 n \\\Rightarrow n= \frac {75}{5} \\\Rightarrow n= 15$

Hence, after $15$ months both the company charges the same amount.

4 0

3 years ago

An angle is bisected, forming two new angles. if the original angle had a measure of 62°, what is the measure of each new angle?

s344n2d4d5 [400]

Bisected means cut in half. half of 62 is ,31

4 0

3 years ago

Rotate the figure 90 degrees about vertex A.

ziro4ka [17]

Answer:

A' is (1,1) B is (4,1) C is (1,-1)

Step-by-step explanation:

Since we rotating the figure about point a, we know a is the center of the rotation meaning no matter how far we rotate point a new image will stay on where point a pre image was which in this case is (1,1). Also since we know the rules of rotating a angle 90 degrees About the origin we are going to translate the figure to have the one point we are rotating about at the orgin. Since translations are a rigid transformations, the figure will stay the same A. Move the figure 1 to the left and 1 down so A becomes 0,0 B becomes 0,3 and C becomes 2,0. Then apply the rules of 90 degree clockwise rotation rules. (x,y) goes to (y,-x) . A stays (0,0) B becomes (3,0) and C becomes (0,-2). Then translate the figure 1 to the right and 1 down since we rotating about point a which is 1,1 and it at 0,0 rn. A' is 1,1. B' becomes (4,1). C' becomes (1,-1).

5 0

3 years ago