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Naya [18.7K]
3 years ago
12

Where does the point (6,2) lie on a circle centered at (7,8) with a radius of 6

Mathematics
1 answer:
olya-2409 [2.1K]3 years ago
5 0

Answer:

<em>The point lies barely outside of the circle</em>

Step-by-step explanation:

<u>Equation of a Circle</u>

Given its center (h,k) and radius r, the equation of a circle is given by

(x-h)^2+(y-k)^2=r^2

The circle given in the question is centered at (7,8) and has a radius of 6, thus its equation is

(x-7)^2+(y-8)^2=6^2

(x-7)^2+(y-8)^2=36

To find out if a point (a,b) is outside or inside the circle area, the following conditions apply.

if (a-7)^2+(b-8)^2>36 then the point lies outside of the circle area

if (a-7)^2+(b-8)^2 then the point lies inside of the circle area

Let's use the point as given (6,2)

(6-7)^2+(2-8)^2=1+36=37

Thus the point lies barely outside of the circle

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snow_tiger [21]

Answer:

Tom’s age is 7 years

Mary’s age is 13 years

Step-by-step explanation:

Since we do not know the ages, let’s represent the ages by variables at first.

Let m represent mary’s age will t represent Tom’s age.

Now, let’s proceed to have equations.

Adding square of Tom’s age (t^2) to mary’s age give 62

t^2 + m = 62 •••••••(i)

Adding square of mary’s age (m^2) to Tom’s age give 176

m^2 + t = 176 •••••••(ii)

Now, to get the individual ages, we will need to solve both equations simultaneously.

Solving both equations simultaneously without mathematical softwares can be a little hard.

By the use of mathematical software ( wolfram alpha to be specific), we can input both equations and allow the software to solve.

By inputing these equations, we have the values of t to be 7 and m to be 13

And if we try to check by inspection, we can see that these values are actually correct.

7^2 + 13 = 62

13^2 + 7 = 176

6 0
3 years ago
A thin wire has the shape of the first-quadrant part of the circle with center the origin and radius q. If the density function
irina [24]

Answer:

Step-by-step explanation:

Check attachment for solution

5 0
3 years ago
If a club charges dues of $200 a year, it will have 50 members. For each $5 it raises its dues, it loses a member. USE AN EQUATI
Vikentia [17]

Answer:

The value is      y  =  \$ 225

Step-by-step explanation:

From the question we are told that

   The amount charge per year is  k  =  \$ 200

   The  number of members it will have at this amount is  n  =  50

   The amount amount increase that will lead to the loss of a single member is   z =  \$ 5

        Generally the total amount the club would obtain from  its members is mathematically represented as

      I  =  Amount \  due\ paid *  Number \  of members

Now let x denote the number of member lost

Hence

      I  =  (k + zx) (n-x )

=>    I  =  (200 + 5x) (50-x )

=>  I  = 10000+50x-5x^2

Thus the number of members that be removed to  give the maximum  income from dues is obtained by differentiating the above equation and equating it to zero

           \frac{dI}{dx}  =  50-10x

=>         x   =  5

So from  I  =  (200 + 5x) (50-x ) we have

          I  =  (200 + 5 (5)) (50-5 )

           I  = \$ 10125

So the amount the club should charge is    

         y  =  \frac{10125}{50 - 5}

         y  =  \$ 225

         

7 0
3 years ago
If K(5,-2) is rotated 90°, what will be the coordinates of its image?
stiks02 [169]

Answer:

I think it is k(2,5) or k'(-2, -5

Step-by-step explanation:

Hope This Helps Have A Good Day

70% sure that it is K(2,5)

4 0
3 years ago
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jolli1 [7]
Direct variation is of the form y=kx   (inverse variation is of the form y=k/x)
5 0
3 years ago
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