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ivann1987 [24]
3 years ago
5

3. Write the standard equation of the circle with the given center that passes through the given

Mathematics
1 answer:
bearhunter [10]3 years ago
5 0

Answer:

D is  correct.

Step-by-step explanation:

(x + 2)^2 + (y - 6)^2 = r^2

(-2+2)^2 + (10 - 6)^2 = r^2

r^2= (10 - 6)^2

r^2=16

You might be interested in
{4x-2y+5z=6 <br> {3x+3y+8z=4 <br> {x-5y-3z=5
lesya692 [45]

There are three possible outcomes that you may encounter when working with these system of equations:


  •    one solution
  •    no solution
  •    infinite solutions

We are going to try and find values of x, y, and z that will satisfy all three equations at the same time. The following are the equations:

  1. 4x-2y+5z = 6
  2. 3x+3y+8z = 4
  3. x-5y-3z = 5

We are going to use elimination(or addition) method

Step 1: Choose to eliminate any one of the variables from any pair of equations.

In this case it looks like if we multiply the third equation by 4 and  subtracting it from equation 1, it will be fairly simple to eliminate the x term from the first and third equation.

So multiplying Left Hand Side(L.H.S) and Right Hand Side(R.H.S) of 3rd equation with 4 gives us a new equation 4.:

4. 4x-20y-12z = 20      

Subtracting eq. 4 from Eq. 1:

(L.HS) : 4x-2y+5z-(4x-20y-12z) = 18y+17z

(R.H.S) : 20 - 6 = 14

5. 18y+17z=14

Step 2:  Eliminate the SAME variable chosen in step 2 from any other pair of equations, creating a system of two equations and 2 unknowns.

Similarly if we multiply 3rd equation with 3 and then subtract it from eq. 2 we get:

(L.HS) : 3x+3y+8z-(3x-15y-9z) = 18y+17z

(R.H.S) : 4 - 15 = -11

6. 18y+17z = -11

Step 3:  Solve the remaining system of equations 6 and 5 found in step 2 and 1.

Now if we try to solve equations 5 and 6 for the variables y and z. Subtracting eq 6 from eq. 5 we get:

(L.HS) : 18y+17z-(18y+17z) = 0

(R.HS) : 14-(-11) = 25

0 = 25

which is false, hence no solution exists



3 0
2 years ago
Two times the smaller of two consecutive integers is equal to 2 more than the larger. What is the LARGER integer?
LenaWriter [7]

Answer:

The larger integer is 4.

Step-by-step explanation:

Given: Two times the smaller of two consecutive integers is equal to 2 more than the larger.

To find: The larger integer.

Solution:

Let the two consecutive integers be x and x+1,  where the smaller integer is x and larger integer is x+1.

Now, according to question.

Two times the smaller integer = 2 more than the larger integer.

\implies 2x=x+1+2

\implies 2x-x=3

\implies x=3

So, the smaller integer is 3, and the larger integer is 3+1=4.

Hence, the larger integer is 4.

8 0
3 years ago
The circumference of a sphere was measured to be 82 cm with a possible error of 0.5 cm.
Nat2105 [25]

Answer:

A) Maximum error = 170.32 cm³

B)Relative error = 0.0575

Step-by-step explanation:

A) Formula for circumference is: C = 2πr

Differentiating with respect to r, we have;

dC/dr = 2π

r is small, so we can write;

ΔC/Δr = 2π

So, Δr = ΔC/2π

We are told that ΔC = 0.5.

Thus; Δr = 0.5/2π = 0.25/π

Now, formula for Volume of a sphere is;

V(r) = (4/3)πr³

Differentiating with respect to r, we have;

dV/dr = 4πr²

Again, r is small, so we can write;

ΔS/Δr = 4πr²

ΔV = 4πr² × Δr

Rewriting, we have;

ΔV = ((2πr)²/π) × Δr

Since C = 2πr, we now have;

ΔV = (C²/π)Δr

ΔV will be maximum when Δr is maximum

Thus, ΔV = (C²/π) × 0.25/π

C = 82 cm

Thus;

ΔV = (82²/π) × 0.25/π

ΔV = 170.32 cm³

B) Formula for relative error = ΔV/V

Relative error = 170.32/((4/3)πr³)

Relative error = 170.32/((4/3)C³/8π³)

Relative errror = 170.32/((4/3)82³/8π³)

Relative error = 170.32/2963.744

Relative error = 0.0575

3 0
2 years ago
Do these side lengths make a triangle? <br> 8, 8, 4,
jeyben [28]

Answer: weird question but yes they should if there is only 3

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
PLEASE HELP ME! I am suck on this math assignment
patriot [66]

Hey there! I'm happy to help!

-----------------------------------------------------------------------------------------

<u>QUESTION 18</u>

Here is how you multiply a 2×2 matrix by a column vector (just one column matrix).

\left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right] *\left[\begin{array}{ccc}x\\y\\\end{array}\right] = \left[\begin{array}{ccc}ax&by\\cx&dy\\\end{array}\right]

Once you get that final matrix, you add the rows which will give you a final column vector. Let's do it with this question, as we are multiplying together the matrices A and v.

\left[\begin{array}{ccc}-1&4\\2&0\\\end{array}\right] *\left[\begin{array}{ccc}8\\6\\\end{array}\right] =\left[\begin{array}{ccc}-8&24\\16&0\\\end{array}\right] =\left[\begin{array}{ccc}16\\16\\\end{array}\right]

So, your answer is \left[\begin{array}{ccc}16\\16\\\end{array}\right].

-----------------------------------------------------------------------------------------

<u>QUESTION 14</u>

We have this equation of an ellipse and we need to solve for y. When we have a more complex equation to solve you get rid of the things furthest from the variable you are solving for first and then you get closer and closer to it.

\frac{x^2}{25} + \frac{y^2}{16}=1

We subtract \frac{x^2}{25} from both sides.

\frac{y^2}{16}=1-\frac{x^2}{25}

We multiply both sides by 16.

y^2=1-\frac{x^2}{25}*16

We square root both sides.

y= \sqrt{1-\frac{x^2}{25}*16

We can take a four out of our root (because 16 is a perfect square so it can be simplified more).

y= 4\sqrt{1-\frac{x^2}{25}

And we take out 1/5 (which is the square root of 1/25).

y=± \frac{4}{5}\sqrt{1-x^2

-----------------------------------------------------------------------------------------

<u>QUESTION 17</u>

We see that Sea Slugs have 3/10 matches won, so they have won 30% of their matches.

From now on, they will be winning 2/3 of their games. Let's look at the answer options.

A. If they play 15 more games, they will win 10 of them. Our total matches will be 25 (our original 10+15). So, we will have 13/25, which is equal to 52%, so this is incorrect.

B. If they play 10 more games they win 6 2/3 games (like that makes any sense) for a total of 9 2/3 games out of 20. This is about 48%, so this is incorrect.

C. If they play 40 games, they are winning fractional games again. They win 29 2/3 games out of 50 total, which is about 59%, but not quite 60. This is also incorrect.

D. If they play 45 matches, they will win 30 games. Add the original 10 and you have 40 games. Our total is 55. 40/55 is about 73%, so they have passed that 60% threshold, so this is the correct answer.

-----------------------------------------------------------------------------------------

<u>QUESTION 16</u>

Our question tells us that if we have two numbers x and y, and we add them, it has to be 24 or greater. By saying it can be equal to 24 or greater, we are going to be using a ≤ or ≥ sign. The opening of the arrow always faces the equal or greater quantity, and in this case it is x+y, so it will look like x+y≥24.

This eliminates answer choices B and D as they do not have the equal part on the inequality.

Product means to multiply, so it will be written as xy. It has to be less than 60, so in this case the greater quantity is 60, so the arrow will opening towards 60, so it will look like xy<60.

So, our final answer is A.

-----------------------------------------------------------------------------------------

<u>QUESTION 12</u>

You can only multiply matrices if the number of columns in the first matrix is equal to the number of rows in the second. So basically the two interior numbers have to be the same (a,b) and (b,c). So, if we follow this, we get these answers:

2×2 times 2×1 YES

2×1 times 2×2= NO

3×3 times 3×1= YES

3×1 times 3×3= NO

-----------------------------------------------------------------------------------------

Have a wonderful day and keep on learning! :D

6 0
2 years ago
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