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zvonat [6]
3 years ago
14

8x+x^2-2y-64+y^2=0 standard form with explanation

Mathematics
1 answer:
xz_007 [3.2K]3 years ago
8 0
X² + 8x +y² - 2y -64 =0
We see that the equation has x² and y² . Also we see that coefficients in front of x² and y² are equal. So this is an equation of the circle.
(x² + 8x) +(y² - 2y) -64 =0
(x² + 8x) +(y² - 2y) = 64
We need to complete square for x and y groups, that means it should be written in form (a+b)² or (a-b)².
Expressions in parenthesis we will write as a²+/-2ab+b², to write it after as (a+/-b)², because  a²+/-2ab+b² = (a+/-b)²

(x² + 2*4x) +(y² - 2*1y) = 64
(x² + 2*4x+4²) +(y² - 2*1y+1²) = 64+4²+1²
(x+4)² + (y-1)²= 81 Sometimes this is called a standard form of the circle.
(x+4)² + (y-1)²= 9² Sometimes it is required to write like this.

And if you are studying circles,ellipses  and hyperbolas, the standard form should look like
\frac{(x+4)^{2}}{9^{2}} + \frac{(y-1)^{2}}{9^{2}} =1






You might be interested in
write the equation of the line using the given information. type your awnser in slope intercept form,y=mx+b​
faltersainse [42]

Answer:

y=3/-1x+4

Step-by-step explanation:

Okay so first thing you need to know is that if there is an ordered pair (x, y) where x is 0, your y-intercept is your y. For example, your problem has (0, 4) your x is 0 and your y is 4. Therefore your y-intercept is 4 which is the b. To find your mx, or slope, you need to do (y2-y1)/(x2-x1). Your y2 will be your y in your second ordered pair and your y1 will be in your y in the first ordered pair. Same for your x. So, (4-1)/(0-1) which equals 3/-1. 3/-1 is your slope. So, your answer in slop intercept form is: y= 3/-1x+4. You could also try y= -3x+4 if that makes you more comfortable.

I know this is long this is my first time doing this lol.  

5 0
3 years ago
Maria's height while jumping on a a trampoline can be modeled by the equation h=-16t^2+18t+5. Where t=time in seconds and h=heig
Vadim26 [7]

Answer:

10.06 ft

Step-by-step explanation:

Maria's maximum height will occur when her velocity reaches zero (0). This means that she has stopped ascending and is about to begin descent.

The equation for the height reached by Maria on the trampoline is given as:

h=-16t^2+18t+5

To find her maximum height, we first have to find the time it will take her to get to that height and corresponding velocity (zero).

Her velocity can be found by differentiating her height i.e. dh/dt:

v = \frac{dh}{dt} = -32t + 18

Therefore, when v = 0:

0 = -32t+ 18\\\\=> 32t= 18\\\\t = 18 / 32 = 0.5625 secs

It takes her 0.5625 seconds to get to her maximum height.

Therefore, her height at that time (0.5625 seconds) is:

h=-16(0.5625)^2+18(0.5625)+5\\\\h = -16 * (0.3164) + 10.125+5\\\\h = -5.0624 + 15.125\\\\h = 10.06 ft

Therefore, her maximum height is 10.06 ft.

3 0
3 years ago
PLEASEEEE
belka [17]

Answer:

The answer to your questions is: 25 new teachers

Step-by-step explanation:

Data

# of students = 2000

ratio = 3:80 teachers to students

New teachers = ?

Process

I suggest to use rule of three to solve this problem

                     3 teachers ----------------  80 students

                      x                ----------------  2000 students

                  x = (2000 x 3) / 80 = 75 teachers

               Number of initial teachers = 75

The ratio change to 1:20

                     1 teacher -------------------  20 students

                     x             -------------------   2000 students

                     x = (2000 x 1) / 20

                    x = 100 teachers

Number of new teachers = 100 - 75 = 25

3 0
3 years ago
Sixty students voted in a class president. 30% of the students voted for Shawn and 70% of the students voted for Jane. How many
JulsSmile [24]
There are 60 students. The winner got 70% of the 60 students votes. Let's work this one out to get the answer.

First, you need to figure out what 70% of 60 is, by using this equation.
60 x .70 = 42.
Now that you know the answer is 42, you now know that 70 percent of 60 is 42.

So, the class president got 42 winning votes!






Hope I could help!
Ossashi(づᵔᗜᵔ)づ








8 0
3 years ago
A certain number of sixes and nines is added to give a sum of 126; if the number of sixes and nines is interchanged, the new sum
galina1969 [7]

Answer:

Original number of sixes = 6

Original number of nines = 10

Step-by-step explanation:

We are told in the question that:

A certain number of sixes and nines is added to give a sum of 126

Let us represent originally

the number of sixes = a

the number of nines = b

Hence:

6 × a + 9 × b = 126

6a + 9b = 126.....Equation 1

If the number of sixes and nines is interchanged, the new sum is 114.

For this second part, because it is interchanged,

Let us represent

the number of sixes = b

the number of nines = a

6 × b + 9 × a = 114

6b + 9a = 114.......Equation 2

9a + 6b = 114 .......Equation 2

6a + 9b = 126.....Equation 1

9a + 6b = 114 .......Equation 2

We solve using Elimination method

Multiply Equation 1 by the coefficient of a in Equation 2

Multiply Equation 2 by the coefficient of a in Equation 1

6a + 9b = 126.....Equation 1 × 9

9a + 6b = 114 .......Equation 2 × 6

54a + 81b = 1134 ........ Equation 3

54a + 36b = 684.........Equation 4

Subtract Equation 4 from Equation 3

= 45b = 450

divide both sides by b

45b/45 = 450/45

b = 10

Therefore, since the original the number of nines = b,

Original number of nines = 10

Also, to find the original number of sixes = a

We substitute 10 for b in Equation 1

6a + 9b = 126.....Equation 1

6a + 9 × 10 = 126

6a + 90 = 126

6a = 126 - 90

6a = 36

a = 36/6

a = 6

Therefore, the original number of sixes is 6

7 0
3 years ago
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