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2 years ago

Which conic section does the equation below describe? x^2+y^2+2x-8y-13=0

Mathematics

1 answer:

Gre4nikov [31]2 years ago

3 0

Answer: B) Circle

Step-by-step explanation:

First, complete the square:

x² + 2x + 1 + y² - 8y + 16 = 13 + 1 + 16

↓ ↑ ↓ ↑

(2/2) = (1)² (-8/2) = (-4)²

(x + 1)² + (y - 4)² = 30

The result is a circle whose center is (-1, 4) and radius is √30

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Evaluate 150 + 3p for p = 30

LiRa [457]

150+3p

p=30

150+3(30)

150+90

240

When p=30 in 150+3p, the final value is 240.

7 0

3 years ago

Read 2 more answers

There are 3 red chips and 2 blue chips. If they form a certain color pattern when arranged in a row, for example RBRRB, how many

svp [43]

Answer:

Option A - 10

Step-by-step explanation:

Given : There are 3 red chips and 2 blue chips. If they form a certain color pattern when arranged in a row, for example RBRRB.

To find : How many color patterns are possible?

Solution :

Total number of chips = 5

So, 5 chips can be arranged in 5! ways.

There are 3 red chips and 2 blue chips.

So, choosing 3 red chips in 3! ways

and choosing 2 blue chips in 2! ways.

As changing the places of similar chip will not create new pattern.

The total pattern is given by,

$T=\frac{5!}{3!\times 2!}$

$T=\frac{5\times 4\times 3!}{3!\times 2}$

$T=10$

Therefore, color patterns are possible are 10.

Option A is correct.

4 0

3 years ago

If a cannonball is shot directly upward with a velocity of 160 ft per second, its height above the ground after t seconds is gi

Contact [7]

Step-by-step explanation:

If a cannonball is shot directly upward with a velocity of 160 ft per second. Its height as a function of time is given by :

$h(t)=160t-16t^2$ .......(1)

t is in seconds

(a) Velocity is given by :

$v=\dfrac{dh}{dt}\\\\v=\dfrac{d(160t-16t^2)}{dt}\\\\v=(160-32t)\ ft/s$

Acceleration is given by :

$a=\dfrac{dv}{dt}\\\\a=\dfrac{d(160-32t)}{dt}\\\\a=-32\ ft/s^2$

(b) For maximum height put $\dfrac{dh}{dt}=0$

i.e.

$160-32t=0\\\\t=5\ s$

Put t = 5 s in equation (1). So,

$h(5)=160t-16t^2\\\\h(5)=160(5)-16(5)^2\\\\h(5)=400\ ft$

h(t) = 0

$160t-16t^2=0\\\\t(160-16t)=0\\\\t=0,t=10\ s$

Hence, this is the required solution.

4 0

2 years ago

Which is the equation for ---

ratelena [41]

Equation of the line:
y=mx+b
Ordinate at the origin (where the line cut the y-axis): b=1

B=(-5,5)=(xb,yb)→xb=-5, yb=5
C=(0,1)=(xc,yc)→xc=0, yc=1
m=(yc-yb)/(xc-xb)
m=(1-5)/(0-(-5))
m=(-4)/(0+5)
m=(-4)/(5)
m=-(4/5)

y=mx+b
y=-(4/5)x+1
Multiplying the equation by 5:
5[y=-(4/5)x+1]
5y=-4x+5
Adding 4x both sides of the equation:
5y+4x=-4x+5+4x
4x+5y=5

Answer: The equation for BC is: Third option 4x+5y=5

7 0

2 years ago

10 points What is the difference of the two polynomials? * (9x2 + 8x) - (2x2 + 3x) 7x² + 5x 7x² + 11x Option 1 Option 2 h 11x² +

Blizzard [7]

Answer:

The answer to your question is 7x2+5x

Step-by-step explanation:

4 0

3 years ago