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3 years ago

PLZ HELP ASAP Geometry help: 2x^2 + 2y^2 - 8x +10y +2=0

1 answer:

6 0

Ok so this is conic sectuion
first group x's with x's and y's with y's
then complete the squra with x's and y's

2x^2-8x+2y^2+10y+2=0
2(x^2-4x)+2(y^2+5y)+2=0
take 1/2 of linear coeficient and square
-4/2=-2, (-2)^2=4
5/2=2.5, 2.5^2=6.25
add that and negative inside

2(x^2-4x+4-4)+2(y^2+5y+6.25-6.25)+2=0
factor perfect squares
2((x-2)^2-4)+2((y+2.5)^2-6.25)+2=0
distribute
2(x-2)^2-8+2(y+2.5)^2-12.5+2=0
2(x-2)^2+2(y+2.5)^2-18.5=0
add 18.5 both sides
2(x-2)^2+2(y+2.5)^2=18.5
divide both sides by 2
(x-2)^2+(y+2.5)^2=9.25

that is a circle center (2,-2.5) with radius √9.25

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The distance Train A travels is represented by d = 67t, where d is the distance in kilometers and t is the time in hours. The di

Thepotemich [5.8K]

Answer:

Train A's unit rate is 67 km per hour.

Train B's unit rate is 75 km per hour.

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Step-by-step explanation:

Train A

Distance traveled by Train A is represented by :

$d=67t$

where $d$ represents distance traveled in kilometers and $t$ is the time in hours.

To find the unit rate of Train A, we will plugin $t=1$ and get the distance traveled by Train A in 1 hour which will be the unit rate of Train A in km/hr.

$d=67(1)$

$d=67$

So, distance traveled by Train A in 1 hour = 67 km

∴ Train A's unit rate is 67 km per hour.

Train B

For Train B, we are given the table for the time in hours and distance traveled in that duration.

Taking time =2 hours the distance traveled by Train B= 75 km

To find distance traveled in 1 hour we apply unitary method.

$2\ hr = 150\ km$

So $1\ hr = \frac{150}{2}\ km = 75\ km$

So, distance traveled by Train B in 1 hour = 75 km

∴ Train B's unit rate is 75 km per hour.

Difference in units rates = $75-67=8\ km/hr$

On comparing their unit rate i.e. the speed of the trains we find out that Train B is faster than Train A by 8 km/hr

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