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topjm [15]
2 years ago
5

Two trains leave the station at the same time, one traveling due east, the other due west. After 46 minutes, they are 140 miles

apart. If one train's speed is 20 mph more than the other train's, what are the speeds of the two trains.
Mathematics
1 answer:
Monica [59]2 years ago
3 0

Train A speed = x + 20

Train B = x

We know that 46 minutes is 23/30 of an hour.

Use D = rt

Take it from here.

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Find a polar equation for the conic with its focus at the pole and the given vertex or vertices:
Schach [20]

Answer:

A) r = 2/(1 - sinθ)

B) r = 16/(5 + 3 cosθ)

C) r = 2/(1 + 2 cosθ)

Step-by-step explanation:

A) We are given the parabola vertex as:

(r, θ) = (1, -π/2)

The vertex coordinates indicates that it's below the pole and thus the equation of the conic section is represented by;

r = ed/(1 - e sinθ)

Since the equation is a parabola, then the eccentricity is 1.

Thus,plugging in the relevant values;

1 = (1 × d)/(1 - (1 × sin-π/2))

1 = d/(1 - (-1))

1 = d/(1 + 1)

1 + 1 = d

d = 2

Therefore the general equation would be gotten by putting 2 for d and 1 for E.

Thus;

r = (1 × 2)/(1 - (1 × sinθ))

r = 2/(1 - sinθ)

B) vertices of Ellipse are given as;

(2,0) and (8, π)

The equation will be represented by;

r = ep/(1 + e cosθ)

Where e which is the eccentricity is given by: e = c/a

c = (8 - 2)/2

c = 6/2

c = 3

And, a = (8 + 2)/2

a = 10/2

a = 5

Thus,e = 3/5

Thus;

r = (3/5)p/(1 + (3/5) cosθ))

Multiply both numerator and denominator by 5;

r = 3p/(5 + 3 cosθ))

Now, using the vertex (2,0) and plugging it, we have;

2 = 3p/(5 + 3 cos0))

2 = 3p/(5 + 3(1))

2 = 3p/8

p = 16/3

Thus,the equation is;

r = 3(16/3)/(5 + 3 cosθ))

r = 16/(5 + 3 cosθ)

C) Since the directrix is x = p, then the function in the denominator would be cosine. This is because x = 4 which is greater than 0.

It means that there will be an addition sign in the denominator. We use the standard form of;

r = ep/(1 + e cosθ)

So, e = 2 and p = 1

Then;

r = (2 × 1)/(1 + 2 cosθ)

r = 2/(1 + 2 cosθ)

3 0
3 years ago
PLEASE HELP
Kipish [7]

Answer:

m=0.7404, b=3.9117m=0.7404,b=3.9117

y=0.7404x+3.9117y=0.7404x+3.9117

x=18x=18

y=0.7404(18)+3.9117=17.2389y=0.7404(18)+3.9117=17.2389

Residual

16-17.2389= -1.238916−17.2389=−1.2389

-

8 0
2 years ago
Read 2 more answers
Jaxson bought a pair of sunglasses online for $71. He used a coupon code to get a 20% discount. The website also applied a 5% pr
poizon [28]

Answer:

$17.75

Step-by-step explanation:

$71-($71×20%)

$71-$14.2

=$56.8

after coupon code

$56.8-($56.8×5%)

=$56.8-$2.84

=$53.96 about .

then applied a 5% processing fee online.

8 0
2 years ago
3xy - ² + 4x for x = -2, y = - and = 6?
Kitty [74]

Answer:

See below

Step-by-step explanation:

Not sure what you are asking....do you want to know what y is when x = -2   and the equation = 6 ?

3 xy^2 + 4x = 6         or is that    3 xy^(-2) + 4x = 6

Could use some serious editing of your question if you are able ....

7 0
1 year ago
2x + 3(x + 5) = 5(x – 3) why is it a no solution answer <br><br><br> 50 POINT!!!!!!!!!!!
Nesterboy [21]
2x +3x + 25 = 5x - 15
5x + 25 = 5x - 15
5x - 5x = -15 - 25
0 ≠ -35
6 0
2 years ago
Read 2 more answers
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