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lbvjy [14]
2 years ago
14

Write the equation of an ellipse with center (-2,-3), vertical major axis of length 14, and minor axis of

Mathematics
1 answer:
Tems11 [23]2 years ago
5 0

Step-by-step explanation:

Since we have a vertical major axis, our ellipse is vertical.

The equation of a vertical ellipse is

\frac{(y - k) {}^{2} }{ {a}^{2} }  +  \frac{(x - h) {}^{2} }{ {b}^{2} }  = 1

where

(h,k) is the center

a is the semi major axis,

b is the semi minor axis

First, let plug in our center

\frac{(y + 3) {}^{2} }{ {a}^{2} }  + \frac{(x + 2) {}^{2} }{ {b}^{2} }  = 1

Semi means half, so

a is half of 14 which is 7

B is half of 8, which is 4.

\frac{(y + 3) {}^{2} }{49}  +  \frac{(x + 2) {}^{2} }{16}  = 1

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Substitute for x+2y=12 and x=y-12<br><br> PLEASE HELP !
yan [13]

Answer:

x = -4, y = 8

Step-by-step explanation:

y - 12 + 2y = 12

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The Robotics Manufacturing Company operates an equipment repair business where emergency jobs arrive randomly at the rate of thr
cluponka [151]

Answer:

The correct answer is:

  • \lambda=0.375 \ jobs \ per \ hour
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Step-by-step explanation:

The given values are:

Service time varies,

Repair time = 2 hours

Standard deviation = 1.5 hours

Robotics uses per hour cost,

= $35

Company's cost per hour,

= $28

(a)

⇒ Arrival rate = Jobs per hours

then,

                       = \frac{8 \ hours}{3 \ jobs}

                       = 2.666 \ hours \ per \ job

The jobs per hour will be:

⇒  \lambda=\frac{1}{2.666}

       =0.375

(b)

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7 0
3 years ago
A plane flew 360km in 3 hrs when flying with the wind.With no change in the wind,the return trip took 4 hrs.Find the speed of th
morpeh [17]
Speed of the plane: 250 mph
Speed of the wind: 50 mph
Explanation:
Let p = the speed of the plane
and w = the speed of the wind
It takes the plane 3 hours to go 600 miles when against the headwind and 2 hours to go 600 miles with the headwind. So we set up a system of equations.
600
m
i
3
h
r
=
p
−
w
600
m
i
2
h
r
=
p
+
w
Solving for the left sides we get:
200mph = p - w
300mph = p + w
Now solve for one variable in either equation. I'll solve for x in the first equation:
200mph = p - w
Add w to both sides:
p = 200mph + w
Now we can substitute the x that we found in the first equation into the second equation so we can solve for w:
300mph = (200mph + w) + w
Combine like terms:
300mph = 200mph + 2w
Subtract 200mph on both sides:
100mph = 2w
Divide by 2:
50mph = w
So the speed of the wind is 50mph.
Now plug the value we just found back in to either equation to find the speed of the plane, I'll plug it into the first equation:
200mph = p - 50mph
Add 50mph on both sides:
250mph = p
So the speed of the plane in still air is 250mph.
6 0
2 years ago
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