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REY [17]
2 years ago
11

Find an equation of a parabola with a vertex at the origin of directrix Y = -2.5

Mathematics
1 answer:
d1i1m1o1n [39]2 years ago
8 0

Answer:

y=\frac{1}{10}x^2

Step-by-step explanation:

Since the directrix is y=-2.5, it means the axis of the parabola is parallel to the y-axis.


Also, the vertex is at the origin so the parabola opens upwards.


The equation of a parabola with these properties is of the form x^2=4py, where |p|=2.5,that is the distance between the vertex and the directrix.


\Rightarrow p=-2.5\:or\:2.5.


Since the parabola opens upwards, we choose p=2.5.


The equation of the parabola now becomes,

x^2=4(2.5)y


\Rightarrow x^2=10y


Or

y=\frac{1}{10}x^2


See graph


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Step-by-step explanation:

Step 1

It is given that the grade(slope) is 4%. This means that for every 100 miles traveled, the elevation changes by 4 miles.

Step 2

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Please help with this me
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Answer:

3/5

Step-by-step explanation:

3 is the X and 5 is the Y add together you get 8                  

but the answer is 3/5 from point C to B

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3 years ago
With a little care, you can find the median and the quartiles from the histogram. what are these numbers? you can also find the
coldgirl [10]

Complete Question

The histogram from this question is shown on the first uploaded image

Answer:

The first quartile is  1st Q = 19^{th} girl (subject ) = 1 \serving\ of\ fruit\ per\ day

The median is   Median  = 38 ^{th} \ girl (subject) =  2 \serving\ of\ fruit\ per\ day

The third quartile  is 3rd Q =  56^{th} \  girl (subject) = 4 \serving\ of\ fruit\ per\ day  

The  mean is  \= x = 2.62

Step-by-step explanation:

From the question we are told that

   The total  number of girls is n =  74

Generally the median is mathematically represented as

       Median  =  \frac{\frac{n}{2}  +[ \frac{n}{2} + 1]  }{2}

So

          Median  =  \frac{\frac{74}{2}  +[ \frac{74}{2} + 1]  }{2}

=>         Median  =  \frac{37  +38 }{2}

=>         Median  =37.5 \  girl    

From the histogram 37.5 \approx 38^{th} \ girl fall under 2 fruits per day

Generally the first quartile is mathematically represented as

      1st \ Q =  \frac{\frac{n}{4} + [\frac{n}{4} + 1]  }{2}

=>    1st \ Q =  \frac{\frac{74}{4} + [\frac{74}{4} + 1]  }{2}

=>     1st \ Q = 19 \  girl

From the histogram 19^{th}girl fall under 1 fruit per day

 Generally the third quartile is mathematically represented as

     3rd\  Q =  \frac{\frac{n}{2}  + n }{2}

=>    3rd\  Q =  \frac{\frac{74}{2}  + 74 }{2}

=>    3rd\  Q =  55.5

From the histogram 55.5 \approx 56^{th} \ girl fall under 4 fruits per day

Generally from the histogram table the frequency  [number of subjects (girls) ]  and the servings of fruit per day can be represented as

                                                                                                               Total

x(servings per day )        0     1     2     3     4     5    6     7      8    

f (number of subjects )   15    11   15     11    8     5    3     3      3    \sum f  =  74

xf                                       0    11    30   33   32  25   18   21     24    \sum xf =  194

Generally the mean is mathematically represented as

      \= x = \frac{1}{ \sum f}  * [\sum xf]

=>     \= x = \frac{1}{ 74}  *194

=>      \= x = 2.62

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Step-by-step explanation:

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