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Alex
3 years ago
6

Write the equation of the parabola in vertex form.vertex (3,2), point (2,-2)

Mathematics
1 answer:
kiruha [24]3 years ago
7 0

Answer:

y=-4(x-3)^2+2

Step-by-step explanation:

y=a(x-p)^2+q - equation of the parabola in vertex form

from vertex (3,2) we know that p=3, \ q=2

from point (2,-2) we know that x=2, \ y=-2

inserting p=3, q=2, x=2 and y=-2 to the equation y=a(x-p)^2+q, we calculate a

-2=a(2-3)^2+2\\ -2=a\cdot(-1)^2+2\\ -2=a\cdot1+2\\ -2=a+2\\ -2-2=a\\ -4=a\\ a=-4

insert a=-4, p=3 and q=2 to the equation

y=-4(x-3)^2+2

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(-1, -1.5)

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What is the surface area of the Triangular Prism rounded to the nearest tenth?
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Answer:

C. 43.6

Step-by-step explanation:

you need to take the area of each shape

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BRAINLYEST
iVinArrow [24]

Given:

The data set is

10, 10, 11, 12, 13, 13, 13, 14, 14, 15, 15, 15, 16, 17, 17, 17, 35

To find:

Effect on mean, median, range after removing the outlier, 35.

Solution:

We have, the data set

10, 10, 11, 12, 13, 13, 13, 14, 14, 15, 15, 15, 16, 17, 17, 17, 35

\text{Mean}=\dfrac{\text{Sum of observations}}{\text{Number of observations}}

\text{Mean}=\dfrac{10+10+11+12+13+13+13+14+14+15+15+15+16+17+17+17+35}{17}

\text{Mean}=\dfrac{257}{17}

\text{Mean}=15.117647

\text{Mean}\approx 15.12

Mean of the data set is 15.12.

Median=\dfrac{n+1}{2}\text{th term} because n=17, which is odd.

Median=\dfrac{17+1}{2}\text{th term}

Median=\dfrac{18}{2}\text{th term}

Median=9\text{th term}

Median=14

Median is 14.

Range=Maximum-Minimum

Range=35-10

Range=25

Range is 25.

After removing the outlier, 35, the data set is

10, 10, 11, 12, 13, 13, 13, 14, 14, 15, 15, 15, 16, 17, 17, 17

\text{Mean}=\dfrac{10+10+11+12+13+13+13+14+14+15+15+15+16+17+17+17}{16}

\text{Mean}=\dfrac{222}{16}

\text{Mean}=13.875

Mean of the new data set is 13.875, which is less than 15.12.

Median=\dfrac{\dfrac{n}{2}\text{th term}+(\dfrac{n}{2}+1)\text{th term}}{2} because n=16, which is even.

Median=\dfrac{\dfrac{16}{2}\text{th term}+(\dfrac{16}{2}+1)\text{th term}}{2}

Median=\dfrac{8\text{th term}+9\text{th term}}{2}

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Median=\dfrac{28}{2}

Median=14

New median is 14, which is same as original median.

Range=17-10

Range=7

So, the new range is 7 which is less than 25.

Therefore, the mean of the data set will decrease, the median of the data set will not change, the Range of the data set will decrease.

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