Find the median of the data 10, 15, 6, 18,16

Mathematics

1 answer:

Ira Lisetskai [31]2 years ago

7 0

Median is 15

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Hitman42 [59]

ANSWER

$( {y - 8)}^{2} = - 28(x + 5)$

EXPLANATION

The given parabola has directrix x=2.

This implies that, the parabola is opens in the direction of the negative x-axis because it must open in a negative direction to the directrix.

The equation of such parabola is of the form:

$( {y - k)}^{2} = 4p(x - h)$

where (h,k)=(-5,8) is the vertex.

$|p| = | - 2 - 5| = 7$

$p = \pm7$

But the parabola opens to the left.

p=-7

The equation now becomes

$( {y - 8)}^{2} = 4( - 7)(x - - 5)$

$( {y - 8)}^{2} = - 28(x + 5)$

4 0

3 years ago

In right angle ABC, angle C is the right angle, AC = 3 and AB = 5. Point D is on hypotenuse AB, such that DB = 1. Find the area

Ivan

Look at the picture.

To find the area of triangle DBC we need to find its base, x, and its height, h.

Triangle ABC is a right triangle, so using the Pythagorean theorem we can find x.
$(\hbox{one leg})^2+(\hbox{the other leg})^2=(\hbox{the hypotenuse})^2 \\
3^2+x^2=5^2 \\
9+x^2=25 \\
x^2=25-9 \\
x^2=16 \\
x=\sqrt{16} \\
x=4$

Now look at triangles ABC and DBH. They both are right triangles and have the same angle α. That means they're similar and their corresponding sides are proportional. The ratio of the side opposite to angle α to the hypotenuse is the same in both triangles - so the ratio of h to 1 is the same as the ratio of 3 to 5.
$\frac{h}{1}=\frac{3}{5} \\
h=\frac{3}{5}$

The base x is 4, the height h is 3/5. Calculate the area:

$A=\frac{xh}{2}=\frac{4 \times \frac{3}{5}}{2}=2 \times \frac{3}{5}=\frac{6}{5}$

The area of triangle DBC is 6/5.