Please help me out with this thingyyy!!!!!

Mathematics

1 answer:

SIZIF [17.4K]3 years ago

5 0

Answer:

1. 18

2. 8

Step-by-step explanation:

the mean is calculated by:

total / number of values

the current total is

10 + 14 + 8 + 16 + 12 = 60

now when we add another number there will be 6 numbers and we want the mean to be 13 so:

total / 6 = 13

total = 13 × 6

total = 78

but our current total is 60

so the missing number is 78 - 60 = 18

for part 2:

if we remove a number there will be 5 values and we want the mean to be 14 so:

total / 5 = 14

total = 14 × 5

total = 70

but we have the total of 6 numbers as 78 so we have to remove 78 - 70 = 8

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Find the point P on the line y=2x that is closest to the point (20,0) .what is the least distance between pans (20,0)?

Vsevolod [243]

The closest point on a line, to another point, will be a point that's on a normal of that line, or a line that is perpendicular to it, notice picture below

so, y = 2x, has a slope of 2, a perpendicular line to it, will have a slope of negative reciprocal that, or $\bf 2\qquad negative\implies -2\qquad reciprocal\implies \cfrac{1}{-2}\implies -\cfrac{1}{2}$

so, we know that line passes through the point 20,0, and has a slope of -1/2

if we plug that in the point-slope form, we get $\bf y-0=-\cfrac{1}{2}(x-20)\implies y=-\cfrac{1}{2}x+10$

now, the point that's on 2x and is also on that perpendicular line, is the closest to 20,0 from 2x, thus, is where both graphs intersect, as you can see in the graph

thus $\bf 2x=-\cfrac{1}{2}x+10$ solve for "x'

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not sure on the 2nd part, but sounds like, what's the distance from that point to 20,0, well, if that's the case, just use the distance equation

$\bf \textit{distance between 2 points}\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
&({{ \square }}\quad ,&{{ \square }})\quad 
% (c,d)
&({{ \square }}\quad ,&{{ \square }})
\end{array}\qquad 
% distance value
d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2}$