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kykrilka [37]
3 years ago
9

Which of the following graphs represents y=x-2

Mathematics
1 answer:
spayn [35]3 years ago
8 0

Answer:

graph 2

Step-by-step explanation:

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Am trying to find the value of r<br> 1/r + 2/1-r = 4/r^2
Mashcka [7]
<span>1/r + 2/1-r = 4/r^2

1-r+2r/r(1-r)=4/r^2
(1+r)/r(1-r)=4/r^2   cancle r both side

1+r/1-r=4/r

cross multiply 
r+r^2=4-4r
r^2+4r+r-4=0
r^2+5r-4=0
r^2+4r+r-4=0
solve it for r factor it...



</span>
6 0
2 years ago
Find the point(s) on the surface z^2 = xy 1 which are closest to the point (7, 11, 0)
leonid [27]
Let P=(x,y,z) be an arbitrary point on the surface. The distance between P and the given point (7,11,0) is given by the function

d(x,y,z)=\sqrt{(x-7)^2+(y-11)^2+z^2}

Note that f(x) and f(x)^2 attain their extrema, if they have any, at the same values of x. This allows us to consider the modified distance function,

d^*(x,y,z)=(x-7)^2+(y-11)^2+z^2

So now you're minimizing d^*(x,y,z) subject to the constraint z^2=xy. This is a perfect candidate for applying the method of Lagrange multipliers.

The Lagrangian in this case would be

\mathcal L(x,y,z,\lambda)=d^*(x,y,z)+\lambda(z^2-xy)

which has partial derivatives

\begin{cases}\dfrac{\mathrm d\mathcal L}{\mathrm dx}=2(x-7)-\lambda y\\\\\dfrac{\mathrm d\mathcal L}{\mathrm dy}=2(y-11)-\lambda x\\\\\dfrac{\mathrm d\mathcal L}{\mathrm dz}=2z+2\lambda z\\\\\dfrac{\mathrm d\mathcal L}{\mathrm d\lambda}=z^2-xy\end{cases}

Setting all four equation equal to 0, you find from the third equation that either z=0 or \lambda=-1. In the first case, you arrive at a possible critical point of (0,0,0). In the second, plugging \lambda=-1 into the first two equations gives

\begin{cases}2(x-7)+y=0\\2(y-11)+x=0\end{cases}\implies\begin{cases}2x+y=14\\x+2y=22\end{cases}\implies x=2,y=10

and plugging these into the last equation gives

z^2=20\implies z=\pm\sqrt{20}=\pm2\sqrt5

So you have three potential points to check: (0,0,0), (2,10,2\sqrt5), and (2,10,-2\sqrt5). Evaluating either distance function (I use d^*), you find that

d^*(0,0,0)=170
d^*(2,10,2\sqrt5)=46
d^*(2,10,-2\sqrt5)=46

So the two points on the surface z^2=xy closest to the point (7,11,0) are (2,10,\pm2\sqrt5).
5 0
3 years ago
R’(-1, 9) is the image of R after a reflection in the x-axis. What are the coordinates of R?
xz_007 [3.2K]

Answer:

<h3>            R(-1, -9)</h3>

Step-by-step explanation:

When we reflect over x-axis then the x-coordinate doesn't change and the y-coordinate changes its sign

in means  if R = (x, y) then R' = (x, -y)

so we have:

x = -1    and      -y = 9

                        y = -9

which gives R = (-1, -9)

6 0
3 years ago
Write the slope-intercept form of the equation of the line described by (−1, −1), parallel to y = −2x − 4
LuckyWell [14K]

Answer:

y = -2x - 3

Step-by-step explanation:

Slope intercept form of line is

y = mx + c

where

m is the slope and c is the y intercept

________________________________________

Given that line

y = −2x − 4

comparing it with y = mx + c

m = -2 and c = -4

Thus, slope of this line is -2

we also know that when two lines are parallel then their slopes are same

thus, slope of required line will be m = -2

___________________________________________

now let the equation of line passing through (-1,-1) be

y = mx + c

we have found m to be -2

using this in above equation we have

y = -2x + c

since (-1,-1) passes through the above line using x = -1 and y = -1

we have

-1 = -2*-1 + c

-1 = 2 + c

c = -1 - 2 = -3

using c = -3 in y = -2x + c

we have

equation of line as

y = -2x - 3 in slope intercept form.

7 0
2 years ago
What is 65.97 rounded to the nearest square inch
ss7ja [257]

Answer:

66

Step-by-step explanation:

have a great day

3 0
2 years ago
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