<img src="https://tex.z-dn.net/?f=%20%5Cfrac%7B4%7D%7B3%7D%20%20%3D%20%20%5Cfrac%7Bx%7D%7B6%7D%20" id="TexFormula1" title=" \fra

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Lynna [10]

3 years ago

c{4}{3} = \frac{x}{6} " alt=" \frac{4}{3} = \frac{x}{6} " align="absmiddle" class="latex-formula">

Mathematics

1 answer:

timurjin [86]3 years ago

5 0

$\bf \cfrac{4}{3}=\cfrac{x}{6}\implies \stackrel{\textit{cross-multiplying}}{(6)4=(3)x}\implies 24=3x\implies \cfrac{24}{3}=x\implies 8=x$

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WILL GIVE BRAINLIEST IF ANSWERED NOW

iren [92.7K]

Answer:

y=3x-7

Step-by-step explanation:

lines are parallel hence gradient from the equation in question is the same as the gradient of the equation to be found.. comparing to y=mx+c, eq in question has grad 3... from the formula y-y1=m(x-x1) where (x1,y1) is equal to the point in question

5 0

3 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 $(2,10,\pm2\sqrt5)$ .

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3 years ago

1.) Identify the domain of the equation y = x2 − 6x + 1.

nikdorinn [45]

1. "All real numbers" is the one domain of the equation y = x2 − 6x + 1 among the following choices given in the question. The correct option among all the options that are given in the question is the fourth option or option "D".

2. "Left by 4 units" is the one among the following choices given in the question that gives the direction and by how many units f(x) be shifted to obtain g(x). The correct option is option "A".

8 0

3 years ago

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Show how you solve the following two equations:<br> x – 15 = 32<br> x – 7.2 = 23.1

Lapatulllka [165]

Х - 15 = 32
х = 32 + 15
x = 47 (answer)
-----------------------
47 - 15 = 32
32 = 32

х - 7.2 = 23,1
х = 23,1 + 7.2
х = 30,3 (answer)
---------------------------
30,3 - 7,2 = 23,1
23,1 = 23,1

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3 years ago

Rodrigo needs to solve the equation x2 – 4x – 18 = 0 by completing the square. Which pair of steps is the most efficient way to

maksim [4K]

Answer:

B.x2-4x=18

x2-4x+4=18+4

Step-by-step explanation:

When you complete the square your quadratic equation must be written in the standard form which is ax^2+bx+c.

First you are going to want to move your c term to the right (in this case move -18 to the right by adding 18 to both sides). This will get you x^2-4x=18. Now you are going to need to complete the square. To complete the square you divide the number in the bx term (in this case -4) by 2 and then square it. (-2^2=4 since a negative times a negative equals a positive). Now that you have 4 you are going to add it to both sides to get x2-4x+4=18+4.

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3 years ago

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