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photoshop1234 [79]
3 years ago
15

What equation in slope intercept form represents the line that passes through the two points (2,5),(9,2)

Mathematics
2 answers:
EastWind [94]3 years ago
7 0
Y = -3/7x + 5 6/7
hope it helps!
Lynna [10]3 years ago
5 0
(7,8) that's your answer because that's what in between 5 and 9
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The sum of five consecutive integers is 55. Find the integers.​
liubo4ka [24]

Answer:

9, 10, 11, 12, 13

Step-by-step explanation:

(x-2)+(x-1)+x+(x+1)+(x+2) = 55

5x = 55

x = 11

8 0
3 years ago
31,059 is rounded by ten thousands in math
kifflom [539]
This would be 30,000
8 0
3 years ago
-3 + (-5) tjjv5grjvkjgkv
mash [69]

Answer

the answer is 8 so your welcome

8 0
2 years ago
Use lagrange multipliers to find the point on the plane x â 2y + 3z = 6 that is closest to the point (0, 2, 4).
Arisa [49]
The distance between a point (x,y,z) on the given plane and the point (0, 2, 4) is

\sqrt{f(x,y,z)}=\sqrt{x^2+(y-2)^2+(z-4)^2}

but since \sqrt{f(x,y,z)} and f(x,y,z) share critical points, we can instead consider the problem of optimizing f(x,y,z) subject to x-2y+3z=6.

The Lagrangian is

L(x,y,z,\lambda)=x^2+(y-2)^2+(z-4)^2+\lambda(x-2y+3z-6)

with partial derivatives (set equal to 0)

L_x=2x+\lambda=0\implies x=-\dfrac\lambda2
L_y=2(y-2)-2\lambda=0\implies y=2+\lambda
L_z=2(z-4)+3\lambda=0\implies z=4-\dfrac{3\lambda}2
L_\lambda=x-2y+3z-6=0\implies x-2y+3z=6

Solve for \lambda:

x-2y+3z=-\dfrac\lambda2-2(2+\lambda)+3\left(4-\dfrac{3\lambda}2\right)=6
\implies2=7\lambda\implies\lambda=\dfrac27

which gives the critical point

x=-\dfrac17,y=\dfrac{16}7,z=\dfrac{25}7

We can confirm that this is a minimum by checking the Hessian matrix of f(x,y,z):

\mathbf H(x,y,z)=\begin{bmatrix}f_{xx}&f_{xy}&f_{xz}\\f_{yx}&f_{yy}&f_{yz}\\f_{zx}&f_{zy}&f_{zz}\end{bmatrix}=\begin{bmatrix}2&0&0\\0&2&0\\0&0&2\end{bmatrix}

\mathbf H is positive definite (we see its determinant and the determinants of its leading principal minors are positive), which indicates that there is a minimum at this critical point.

At this point, we get a distance from (0, 2, 4) of

\sqrt{f\left(-\dfrac17,\dfrac{16}7,\dfrac{25}7\right)}=\sqrt{\dfrac27}
8 0
3 years ago
A goat is tethered to a stake in the ground with a 5-m rope. The goat can graze to the full length of the rope a full 360 degree
Nina [5.8K]
The length of the rope in this case becomes the radius of the circle that the goat is able to graze. The area of the circle is calculated through the equation,
                            A = πr²
Substituting,
                              A = π(5m)² = 78.54 m²
Thus, the area that the goat is able to graze is equal to 78.54 m². 
5 0
3 years ago
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