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Amiraneli [1.4K]
2 years ago
15

Find the answer for the angles and give a reason for your answer

Mathematics
1 answer:
Andreas93 [3]2 years ago
5 0

Answer:

each piece combined= 180

do 180- the # thats next to another

Step-by-step explanation:

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Find all points on the portion of the plane x+y+z=5 in the first octant at which f(x, y, z) = xy2z2 has a maximum value.
irina1246 [14]
Lagrange multipliers:

L(x,y,z,\lambda)=xy^2z^2+\lambda(x+y+z-5)

L_x=y^2z^2+\lambda=0
L_y=2xyz^2+\lambda=0
L_z=2xy^2z+\lambda=0
L_\lambda=x+y+z-5=0

\lambda=-y^2z^2=-2xyz^2=-2xy^2z

-y^2z^2=-2xyz^2\implies y=2x (if y,z\neq0)

-y^2z^2=-2xy^2z\implies z=2x (if y,z\neq0)

-2xyz^2=-2xy^2z\implies z=y (if x,y,z\neq0)

In the first octant, we assume x,y,z>0, so we can ignore the caveats above. Now,

x+y+z=5\iff x+2x+2x=5x=5\implies x=1\implies y=z=2

so that the only critical point in the region of interest is (1, 2, 2), for which we get a maximum value of f(1,2,2)=16.

We also need to check the boundary of the region, i.e. the intersection of x+y+z=5 with the three coordinate axes. But in each case, we would end up setting at least one of the variables to 0, which would force f(x,y,z)=0, so the point we found is the only extremum.
4 0
3 years ago
Edgar is scuba diving 50 feet below the water. He is swimming to the surface at a rate of 3 feet per second. Write an equation t
____ [38]

Answer:

I know this is late but the actual answer is d=3s+-50

Step-by-step explanation:

The reason is because he is swimming down, so yeah.

5 0
3 years ago
5 less than the quotient of a number y and 2
Marta_Voda [28]
Quotient means division....less then means subtract
(y/2) - 5
5 0
3 years ago
write the equation of a line in slope intercept form that is perpendicular to the line y = 3/5 x - 1 and passes through the poin
Simora [160]
Can you write complete question
4 0
3 years ago
Q3: Identify the graph of the equation and write and equation of the translated or rotated graph in general form. (Picture Provi
natta225 [31]

Answer:

b. circle; 2(x')^2+2(y')^2-5x'-5\sqrt{3}y'-6 =0

Step-by-step explanation:

The given conic has equation;

x^2-5x+y^2=3

We complete the square to obtain;

(x-\frac{5}{2})^2+(y-0)^2=\frac{37}{4}

This is a circle with center;

(\frac{5}{2},0)

This implies that;

x=\frac{5}{2},y=0

When the circle is rotated through an angle of \theta=\frac{\pi}{3},

The new center is obtained using;

x'=x\cos(\theta)+y\sin(\theta) and y'=-x\sin(\theta)+y\cos(\theta)

We plug in the given angle with x and y values to get;

x'=(\frac{5}{2})\cos(\frac{\pi}{3})+(0)\sin(\frac{\pi}{3}) and y'=--(\frac{5}{2})\sin(\frac{\pi}{3})+(0)\cos(\frac{\pi}{3})

This gives us;

x'=\frac{5}{4} ,y'=\frac{5\sqrt{3} }{4}

The equation of the rotated circle is;

(x'-\frac{5}{4})^2+(y'-\frac{5\sqrt{3} }{4})^2=\frac{37}{4}

Expand;

(x')^2+(y')^2-\frac{5\sqrt{3} }{2}y'-\frac{5}{2}x'+\frac{25}{4} =\frac{37}{4}

Multiply through by 4; to get

4(x')^2+4(y')^2-10\sqrt{3}y'-10x'+25 =37

Write in general form;

4(x')^2+4(y')^2-10x'-10\sqrt{3}y'-12 =0

Divide through by 2.

2(x')^2+2(y')^2-5x'-5\sqrt{3}y'-6 =0

8 0
3 years ago
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