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3 years ago

Define a Variable in a equation

1 answer:

3 0

A variable is a symbol that’s used in a number. It typically uses a variation of letters such as x,y,etc. for instance 3x=6

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Find the maximum and minimum values of the function f(x,y)=2x2+3y2−4x−5 on the domain x2+y2≤100. The maximum value of f(x,y) is:

ryzh [129]

First find the critical points of f :

$f(x,y)=2x^2+3y^2-4x-5=2(x-1)^2+3y^2-7$

$\dfrac{\partial f}{\partial x}=2(x-1)=0\implies x=1$

$\dfrac{\partial f}{\partial y}=6y=0\implies y=0$

so the point (1, 0) is the only critical point, at which we have

$f(1,0)=-7$

Next check for critical points along the boundary, which can be found by converting to polar coordinates:

$f(x,y)=f(10\cos t,10\sin t)=g(t)=295-40\cos t-100\cos^2t$

Find the critical points of g :

$\dfrac{\mathrm dg}{\mathrm dt}=40\sin t+200\sin t\cos t=40\sin t(1+5\cos t)=0$

$\implies\sin t=0\text{ OR }1+5\cos t=0$

$\implies t=n\pi\text{ OR }t=\cos^{-1}\left(-\dfrac15\right)+2n\pi\text{ OR }t=-\cos^{-1}\left(-\dfrac15\right)+2n\pi$

where n is any integer. We get 4 critical points in the interval [0, 2π) at

$t=0\implies f(10,0)=155$

$t=\cos^{-1}\left(-\dfrac15\right)\implies f(-2,4\sqrt6)=299$

$t=\pi\implies f(-10,0)=235$

$t=2\pi-\cos^{-1}\left(-\dfrac15\right)\implies f(-2,-4\sqrt6)=299$

So f has a minimum of -7 and a maximum of 299.

4 0

3 years ago

Substitution for: X-5y=10 2x-10y=20

sergey [27]

Since you need an isolated variable to use the substitution method, we need to re-arrange one of the equations. This will probably be easiest to do with the first one.
Add 5y to both sides of the first equation.
x=10+5y
Now, in the second equation, put in 10+5y in any spot that has an x.
2(10+5y)-10y=20
Distribute the 2 to both numbers in the parenthesis.
20+10y-10y=20
Combine like terms.
20=20
This means that the two equations are actually the same. You can see this if you multiply the whole first equation by 2
2(x-5y=10)
2x-10y=20, which is the same as the second equation. Therefore, the two equations are actually the same one.

5 0

3 years ago

Para reformar la cocina de su caja Berta compro la semana pasada 2 cajas de plaquetas para el suelo y 4 de azulejos para la pare

Anvisha [2.4K]

Answer:

Caja de plaquetas = x = 30 €

Caja de azulejos = y = 35 €

Step-by-step explanation:

Deje que el costo de

Caja de plaquetas = x

Cuadro de mosaico = y

Por Berta

Para reformar su cocina, Berta compró la semana pasada 2 cajas de baldosas de plaquetas para el suelo y 4 cajas de baldosas para la pared por 200 €.

2x + 4y = 200 ...... Ecuación 1

Hoy

Hoy compré 2 cajas más de plaquetas y otras 2 de tejas por 130 €.

2x + 2y = 130 ..... Ecuación 2

Resolvemos usando el método de Eliminación

2x + 4y = 200 ...... Ecuación 1

2x + 2y = 130 ..... Ecuación 2

Restar la ecuación 2 de 1

2 años = 70

y = 70/2

y = 35 €

Resolviendo para x

2x + 4y = 200 ...... Ecuación 1.

2x + 4 × 35 = 200

2x + 140 = 200

2x = 200 - 140

2x = 60

x = 60/2

x = 30 €

el costo de

Caja de plaquetas = x = 30 €

Caja de azulejos = y = 35 €

6 0

3 years ago

Andre and Ronnie used a stopwatch to record the amount of time it took a golf ball to roll down a three-story ramp. Andre's ball

iren [92.7K]

Answer:

The answer would be A

Step-by-step explanation:

This is because when you take 1.625 it rounds back to 6 because 2 isnt more then 5 or 5 so it wouldn't round just like 1.635. I believe thats the answer im not positive

5 0

3 years ago

Read 2 more answers

Please help me with this problem

Maru [420]

Answer:

g(x) = -5x

Step-by-step explanation:

If the point from f(x) is plotted using the slope, the coordinate would be located at (1, 5) since the slope of 5x tells us we go up 5 units from the origin and over 1 unit to the right. That point will be reflected through the x-axis to land at (1, -5). That means that the equation of the new line would be

g(x) = -5x

7 0

3 years ago

Read 2 more answers

Define a Variable in a equation​

Define a Variable in a equation