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Nutka1998 [239]

2 years ago

7

Explain how to determine which method you would use to solve various systems. Explain what characteristics a system has that mak

es it easier to solve using one method versus another.

1 answer:

OlgaM077 [116]2 years ago

5 0

Answer:

Step-by-step explanation:

The best method I know is elimination, i explained it in the chat in the prev question. It's applicable in any scenario.

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The perimeter of a rectangle is 40 cm. The length is 14 cm. Let x = width of the rectangle. Ravi says he can find the width usin

Usimov [2.4K]

Answer:

Divide both sides by 2

Step-by-step explanation:

We have the equation

2(x + 14) = 40

We divide both sides by 2

2(x + 14) = 40/2

x + 14 = 20

x = 20 - 14

x = 6

Therefore, the most helpful first step for solving Ravi's equation is: Divide both sides by 2

3 0

2 years ago

The ratio between diameter and dircumference of circle is ......................

marysya [2.9K]

Answer:

The ratio of the circumference of a circle to its diameter and is called π (Pi).

Step-by-step explanation:

7 0

1 year ago

What is the solution of the system x - 3y= -13

n200080 [17]

Answer:

There should be one more equation

Step-by-step explanation:

7 0

2 years ago

Use Lagrange multipliers to find the maximum and minimum values of (i) f(x,y)-81x^2+y^2 subject to the constraint 4x^2+y^2=9. (i

sp2606 [1]

i. The Lagrangian is

$L(x,y,\lambda)=81x^2+y^2+\lambda(4x^2+y^2-9)$

with critical points whenever

$L_x=162x+8\lambda x=0\implies2x(81+4\lambda)=0\implies x=0\text{ or }\lambda=-\dfrac{81}4$

$L_y=2y+2\lambda y=0\implies2y(1+\lambda)=0\implies y=0\text{ or }\lambda=-1$

$L_\lambda=4x^2+y^2-9=0$

If $x=0$ , then $L_\lambda=0\implies y=\pm3$ .
If $y=0$ , then $L_\lambda=0\implies x=\pm\dfrac32$ .
Either value of $\lambda$ found above requires that either $x=0$ or $y=0$ , so we get the same critical points as in the previous two cases.

We have $f(0,-3)=9$ , $f(0,3)=9$ , $f\left(-\dfrac32,0\right)=\dfrac{729}4=182.25$ , and $f\left(\dfrac32,0\right)=\dfrac{729}4$ , so $f$ has a minimum value of 9 and a maximum value of 182.25.

ii. The Lagrangian is

$L(x,y,z,\lambda)=y^2-10z+\lambda(x^2+y^2+z^2-36)$

with critical points whenever

$L_x=2\lambda x=0\implies x=0$ (because we assume $\lambda\neq0$ )

$L_y=2y+2\lambda y=0\implies 2y(1+\lambda)=0\implies y=0\text{ or }\lambda=-1$

$L_z=-10+2\lambda z=0\implies z=\dfrac5\lambda$

$L_\lambda=x^2+y^2+z^2-36=0$

If $x=y=0$ , then $L_\lambda=0\implies z=\pm6$ .
If $\lambda=-1$ , then $z=-5$ , and with $x=0$ we have $L_\lambda=0\implies y=\pm\sqrt{11}$ .

We have $f(0,0,-6)=60$ , $f(0,0,6)=-60$ , $f(0,-\sqrt{11},-5)=61$ , and $f(0,\sqrt{11},-5)=61$ . So $f$ has a maximum value of 61 and a minimum value of -60.

5 0

2 years ago

Which statement is true about the circumference of a circle? The circumference is equal to the radius of the circle. The circumf

Irina18 [472]

<h3>The true statement about circumference of a circle is: circumference is found by multiplying Pi by the diameter</h3>

<em><u>Solution:</u></em>

<em><u>The circumference of a circle is given as:</u></em>

$\text{circumference } = 2 \pi r$

Where,

"r" is the radius of circle

We know that,

$diameter = 2 \times radius\\\\d = 2 \times r\\\\d = 2r$

<em><u>Thus the circumference can also written as:</u></em>

$\text{circumference } = 2 \pi r\\\\\text{circumference } = \pi \times d$

Thus, the circumference is found by multiplying Pi by the diameter is correct statement

7 0

2 years ago

Read 2 more answers