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3 years ago

(-3,2) 90 degrees about the origin clockwise

Mathematics

1 answer:

drek231 [11]3 years ago

8 0

For 90° clockwise rotation, (x, y) becomes (y, -x).

Your rotated point is (2, 3).

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This extreme value problem has a solution with both a maximum value and a minimum value. use lagrange multipliers to find the ex

noname [10]

$L(x,y,z,\lambda)=10x+10y+2z+\lambda(5x^2+5y^2+2z^2-42)$

$L_x=10+10\lambda x=0\implies1+\lambda x=0$

$L_y=10+10\lambda y=0\implies1+\lambda y=0$

$L_z=2+4\lambda z=0\implies1+2\lambda z=0$

$L_\lambda=5x^2+5y^2+2z^2-42=0$

$\begin{cases}L_x=0\\L_y=0\\L_z=0\end{cases}\implies1+\lambda x=1+\lambda y=1+2\lambda z=0\implies x=y=2z$

$5x^2+5y^2+2z^2=5(2z)^2+5(2z)^2+2z^2=42z^2=42\implies z^2=1$

$z^2=1\implies z=\pm1\implies x=y=\pm2$

There are two critical points, at which we have

$f\left(2,2,1\right)=42\text{ (a maximum value)}$

$f\left(-2,-2,-1\right)=-42\text{ (a minimum value)}$

3 0

3 years ago

Find the area of the triangle

kupik [55]

Area = 1/2 * base * height
= 1/2 * 20 * 6
= 1/2 * 120
= 60 ft^2

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2 years ago

What is the atomic number of an atom?

Anastasy [175]

Answer:

the number of protons in the nuclues of an atom

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2 years ago

What is the LCM of 24 and 32?

Sphinxa [80]

96 is the answer i beilive

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3 years ago

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A company has 2 photocopy machines. The probability that machine A will breakdown on a given day is 2%. The probability that mac

pickupchik [31]

Answer: 95.55%

--------------------------------

Work Shown:

A = event that copier A breaks down
B = event that copier B breaks down

P(A) = probability that copier A breaks down
P(A) = 2% = 0.02

P(B) = probability that copier B breaks down
P(B) = 2.5% = 0.025

P(neither break down) = (1-P(A))*(1-P(B))
P(neither break down) = (1-0.02)*(1-0.025)
P(neither break down) = 0.9555
P(neither break down) = 95.55%

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2 years ago

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