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2 years ago

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Can somebody help me ???

1 answer:

Bezzdna [24]2 years ago

5 0

Y=-1/3x-.75

why:
y-intercept is -.75 five or take.
slope is down 1, over 3
since line (going left to right) is going down, it’s negative

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What is the area of the composite figure in problem 3?

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trapazoid

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3 years ago

What is the distance between the points (–3, 4) and (–7, 4)?

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Answer:

$d = \sqrt{( - 7 + 3) {}^{2} + (4 - 4) {}^{2} } \\ d = \sqrt{16} \\ d = 4$

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I have 4 congruent sides, but my diagonals are not congruent. What is my most specific classification?

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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

3 years ago

In August, Cory begins school shopping for his triple daughters. Part A One day, he bought 10 pairs of socks for $2.59 each for

Dovator [93]

Answer: $36.69

Step-by-step explanation:

Okay, so let's first write the equation:

2.59*10 + 3d = 135.97

Now, let's work on isolating d by first simplifying the equation:

25.9 + 3d = 135.97

25.9 + 3d - 25.9 = 135.97 - 25.9

3d = 110.07

3d/3 = 110.07/3

d = 36.69

Okay, now let's check:

2.59*10 + 3*36.69 = 135.97

25.9 + 110.07 = 135.97

135.97 = 135.97

Okay, so so it costs $36.69 per pair of shoe.

5 0

2 years ago