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2 years ago

6

find the measure of the side of the right triangle whose length is designated by a lowercase letter. Round answers to the neares

t whole number.

1 answer:

mario62 [17]2 years ago

8 0

Ah yes, math, I believe the answer you are looking for, my young scholar, is A

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Use lagrange multipliers to find the point on the plane x − 2y + 3z = 6 that is closest to the point (0, 2, 5).

horsena [70]

Lagrangian:

$L(x,y,z,\lambda)=x^2+(y-2)^2+(z-5)^2+\lambda(x-2y+3z-6)$

where the function we want to minimize is actually $\sqrt{x^2+(y-2)^2+(z-5)^2}$ , but it's easy to see that $\sqrt{f(\mathbf x)}$ and $f(\mathbf x)$ have critical points at the same vector $\mathbf x$ .

Derivatives of the Lagrangian set equal to zero:

$L_x=2x+\lambda=0\implies x=-\dfrac\lambda2$
$L_y=2(y-2)-2\lambda=0\implies y=2+\lambda$
$L_z=2(z-5)+3\lambda=0\implies z=5-\dfrac{3\lambda}2$
$L_\lambda=x-2y+3z-6=0$

Substituting the first three equations into the fourth gives

$-\dfrac\lambda2-2(2+\lambda)+3\left(5-\dfrac{3\lambda}2\right)=6$
$11-7\lambda=6\implies \lambda=\dfrac57$

Solving for $x,y,z$ , we get a single critical point at $\left(-\dfrac5{14},\dfrac{19}7,\dfrac{55}{14}\right)$ , which in turn gives the least distance between the plane and (0, 2, 5) of $\dfrac5{\sqrt{14}}$ .

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3 years ago

Find the first and second derivative of the function defined by the parametric equation.

Sergeu [11.5K]

Answer:

Step-by-step explanation:

Given two parametric equations $x(t)$ and $y(t)$ , the first derivative can be found using the following equation:

$\frac{dy}{dx} = \frac{\frac{dy}{dt}}{\frac{dx}{dt}}$

In this problem, $x(t) = 3e$ and $y(t) = 3^{3t} - 1$ . Finding the derivative of each of these functions with respect to $t$ gives us the following:

$\frac{dx}{dt} = 0$

$\frac{dy}{dt} = 3^{3t + 1}\log{3}$

Because $\frac{dx}{dt} = 0$ , that means the function is a vertical line and has an infinite first derivative.

6 0

3 years ago

What is 591.3 divided by 29?

vaieri [72.5K]

The answer is <span>20.3896551724</span>

6 0

3 years ago

Read 2 more answers

Two hiking groups made the purchases shown below. What is the cost of each item. GROUP 1: 6 muffins, 12 granola bars, Total=$26.

stepladder [879]

Answer:

Price of each muffin = $1.25

Price of each granola bar = $1.6

Step-by-step explanation:

Group 1:

6 muffins, 12 granola bars

Total money paid = $26.70

Group 2:

8 muffins, 15 granola bars,

Total money paid = $34.00

To find:

Price of each item?

Solution:

Let the price of one muffin = $ $x$

Let the price of one granola bar = $ $y$

As per group 1, the equation can be written as:

$6x+12y=26.70\\\Rightarrow x+2y=4.45 .... (1)$

As per group 2, the equation can be written as:

$8x+15y = 34$ .... (2)

Let us use elimination method to solve for $x$ and $y$ .

Multiplying equation (1) with 8 and subtracting (2) from it:

$16y-15y = 35.6 - 34\\\Rightarrow y = 1.6$

Using equation (1):

$x+3.2=4.45\\\Rightarrow x = 1.25$

Therefore, the answer is:

Price of each muffin = $1.6

Price of each granola bar = $1.25

7 0

3 years ago

Suppose exercise 2 asked how many photos fit on the first 6 pages of Miguel’s album. Explain how you could find the answer.

gladu [14]

Do 6 right hand times 4 right hand photos. Then you do 6 left hand with 3 left hand photos. 24 plus 18 is 42

4 0

3 years ago