Donte simplified the expression below. 4(1+3i)

Jenna is having a sidewalk sale. She pays $12 for a

RSB [31]

Answer:

25.5

Step-by-step explanation:

because you have to do 25×1.50 -12

4 0

3 years ago

Use lagrange multipliers to find the point on the plane x â 2y + 3z = 6 that is closest to the point (0, 2, 4).

Arisa [49]

The distance between a point $(x,y,z)$ on the given plane and the point (0, 2, 4) is

$\sqrt{f(x,y,z)}=\sqrt{x^2+(y-2)^2+(z-4)^2}$

but since $\sqrt{f(x,y,z)}$ and $f(x,y,z)$ share critical points, we can instead consider the problem of optimizing $f(x,y,z)$ subject to $x-2y+3z=6$ .

The Lagrangian is

$L(x,y,z,\lambda)=x^2+(y-2)^2+(z-4)^2+\lambda(x-2y+3z-6)$

with partial derivatives (set equal to 0)

$L_x=2x+\lambda=0\implies x=-\dfrac\lambda2$
$L_y=2(y-2)-2\lambda=0\implies y=2+\lambda$
$L_z=2(z-4)+3\lambda=0\implies z=4-\dfrac{3\lambda}2$
$L_\lambda=x-2y+3z-6=0\implies x-2y+3z=6$

Solve for $\lambda$ :

$x-2y+3z=-\dfrac\lambda2-2(2+\lambda)+3\left(4-\dfrac{3\lambda}2\right)=6$
$\implies2=7\lambda\implies\lambda=\dfrac27$

which gives the critical point

$x=-\dfrac17,y=\dfrac{16}7,z=\dfrac{25}7$

We can confirm that this is a minimum by checking the Hessian matrix of $f(x,y,z)$ :

$\mathbf H(x,y,z)=\begin{bmatrix}f_{xx}&f_{xy}&f_{xz}\\f_{yx}&f_{yy}&f_{yz}\\f_{zx}&f_{zy}&f_{zz}\end{bmatrix}=\begin{bmatrix}2&0&0\\0&2&0\\0&0&2\end{bmatrix}$

$\mathbf H$ is positive definite (we see its determinant and the determinants of its leading principal minors are positive), which indicates that there is a minimum at this critical point.

At this point, we get a distance from (0, 2, 4) of

$\sqrt{f\left(-\dfrac17,\dfrac{16}7,\dfrac{25}7\right)}=\sqrt{\dfrac27}$

8 0

3 years ago

What is the radian measure of 75

Brilliant_brown [7]

Answer:

1.309 radians is the measure to 75

3 0

3 years ago

According to a study conducted by an organization, the proportion of americans who were afraid to fly in 2006 was 0. 10. A rand

algol13

According to the the concept of hypothesis testing, there is no evidence that the proportion of Americans who are afraid to fly has decreased.

Hypothesis testing:

Basically, in math hypothesis, it test the population on the basis of the sample data taken from the population using a simple random sampling.

Given,

According to a study conducted by an organization, the proportion of Americans who were afraid to fly in 2006 was 0. 10. A random sample of 1300 Americans results in 117 indicating that they are afraid to fly.

Now, we need to explain why this is not necessarily evidence that the proportion of Americans who are afraid to fly has.

While we looking into the given question,

Sample size, n = 1300

Number of Americans who were afraid to fly, x = 117

Now, we have to computing the sample proportion of Americans who afraid to fly,

Therefore, p = 117 / 1300 = 0.09

Then the Formulation of Hypotheses is written as,

Here the Null Hypothesis: H0: p≥0.10

And the alternative Hypothesis: Ha: p<0.10

Then the Left-tailed test of Test statistic is written as,

Here Let us assume that the level of significance, α = 0.05.

Then the Critical value, z≈−1.645

And the Decision rule is written as

If the value of |z|<|z0.05|≈1.645: Do not reject the null hypothesis.

Otherwise If value of |z|≥|z0.05|≈1.645: Reject the null hypothesis.

To know more about Hypothesis testing here.

brainly.com/question/28920252

#SPJ4

5 0

1 year ago

<img src="https://tex.z-dn.net/?f=frac%7Bx%5E%7B2%7D%20%7D%7Bx-1%7D" id="TexFormula1" title="frac{x^{2} }{x-1}" alt="frac{x^{2}

ICE Princess25 [194]

Answer:

$\frac{ {x}^{2} }{(x - 1)} = \frac{ {x}^{2}(x + 1) }{( {x}^{2} - 1)} \\ = \frac{( {x}^{3} + {x}^{2}) }{( {x}^{2} - 1) }$

5 0

2 years ago

Donte simplified the expression below. 4(1+3i) - (8-5i)