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23 days ago

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Laura has $1000 bond with a 3.4% coupon. Laura purchased this bond for $1065. What is the yield of this new bond?

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The equation of the tangent plane to the ellipsoid x2/a2 + y2/b2 + z2/c2 = 1 at the point (x0, y0, z0) can be written as xx0 a2

PIT_PIT [12445]

Answer:

The tangent plane equation for the hyperboloid

$\frac{xx_0}{a^2}+\frac{yy_0}{b^2}-\frac{zz_0}{c^2}=1$ .

Step-by-step explanation:

We have

The ellipsoid's equation is

$\frac{x^2}{a^2}+\frac{y^2}{b^2}+\frac{z^2}{c^2}=1$

The equation for the tangent plane at the point $\left(x_0,y_0,z_0\right)$

$\frac{xx_0}{a^2}+\frac{yy_0}{b^2}+\frac{zz_0}{c^2}=1$ (Given)

The hyperboloid's equation is

$\frac{x^2}{a^2}+\frac{y^2}{b^2}-\frac{z^2}{c^2}=1$

F(x,y,z)= $\frac{x^2}{a^2}+\frac{y^2}{b^2}-\frac{z^2}[c^2}$

$F_x=\frac{2x}{a^2},F_y=\frac{2y}{b^2},F_z=-\frac{2z}{c^2}$

$(F_x,F_y,F_z)(x_0,y_0,z_0)=\left(\frac{2x_0}{a^2},\frac{2y_0}{b^2},-\frac{2z_0}{c^2}\right)$

The tangent plane equation at point $\left(x_0,y_0,z_0\right)$

$\frac{2x_0}{a^2}(x-x_0)+\frac{2y_0}{b^2}(y-y_0)-\farc{2z_0}{c^2}(z-z_0)=0$

The tangent plane equation for the hyperboloid is

$\frac{2xx_0}{a^2}+\frac{2yy_0}{b^2}-\frac{2zz_0}{c^2}-2\left(\frac{x_0^2}{a^2}+\frac{y_0^2}{b^2}-\frac{z_0^2}{c^2}\right)=0$

The tangent plane equation

$2\left(\frac{xx_0}{a^2}+\frac{yy_0}{b^2}-\frac{zz_0}{c^2}\right)=2$

Hence, the required tangent plane equation for the hyperboloid is

$\frac{xx_0}{a^2}+\frac{yy_0}{b^2}-\frac{zz_0}{c^2}=0$

7 0

4 months ago

1. Which of the following is the first step in the licensing process?

Leona [12618]

I think the answer is A
Idnjnxjxnnxnndknxjnxjjd

3 0

4 months ago

Read 2 more answers

A politician wants to estimate the proportion of constituents favoring a controversial piece of proposed legislation. suppose th

babunello [11817]

Answer:

We have the following details:

Confidence level = 99%. Hence, the critical value at a 0.01 significance level is provided below:

$z_{\frac{0.01}{2}}=2.576$

The margin of error is mentioned in the question as:

$E=0.05$

Since we lack information about the previous proportion, we need to assume $\hat{p} = 0.5$ .

Therefore, the required sample size is:

$n=\hat{p}(1-\hat{p}) \left( \frac{z_{\frac{0.01}{2}} }{E} \right)$

$=0.5(1-0.5) \left( \frac{2.576}{0.05} \right)$

$=0.25 \times 51.52^2$

$=663.6 \approx 664$

Thus, it requires 664 sample observations.

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3 months ago

Math 1314 lab module 2

Svet_ta [12734]

Is there a question or not?

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3 months ago