All categories

3 years ago

Which of the following represents a problem that could be solved by the

Mathematics

1 answer:

gregori [183]3 years ago

8 0

Answer:

inaviodfhiovhefoinvoierfoubdskjvbdnxc vkjfbd hhhhj hdf bvhzbvhsfvhjaebsdvbj

Step-by-step explanation:

hvytuvuhygtfrthjojuhygtfrtghbjnknhobgvytcfrxehgghjggkg\

You might be interested in

Find an equation of the tangent plane to the given parametric surface at the specified point.

Neko [114]

Answer:

Equation of tangent plane to given parametric equation is:

$\frac{\sqrt{3}}{2}x-\frac{1}{2}y+z=\frac{\pi}{3}$

Step-by-step explanation:

Given equation

$r(u, v)=u cos (v)\hat{i}+u sin (v)\hat{j}+v\hat{k}$ ---(1)

Normal vector tangent to plane is:

$\hat{n} = \hat{r_{u}} \times \hat{r_{v}}\\r_{u}=\frac{\partial r}{\partial u}\\r_{v}=\frac{\partial r}{\partial v}$

$\frac{\partial r}{\partial u} =cos(v)\hat{i}+sin(v)\hat{j}\\\frac{\partial r}{\partial v}=-usin(v)\hat{i}+u cos(v)\hat{j}+\hat{k}$

Normal vector tangent to plane is given by:

$r_{u} \times r_{v} =det\left[\begin{array}{ccc}\hat{i}&\hat{j}&\hat{k}\\cos(v)&sin(v)&0\\-usin(v)&ucos(v)&1\end{array}\right]$

Expanding with first row

$\hat{n} = \hat{i} \begin{vmatrix} sin(v)&0\\ucos(v) &1\end{vmatrix}- \hat{j} \begin{vmatrix} cos(v)&0\\-usin(v) &1\end{vmatrix}+\hat{k} \begin{vmatrix} cos(v)&sin(v)\\-usin(v) &ucos(v)\end{vmatrix}\\\hat{n}=sin(v)\hat{i}-cos(v)\hat{j}+u(cos^{2}v+sin^{2}v)\hat{k}\\\hat{n}=sin(v)\hat{i}-cos(v)\hat{j}+u\hat{k}\\$

at u=5, v =π/3

$=\frac{\sqrt{3} }{2}\hat{i}-\frac{1}{2}\hat{j}+\hat{k}$ ---(2)

at u=5, v =π/3 (1) becomes,

$r(5, \frac{\pi}{3})=5 cos (\frac{\pi}{3})\hat{i}+5sin (\frac{\pi}{3})\hat{j}+\frac{\pi}{3}\hat{k}$

$r(5, \frac{\pi}{3})=5(\frac{1}{2})\hat{i}+5 (\frac{\sqrt{3}}{2})\hat{j}+\frac{\pi}{3}\hat{k}$

$r(5, \frac{\pi}{3})=\frac{5}{2}\hat{i}+(\frac{5\sqrt{3}}{2})\hat{j}+\frac{\pi}{3}\hat{k}$

From above eq coordinates of r₀ can be found as:

$r_{o}=(\frac{5}{2},\frac{5\sqrt{3}}{2},\frac{\pi}{3})$

From (2) coordinates of normal vector can be found as

$n=(\frac{\sqrt{3} }{2},-\frac{1}{2},1)$

Equation of tangent line can be found as:

$(\hat{r}-\hat{r_{o}}).\hat{n}=0\\((x-\frac{5}{2})\hat{i}+(y-\frac{5\sqrt{3}}{2})\hat{j}+(z-\frac{\pi}{3})\hat{k})(\frac{\sqrt{3} }{2}\hat{i}-\frac{1}{2}\hat{j}+\hat{k})=0\\\frac{\sqrt{3}}{2}x-\frac{5\sqrt{3}}{4}-\frac{1}{2}y+\frac{5\sqrt{3}}{4}+z-\frac{\pi}{3}=0\\\frac{\sqrt{3}}{2}x-\frac{1}{2}y+z=\frac{\pi}{3}$

5 0

3 years ago

The area of a circle is 497 squared meters.<br> What is the radius, in meters?

frutty [35]

Answer: r= 12.58m

Step-by-step explanation:

100% SURE

7 0

3 years ago

A pair of shoes usually sells for $61. If the shoes are 30% off, and sales tax is 6%, what is the total price of the shoes, incl

Vinil7 [7]

Answer:

$45.26

Step-by-step explanation:

30% × 61 = 18.3

= $18.30 off, 61 - 18.3 = 42.7

6% × 42.7 = 2.562

= 42.7 + 2.562

= 45.26

8 0

3 years ago

Find the area of the figure.

Kruka [31]

Divide the shape into a rectangle and a triangle.

A(rectangle) = bh
A = 8*3
A = 24

A (triangle) = (bh)/2
A = (3*3)/2
A = 4.5

24 + 4.5 = 28.5

8 0

3 years ago

EXPERT HELP I'LL GIVE BRAINLIEST:

ICE Princess25 [194]

Answer:

990, C

Step-by-step explanation:

The formula for the surface area of the bottom cushion is

A = 2wl + 2lh + 2hw (w is width, l is length, h is height)

w = 18, l = 21, h = 3

A = 2(18)(21) + 2(21)(3) + 2(3)(18)

A = 2(378) + 2(63) + 2(54)

A = 756 + 126 + 108

A = 990 (C)

5 0

3 years ago