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3 years ago

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Mathematics

1 answer:

Paha777 [63]3 years ago

7 0

Answer:

Step-by-step explanation:

The multiplication symbol is often referred to as "____ times as large" when written in text form

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Let S be the surface defined by x 2 + 2y 3 + 3z 4 = 6. Let T be the surface defined parametrically by r(u, v) = (1+ln u, 2e v+u−

aleksandrvk [35]

The tangent to $C$ through (1, 1, 1) must be perpendicular to the normal vectors to the surfaces $S$ and $T$ at that point.

Let $f(x,y,z)=x^2+2y^3+3z^4$ . Then $S$ is the level curve $f(x,y,z)=6$ . Recall that the gradient vector is perpendicular to level curves; we have

$\nabla f(x,y,z)=(2x,6y,12z^2)$

so that the gradient of $f$ at (1, 1, 1) is

$\nabla f(1,1,1)=(2,6,12)$

For the surface $T$ , we have

$\begin{cases}1+\ln u=1\\2e^v+u-2=1\\uv+1=1\end{cases}\implies u=1,v=0$

so that $\vec r(1,0)=(1,1,1)$ . We can obtain a vector normal to $T$ by taking the cross product of the partial derivatives of $\vec r(u,v)$ , and evaluating that product for $u=1,v=0$ :

$\dfrac{\partial\vec r}{\partial u}\times\dfrac{\partial\vec r}{\partial v}=\left(u-2ve^v,-1,\dfrac{2e^v}u\right)$

$\left(\dfrac{\partial\vec r}{\partial u}\times\dfrac{\partial\vec r}{\partial v}\right)(1,0)=(1,-1,2)$

Now take the cross product of the two normal vectors to $S$ and $T$ :

$(2,6,12)\times(1,-1,2)=(24,8,-8)$

The direction of vector (24, 8, -8) is the direction of the tangent line to $C$ at (1, 1, 1). We can capture all points on the line containing this vector by scaling it by $t\in\Bbb R$ . Then adding (1, 1, 1) shifts this line to the point of tangency on $C$ . So the tangent line has equation

$\vec\ell(t)=(1,1,1)+t(24,8,-8)=(1+24t,1+8t,1-8t)$

7 0

3 years ago

Can someone please help to answer this question

kogti [31]

The relationship between the diameter of the tree trunk snd the height of the tree is as the diameter increases the tree will get taller therefor the height will increase too. As you can see on the scatter graph the points are going in a upwards slant meaning its increasing.

4 0

4 years ago

Read 2 more answers

A bakery makes a $5 profit for each cake it sells. It makes

oee [108]

Answer:

$92

Step-by-step explanation:

Find the profit by plugging in 10 as c and 7 as p into the expression:

5c + 6p

5(10) + 6(7)

50 + 42

= 92

So, the bakery will make $92

7 0

3 years ago

Please Help <br><br> Factor the polynomial: x^3 + 3x - 2x - 6

madreJ [45]

Answer:

(x^2-2)(x+3)

Step-by-step explanation:

x^3 + 3x^2 - 2x - 6

x^2(x+3)-2(x+3)

(x^2-2)(x+3)

6 0

2 years ago

Most of the geometry concepts and theorems that are learned in high school today were first discovered and proved by mathematici

sweet-ann [11.9K]

Answer:

self realization, confidence

Step-by-step explanation:

also these concepts are used in real life jobs but most people think otherwise because you dont use them in a grocery store... yeah people think that, but also its so these concepts that were figured out thousands of years ago dont fade away with the newer generations

8 0

3 years ago