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3 years ago

Hello I need help for this math homework please

Mathematics

1 answer:

LekaFEV [45]3 years ago

5 0

Answer:

1. first option

2. second option

3. second option

Step-by-step explanation:

i dunno i did the math and used a calculator. im pretty confident with my answers so hopefully theyre right

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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

A square market has an area of 36 square meters. How long is each side?

podryga [215]

Answer:The area of a square is equal to the length of one side squared. Since the square root of 36 is 6, the length of 1 side is 6.

Step-by-step explanation:

6 0

3 years ago

On the first

liubo4ka [24]

Answer:

0.93

Step-by-step explanation:

u have to add them all and divide by 12. then u add all of them but the outlier and divide by 11. then u subtract.

4 0

3 years ago

A quadratic function and an exponential function are graphed below. How do the decay rates of the functions compareover the inte

Kobotan [32]

To check the decay rate, we need to check the variation in y-axis.

Since our interval is

$-2We need to evaluate both function at those limits.At x = -2, we have a value of 4 for both of them, at x = 0 we have 1 for the exponential function and 0 to the quadratic function. Let's call the exponential f(x), and the quadratic g(x).[tex]\begin{gathered} f(-2)=g(-2)=4 \\ f(0)=1 \\ g(0)=0 \end{gathered}$

To compare the decay rates we need to check the variation on the y-axis of both functions.

$\begin{gathered} \Delta y_1=f(-2)-f(0)=4-1=3 \\ \Delta y_2=g(-2)-g(0)=4-0=4 \end{gathered}$

Now, we calculate their ratio to find how they compare:

$\frac{\Delta y_1}{\Delta y_2}=\frac{3}{4}$

This tell us that the exponential function decays at three-fourths the rate of the quadratic function.

And this is the fourth option.

4 0

1 year ago

Find the distance between the two points rounding to the nearest tenth (if

Sunny_sXe [5.5K]

Distance: (sqroot(x2-x1)^2 + (y2-y1)^2)
sqroot(1-3)^2 + (8-6)^2
sqroot(-2)^2 + (2)^2
sqroot(4) + 4
Square root of 8 = 2.82843
Round to nearest tenth
Solution: 2.8

7 0

3 years ago