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3 years ago

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Please helpppp!!!!!!!

1 answer:

vfiekz [6]3 years ago

6 0

Answer:

read below

Step-by-step explanation:

If you know tangent of theta is 5/3 and it is in the 3rd quadrant, then you know the sides will be going in the negative direction and the real values of the sides would be -5/-3. You can use pythagorean theorem to figure out that the hypotenuse would be sqrt(5^2+3^2) = sqrt(34). Then you can use soh cah toa: sin = opp/hyp, cos=adj/hyp tan = opp/adj. You know that opp = -5, adj = -3, and hyp = sqrt(34) For cosine theta, it would be -3/sqrt(34) and csc is just 1/sin so csc would be hyp/opp = sqrt(34)/-5.

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Consider the paraboloid surface z = x 2 + y 2 .

Charra [1.4K]

a. We don't really need calculus to do this

$z = f(x,y) = x^2 + y^2$

We're interested in f near (1,1,f(1,1))

$f(x,y)=f(1+(x-1), 1+(y-1)) = (1+(x-1))^2 + (1+(y-1))^2$

$f(x,y)=2 + 2(x-1) + 2(y-1) + (x-1)^2 + (y-1)^2$

The tangent plane at (1,1,2) is the best linear approximation to f at (1,1). We just drop the squared terms:

$z =2 + 2(x-1) + 2(y-1)$

$z=2x + 2y - 2$

Answer: 2x + 2y - z = 2

b.

We repeat the above in general, near f(r,s)

$f(x,y)=f(r + (x-r), s+(x-s))$

$f(x,y) = (r + (x-r))^2 + (s + (x-s))^2$

$f(x,y)= r^2 + s^2 + 2r(x-r) + 2s(y-s) + (x-r)^2 + (y-s)^2$

Again the tangent plane at (r,s,f(r,s)) is gotten by dropping the squared terms,

$z = r^2 + s^2 + 2r(x-r) + 2s(y-s)$

This has to contain

$(x,y,z)=(t, 2-2t, -1)=(0,2,-1) + t(1,-2,0)$

$-1 = r^2 + s^2 + 2r(0-r) + 2s(2-s)$

$r^2 + s^2 - 4s - 1 = 0$

The line is perpendicular to the normal of the plane, so a zero dot product.

$2r x + 2sy - z = r^2 + s^2$

$(2r, 2s, -1) \cdot (1, -2, 0) = 0$

$2r - 4s=0$

$r = 2s$

$(2s)^2 + s^2 - 4s -1=0$

$5s^2 - 4s -1 = 0$

$(5s + 1)(s - 1) = 0$

$s=1 \textrm{ or } s=-1/5$

$r=2, s=1 \textrm{ or } r=-2/5, s=-1/5$

Two tangent planes contain the line.

$2r x + 2sy - z = r^2 + s^2$

$4x + 2y - z = 5 \textrm{ and } (-4/5)x - (2/5)y - z = (-2/5)^2+(-1/5)^2$

Answer: 4x + 2y - z = 5 and 4x + 2y + 5z = -1

Let's check two points on the line are in our planes, (0,2,-1), (1,0,-1)

Looks good.

7 0

4 years ago

Landon has 2/3 times 1/6 is he right

MissTica

Sorry I just need points

4 0

3 years ago

a warehouse has three shelves that can hold 8,12, or 16 each shelf has sections holding the same number of skateboards what is t

Galina-37 [17]

The greatest number of skateboards that can be stored would be the number that is the highest common factor of 8, 12, and 16

Factors of 8 = 1, 2, 4, 8

Factors of 12 = 1, 2, 3, 4, 6, 12

Factors of 16 = 1, 2, 4, 8, 16

The highest common factor = 4

Hence, the greatest numbers of skateboard that can be stored in each section is 4

Read more on Brainly.com - brainly.com/question/4694383#readmore

8 0

4 years ago

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Figure 1 and figure 2 are show on the coordinate plane below.

Mekhanik [1.2K]

Answer:

d think

Step-by-step explanation:

I don't really know but I'm pretty sure that's it.

6 0

3 years ago

200, 100,<br> 50, 25,<br> b. What is the fifth term?

damaskus [11]

Answer:

12.5

Step-by-step explanation:

Keep dividing by 2, 25 divided by 2 is 12.5

4 0

3 years ago

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