1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
jeyben [28]
3 years ago
8

(a) Find a vector-parametric equation r⃗ 1(t)=⟨x(t),y(t),z(t)⟩r→1(t)=⟨x(t),y(t),z(t)⟩ for the shadow of the circular cylinder x2

+z2=5x2+z2=5 in the xzxz-plane. Shadow: r⃗ 1(t)=r→1(t)= for 0≤t≤2π0≤t≤2π. (b) Find a vector-parametric equation for intersection of the circular cylinder x2+z2=5x2+z2=5 and the plane 3x+2y+8z=13x+2y+8z=1. Intersection: r⃗ 2(t)=r→2(t)= for 0≤t≤2π0≤t≤2π.
Mathematics
1 answer:
motikmotik3 years ago
6 0

Answer: (a) r1(t) = <2cost , 0 , 2sint>

(b) <2cost , (1 - 12sint - 10cost)/8 , 2sint>

Step-by-step explanation:

x2+z2=4

a)

Now, in the xz plane, we know that y = 0...

So, x^2 + z^2 = 4 will simply be a circle centered at (0,0)..

This can be easily parameterized as

x = 2cos(t)

z = 2sin(t)

So, the required parameterization is :

r1(t) = <2cost , 0 , 2sint>

b)

Cylinder : x^2 + z^2 = 4

Plane : 5x+8y+6z=1

Easily enough, the x^2 + z^2 = 4 can again be parameterized as

x = 2cost , z = 2sint

With this, we can find y using plane equation...

5x+8y+6z=1

5(2cost) + 8y + 6(2sint) = 1

8y = 1 - 12sint - 10cost

y = (1 - 12sint - 10cost)/8

So, the parameterization is :

<2cost , (1 - 12sint - 10cost)/8 , 2sint>

You might be interested in
How many kilograms are 0.54 decalitres?
Anarel [89]

Answer:

A measure of capacity or volume in the metric system equal to one-tenth (10-1) of a liter. One deciliter is also equal to 6.1022 cubic inches, or 3.38 fluid ounces

Step-by-step explanation:


4 0
3 years ago
Read 2 more answers
HCPS Algebra
ira [324]

Answer:

Step-by-step explanation:

7 0
3 years ago
A rectangular poster is 3 times as long as it is wide. A rectangular banner is 5 times a long as it is wide. Both the banner and
deff fn [24]

Answer:

The answer to your question is

a) Poster             width = 3 in

                            lenght = 9 in

b) banner

                           width = 2 in

                           lenght = 10 in

Step-by-step explanation:

a) For the poster

   width = x

   lenght = 3x

Perimeter of a rectangle = 2base + 2 height

                                         = 2(x) + 2(3x) = 24

                                         2x + 6x = 24

                                         8x = 24

                                           x = 24/8

                                           x = 3

    width = 3 in

     lenght = 3(3) = 9 in

b) For the banner

    width = y

    lenght = 5y

Perimeter of a banner = 2 base + 2 height

                                        2 (y) + 2(5y) = 24

                                        2y + 10y = 24

                                        12y = 24

                                           y = 24/12

                                           y = 2

     width = 2 in

     lenght = 5(2) = 10 in

7 0
3 years ago
Adult tickets to a basketball game cost $5. Student tickets cost $1. A total of $2,699 was collected on the sale of 1,179 ticket
lana66690 [7]

Answer:

Step-by-step explanation:

The Answer 3182121

4 0
2 years ago
Charlie has a discount card that reduces the price of his grocery bill in a certain grocery store by 25 percent. If c represents
Valentin [98]

Answer:

C= x*.75

Step-by-step explanation:

if X is the grocery bill before the discount, Charlie only pays 75% of x

6 0
3 years ago
Other questions:
  • the original recipe calls for 2 pounds of pasta and serves 8 people. The party will have 40 people . how many pounds of pasta do
    11·1 answer
  • For the following inequality, indicate whether the boundary line should be dashed or solid. x ≤ 5
    9·1 answer
  • a triangle has side measuring 8 inches and 12 inches if x represents the length in inches o the third side which inequality give
    12·1 answer
  • There are six roses in the vase. Alyssa cut some more roses from her flower garden. There are now 16 roses in a vase. How many r
    7·1 answer
  • Please help freshman math much-needed
    12·2 answers
  • Find AC.<br> Round to the nearest tenth.<br> B<br> 86°<br> 16<br> С<br> 11<br> A
    14·1 answer
  • This table shows values that represent an exponential function.what is the average rate of change for this function for the inte
    6·1 answer
  • A fish starts swimming at -50m and increases 13m. Which equation best represents the situation and the fish's final elevation? a
    10·1 answer
  • Solve x for 7× + 3 = 31​
    13·2 answers
  • Someone pls help me with this
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!