answer.
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
DerKrebs
1 month 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:
zzz [12.3K]1 month 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)

Within the xz plane, since y = 0...

Thus, x² + z² = 4 describes a circle centered at (0,0)..

This can be parameterized as

x = 2cos(t)

z = 2sin(t)

The necessary parameterization is:

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

b)

Cylinder equation: x² + z² = 4

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

Once again, the x² + z² = 4 can be parameterized as

x = 2cost, z = 2sint

Now, we can determine y using the plane equation...

5x+8y+6z=1

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

8y = 1 - 12sint - 10cost

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

Thus, the parameterization becomes:

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

You might be interested in
Your job is to sort and sack marbles for sale. A bag contains 44 marbles, some red and some green. If there are 11 red marbles,
AnnZ [12381]

Response:

The correct choice is option C

The proportion of green marbles to red marbles is 3: 1

Step-by-step breakdown:

According to the problem statement:

A bag holds 44 marbles, comprising both red and green ones.

⇒Total marbles = 44

If it includes 11 red marbles.

Then;

Green marbles = Total marbles - red marbles.

By substituting the values provided,

Green marbles = 44 - 11 = 33

We are tasked with determining the ratio of green marbles to red marbles.

\frac{\text{Green marbles}}{\text{Red marbles}} = \frac{33}{11} = \frac{3}{1} = 3: 1

Consequently, the ratio of green to red marbles is 3: 1

8 0
22 days ago
Lauren is running in a marathon to raise money for her favorite charity. The total distance of the marathon is 12.5 miles. So fa
Svet_ta [12734]
Hello! Dividing or multiplying a decimal by 10 is simpler than it may seem. When dividing by 10, shift the decimal point one place to the left. Conversely, when multiplying a decimal by 10, move the decimal point one place to the right. In this case, dividing 12.5 by 10 means shifting the decimal left one position, resulting in 1.25. Therefore, Lauren has covered 1.25 miles. To verify, you can multiply 1.25 by 10, which returns you to 12.5. The answer is 1.25! I hope this is helpful!
3 0
22 days ago
What is the solution to the system of equations graphed below? Please Help (:
Zina [12379]
C. (1,5) The solution represents where two lines intersect.
5 0
13 days ago
Cameras R Us has a sale for 25% off camera bags, which is a discount of $20. Explain how you can set up a diagram to find the or
Zina [12379]

Answer:

Example Response: The diagram ought to consist of five columns; one for each 25% segment and an additional one for the total, since 25% represents 1

4

of 100%. There should be 2 rows, one designated for percentages and another for dollar figures.

Step-by-step explanation:

Edg2020

8 0
1 month ago
Read 2 more answers
Rename 120,000 = ten thousands
Inessa [12570]
The answer is twelve ten thousands. To find how many ten thousands are in 120,000, we recognize that ten thousand equals 10,000. Dividing 120,000 by 10,000 yields 12, meaning there are twelve ten thousands in 120,000. I hope this is helpful, and let me know if you need more assistance!
4 0
1 month ago
Other questions:
  • 13. En un pueblo, 5 personas escucharon una noticia. En una hora, cada una de ellas
    11·1 answer
  • Pedro cut a sheet of poster board into 10 equal parts. His brother used some of the poster board and now 8/10 is left. Pedro wan
    8·2 answers
  • Which of the following values are in the range of the function graphed below? Check all that apply.
    13·2 answers
  • You earned $62,715 this year and your Income tax calculator says you owe $8,818 in taxes. But you neglected to deduct $1,000 for
    6·1 answer
  • The graphs below have the same shape. What is the equation of the blue
    11·1 answer
  • You invest $2,500.00 in a stock plan, buying 125 shares. If each share increases in value by 10%, how much is each share worth?
    12·2 answers
  • A billfold holds one-dollar, five-dollar, and ten-dollar bills and has a value of $210. There are 50 bills total where the numbe
    10·1 answer
  • 1 European euro = 1.3687 US dollars. While traveling to Europe, Phelan exchanged 250 US dollars for euros. He spent 150 euros on
    6·1 answer
  • Jason inherited a piece of land from his great-uncle. Owners in the area claim that there is a 45% chance that the land has oil.
    6·1 answer
  • A teacher plans to buy air fresheners that cost $3.50 each. If the teacher can spend no more than $10 on the air fresheners and
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!