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
cestrela7 [59]
2 years ago
11

Plz need help badly

Mathematics
1 answer:
marissa [1.9K]2 years ago
7 0
You need to put a y value which when you multiply with 15 will give you an answer smaller than 180.
You might be interested in
(a) Find the unit tangent and unit normal vectors T(t) and N(t).
andrey2020 [161]

Answer:

a. i. (i + tj + 2tk)/√(1 + 5t²)

ii.  (-5ti + j + 2k)/√[25t² + 5]

b. √5/[√(1 + 5t²)]³

Step-by-step explanation:

a. The unit tangent

The unit tangent T(t) = r'(t)/|r'(t)| where |r'(t)| = magnitude of r'(t)

r(t) = (t, t²/2, t²)

r'(t) = dr(t)/dt = d(t, t²/2, t²)/dt = (1, t, 2t)

|r'(t)| = √[1² + t² + (2t)²] = √[1² + t² + 4t²] = √(1 + 5t²)

So, T(t) = r'(t)/|r'(t)| = (1, t, 2t)/√(1 + 5t²)  = (i + tj + 2tk)/√(1 + 5t²)

ii. The unit normal

The unit normal N(t) = T'(t)/|T'(t)|

T'(t) = dT(t)/dt = d[ (i + tj + 2tk)/√(1 + 5t²)]/dt

= -5ti/√(1 + 5t²)⁻³ + [-5t²j/√(1 + 5t²)⁻³] + [-10tk/√(1 + 5t²)⁻³]

= -5ti/√(1 + 5t²)⁻³ + [-5t²j/√(1 + 5t²)⁻³] + j/√(1 + 5t²)+ [-10t²k/√(1 + 5t²)⁻³] + 2k/√(1 + 5t²)

= -5ti/√(1 + 5t²)⁻³ - 5t²j/[√(1 + 5t²)]⁻³ + j/√(1 + 5t²) - 10t²k/[√(1 + 5t²)]⁻³ + 2k/√(1 + 5t²)

= -5ti/√(1 + 5t²)⁻³ - 5t²j/[√(1 + 5t²)]⁻³ - 10t²k/[√(1 + 5t²)]⁻³ + j/√(1 + 5t²) + 2k/√(1 + 5t²)

= -(i + tj + 2tk)5t/[√(1 + 5t²)]⁻³ + (j + 2k)/√(1 + 5t²)

We multiply by the L.C.M [√(1 + 5t²)]³  to simplify it further

= [√(1 + 5t²)]³ × -(i + tj + 2tk)5t/[√(1 + 5t²)]⁻³ + [√(1 + 5t²)]³ × (j + 2k)/√(1 + 5t²)

= -(i + tj + 2tk)5t + (j + 2k)(1 + 5t²)

= -5ti - 5²tj - 10t²k + j + 5t²j + 2k + 10t²k

= -5ti + j + 2k

So, the magnitude of T'(t) = |T'(t)| = √[(-5t)² + 1² + 2²] = √[25t² + 1 + 4] = √[25t² + 5]

So, the normal vector N(t) = T'(t)/|T'(t)| = (-5ti + j + 2k)/√[25t² + 5]

(b) Use Formula 9 to find the curvature.

The curvature κ = |r'(t) × r"(t)|/|r'(t)|³

since r'(t) = (1, t, 2t), r"(t) = dr'/dt = d(1, t, 2t)/dt  = (0, 1, 2)

r'(t) = i + tj + 2tk and r"(t) = j + 2k

r'(t) × r"(t) =  (i + tj + 2tk) × (j + 2k)

= i × j + i × 2k + tj × j + tj × 2k + 2tk × j + 2tk × k

= k - 2j + 0 + 2ti - 2ti + 0

= -2j + k

So magnitude r'(t) × r"(t) = |r'(t) × r"(t)| = √[(-2)² + 1²] = √(4 + 1) = √5

magnitude of r'(t) = |r'(t)| = √(1 + 5t²)

|r'(t)|³ = [√(1 + 5t²)]³

κ = |r'(t) × r"(t)|/|r'(t)|³ = √5/[√(1 + 5t²)]³

8 0
2 years ago
On monday andres bought a new bike for 112.50 if his bike depreciates by 15% what is his bike worth now
ioda

Answer:

$95.62

Step-by-step explanation:

15% of $112.50 = $16.875. round that to $16.88.

$112.50-$16.88=$95.62

5 0
3 years ago
Larry has $150 in his bank account. He deposits $27 and then writes a check for $96
IgorC [24]

Answer:

$-4

Step-by-step explanation:

Your welcome

5 0
3 years ago
Read 2 more answers
Find the domain and range of the relation: {(–20, 11), (6, –8), (1, –20), (–13, 13)}
user100 [1]

Answer:

D: {-20, -13, 1, 6}

R: {-20, -8, 11, 13}

Step-by-step explanation:

Given the relation, {(–20, 11), (6, –8), (1, –20), (–13, 13)}, all x-values (inputs) make up the domain of the relation while all y-values make up the range of the relation.

Therefore:

Domain: {-20, -13, 1, 6}

Range: {-20, -8, 11, 13}

4 0
3 years ago
How many times can 27 go into 192
lutik1710 [3]
It can go into 192 7.1 times
7 0
3 years ago
Read 2 more answers
Other questions:
  • What is an indicated function?
    13·1 answer
  • Is the following sentence a statement or not a statement? X and Y define a line.
    12·2 answers
  • What is the smallest number 13, 0.13, 1.03, 0.103, 1.3
    7·2 answers
  • in one day, annie traveled 5 times the sum if the number of hours brian traveled and 2. Together they traveled 20 hours. Find th
    13·1 answer
  • Will mark as a brainlist if i get help w these two
    9·1 answer
  •  please  help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!                 
    13·1 answer
  • The 5th grade students at Fox Middle School went to a movie. They spent a total of $1357.50 on movie tickets. If each movie tick
    15·1 answer
  • What is - 9 + 3 = I know its -6 but how
    11·2 answers
  • Every day, Kim practices volleyball and clarinet. Each day, she practices volleyball for 2.5 hours. If after 8 days she practice
    7·1 answer
  • letter H represent marks height in inches Suzanne is 7 in shorter than Mark write an algebraic expression that represents Susan'
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!