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
Yuri [45]
3 years ago
6

The curves r1(t) = 2t, t2, t3 and r2(t) = sin t, sin 5t, 3t intersect at the origin. Find their angle of intersection, θ, correc

t to the nearest degree.
Mathematics
1 answer:
anastassius [24]3 years ago
5 0

Answer:

The angle between the curves is 80.27°.

Step-by-step explanation:

Given that

r₁(t) = <2t, t²,t³>

Differentiating with respect to t

r'₁(t) = <2, 2t,3t²>

Since it is intersect at origin.

Then r'₁(0)= <2,0,0>      [ putting t=0]

The tangent vector at origin of r₁(t) is

r'₁(0)= <2,0,0>

Again,

r₂(t)= <sin t, sin 5t, 3t>

Differentiating with respect to t

r'₂(t)= <cost, 5 cos 5t, 3>

Since it is intersect at origin.

Then r'₂(0)= <1,5,3>      [ putting t=0]

The tangent vector at origin of r₂(t) is

r'₂(0)= <1,5,3>      

The angle between the carves is equal to the angle between their tangent.

We know that

Cos \theta = \frac{r'_1(0).r'_2(0)}{|r'_1(0)||r'_2(0)|}

Putting the all values

Cos \theta = \frac{.}{\sqrt{2^2+0^2+0^2}\sqrt{1^2+5^2+3^2}}

 \Rightarrow \theta =cos^{-1}(\frac{2}{2\sqrt{35}})

 ⇒θ= 80.27°

The angle between the curves are 80.27°.

You might be interested in
4 (×+2) show step if you can
chubhunter [2.5K]
I believe the answer is 4x + 8. you multiply 4 by x which makes 4x. Than you multiply 4 by 2, making 8. 
5 0
3 years ago
Read 2 more answers
Consider the following function G(x) = 2 (x-3)<br><br><br> Find G(4) + G (5)​
NNADVOKAT [17]
Answer: 6

Solution: 2(4-3) + 2(5-3) = 8-6+10-6=6
4 0
2 years ago
Last month Albert earned half of what Betty earned, while Betty earned $5000 more than what Calvin earned. If Donna earned twice
irinina [24]

Answer:

Calving earning = 4400

Betty earning = 9400

Albert earning = 4700

Donna = 8800

Step-by-step explanation:

Given that :

Calving earning = c

Betty earning = c + 5000

Albert earning = (c + 5000) /2

Donna = 2c

c + 5000 + (c + 5000) /2 = 900 + c + 2c

c + 5000 + 0.5c + 2500 = 900 + 3c

1.5c + 7500 = 900 + 3c

7500 - 900 = 3c - 1.5c

6600 = 1.5c

c = 6600 / 1.5

c = 4400

Calving earning = c = 4400

Betty earning = 4400 + 5000 = 9400

Albert earning = (4400 + 5000) /2 = 4700

Donna = 2(4400) = 8800

5 0
2 years ago
Y
alina1380 [7]

Answer:

the coordinates of the point of x and y is -1÷ 2 and -√3÷ 2

Step-by-step explanation:

The computation of the coordinates of the point is shown below:

The angle is

= 4π ÷ 3

The radius is 1 unit

Now

x = rcos\theta, and y = rsin\theta

Now

x = 1cos(4π ÷ 3) = -1÷ 2

y = 1sin(4π ÷ 3) = -√3÷ 2

hence, the corordinates of the point of x and y is -1÷ 2 and -√3÷ 2

8 0
3 years ago
Read 2 more answers
The velocity of sound in air is given by the equation v=20\sqrt(273+t) where v is the velocity in meters per second and t is the
adelina 88 [10]

Step-by-step explanation:

Jupiter's

Jupiter's menagerie of moons includes the largest in the solar system (Ganymede), an ocean moon (Europa) and a volcanic moon (Io). Many of Jupiter's outer moons have highly elliptical orbits and orbit backwards (opposite to the spin of the planet).

i want 3 brainliest

7 0
3 years ago
Read 2 more answers
Other questions:
  • Rounded 70,652 to the nearest 100
    15·1 answer
  • Is 1/10 of 8000 equal 80
    12·1 answer
  • How do you take a square, triangle, or circle to create 3d figures?
    7·1 answer
  • What is the probability of getting either a sum of 6 or at least one 5 in the roll of a pair of​ dice
    5·1 answer
  • Can someone tell me this answer plsss and thank you
    6·1 answer
  • I need help with this.<br><br> please show me how you do it
    6·1 answer
  • What is 38 percent of 22<br><br> (In percentage) :)
    11·2 answers
  • 1. Is the following a Function? (2,3) (4,7) (3,9) (5,7)
    8·2 answers
  • Find the perimeter of ABHG. Round your answer to the nearest tenth of an inch.
    13·1 answer
  • A package of twelve eggs cost $5 at this price, how much does each individual egg cost?
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!