All categories

3 years ago

5. If position of object x = 3 sinΘ – 7 cosΘ then motion of object is bounded between position.

Mathematics

1 answer:

lesya692 [45]3 years ago

3 0

9514 1404 393

Answer:

±√58 ≈ ±7.616

Step-by-step explanation:

The linear combination of sine and cosine functions will have an amplitude that is the root of the sum of the squares of the individual amplitudes.

|x| = √(3² +7²) = √58

The motion is bounded between positions ±√58.

_____

Here's a way to get to the relation used above.

The sine of the sum of angles is given by ...

sin(θ+c) = sin(θ)cos(c) +cos(θ)sin(c)

If this is multiplied by some amplitude A, then we have ...

A·sin(θ+c) = A·sin(θ)cos(c) +A·cos(θ)sin(c)

Comparing this to the given expression, we find ...

A·cos(c) = 3 and A·sin(c) = -7

We know that sin²+cos² = 1, so the sum of the squares of these values is ...

(A·cos(c))² +(A·sin(c))² = A²(cos(c)² +sin(c)²) = A²(1) = A²

That is, A² = (3)² +(-7)² = 9+49 = 58. This tells us the position function can be written as ...

x = A·sin(θ +c) . . . . for some angle c

x = (√58)sin(θ +c)

This has the bounds ±√58.

You might be interested in

jeordine spreads out a rectangular picnic blanket with an area of 42 square feet. its width is 6 feet. which equation could you

Bas_tet [7]

L(which is length) is equal to 42 divided by width which is 6. so the equation is L=42/6

5 0

3 years ago

Find the equation of a circle with a center at (7,2) and a point on the circle at (2,5)?

monitta

Answer:

$(x-7)^2+(y-2)^2=34$

Step-by-step explanation:

We want to find the equation of a circle with a center at (7, 2) and a point on the circle at (2, 5).

First, recall that the equation of a circle is given by:

$(x-h)^2+(y-k)^2=r^2$

Where (h, k) is the center and r is the radius.

Since our center is at (7, 2), h = 7 and k = 2. Substitute:

$(x-7)^2+(y-2)^2=r^2$

Next, the since a point on the circle is (2, 5), y = 5 when x = 2. Substitute:

$(2-7)^2+(5-2)^2=r^2$

Solve for r:

$(-5)^2+(3)^2=r^2$

Simplify. Thus:

$25+9=r^2$

Finally, add:

$r^2=34$

We don't need to take the square root of both sides, as we will have the square it again anyways.

Therefore, our equation is:

$(x-7)^2+(y-2)^2=34$

4 0

2 years ago

Find 4 + (-1 2/3)and write the answer in its simplest form

SIZIF [17.4K]

11/3

Mark brainliest please

Hope this helps you

3 0

3 years ago

At what points does the helix r(t) = sin t, cos t, t intersect the sphere x2 + y2 + z2 = 65? (round your answers to three decima

Firdavs [7]

$\mathbf r(t)=\langle x(t),y(t),z(t)\rangle=\langle\sin t,\cos t,t\rangle$

$x^2+y^2+z^2=\sin^2t+\cos^2t+t^2=65$
$\implies t^2=64$
$\implies t=\pm8$

7 0

3 years ago

In a class there are 10 students who play football and cricket 7 students who do not play football or cricket 14 students who pl

alisha [4.7K]

Answer:

110 members of a sports club play atleast one of the games, football, basketball and volleyball. If 20 play football and basketball only, 15 play football and volleyball only, 26 play basketball and volleyball only, x play all the three games, 2x each play

math

Of 45 students 30 play badminton and 26 play tennis. Each student play either badminton or tennis,determine how many students play:(a)badminton only (b) tennis only

probability and statistics

At a particular school with 200 male students, 58-play football, 40-play basketball, and 8 play both. What is the probability that a randomly selected male student plays a) At least one sport b) Neither sport c) Only basketball

7 0

2 years ago

5. If position of object x = 3 sinΘ – 7 cosΘ then motion of object is bounded between position.​

5. If position of object x = 3 sinΘ – 7 cosΘ then motion of object is bounded between position.