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kondaur [170]
3 years ago
6

In this exercise, consider a particle moving on a circular path of radius b described by r(t) = b cos(ωt)i + b sin(ωt)j, where ω

= du/dt is the constant angular velocity. Find the acceleration vector and show that its direction is always toward the center of the circle.
Mathematics
1 answer:
Bingel [31]3 years ago
3 0

Answer:

Acceleration of the particle = bw^{2}

Step-by-step explanation:

We are given the position vector of a particle moving in a circle of radius b units.

r(t) = b cos(ωt)i + b sin(ωt)j

Velocity , v =\frac{dr}{dt} = -bω sin(ωt)i + bω cos(ωt)j

The magnitude of velocity, v =\sqrt{v_x^{2} +v_y^{2} }

Squaring both sides,

v^{2} = b^{2} w^{2}(sin^{2}(wt)+cos^{2}(wt))

Since sin^{2}(wt)+cos^{2}(wt)) = 1

v^{2} = b^{2}w^{2}

The acceleration towards the centre is called the centripetal acceleration and is given by

a = \frac{v^{2} }{r}

a = \frac{b^{2}w^{2}}{b}

a = bw^{2}

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(a+b)2 ;a=1/2 and b=2
FrozenT [24]

Answer:

\frac{25}{4}

Step-by-step explanation:

a + b = \frac{1}{2} + 2 = 2 \frac{1}{2} = \frac{5}{2}, thus

(a + b)² = (\frac{5}{2} )² = \frac{5}{2} × \frac{5}{2} = \frac{5(5)}{2(2)} = \frac{25}{4}

8 0
3 years ago
Read 2 more answers
What is the answer to 3/x=-3/3x+5
Aleonysh [2.5K]

Answer:

-\frac{5}{4} =x

Step-by-step explanation:

We first need to bring x up into the numerator. I will find common denominators by multiplying both sides by each denominator.

\frac{x(3x+5)}{1} *\frac{3}{x} =\frac{-3}{3x+5}*\frac{x(3x+5)}{1}

This will eliminate both denominators and leave me with

(3x+5)3=-3(x)\\9x+15=-3x after I simplify the parenthesis.

Now I will solve the equation for x by subtracting 9x from both sides.

9x-9x+15=-3x-9x\\15=-12x

Then divide by the coefficient of x.

\frac{15}{-12}=\frac{-12x}{-12}

-\frac{5}{4} =x


7 0
3 years ago
Algebra 2 (picture shown)
TEA [102]

Answer:

<em>M(13)=14.3 gram</em>

Step-by-step explanation:

<u>Exponential Decay Function</u>

The exponential function is used to model natural decaying processes, where the change is proportional to the actual quantity.

An exponential decaying function is expressed as:

C(t)=C_o\cdot(1-r)^t

Where:

C(t) is the actual value of the function at time t

Co is the initial value of C at t=0

r is the decaying rate, expressed in decimal

The element has an initial mass of Mo=970 grams, the decaying rate is r=27.7% = 0.277 per minute.

The equation of the model is:

M(t)=M_o\cdot(1-r)^t

M(t)=970\cdot(1-0.277)^t

Operating:

M(t)=970\cdot 0.723^t

After t=13 minutes the remaining mass is:

M(13)=970\cdot 0.723^{13}

Calculating:

M(13)=14.3 gram

4 0
3 years ago
suppose 5 men and 7 women are on a crowded elevator. at the next floor, four people get off the elevator. find the probability t
lubasha [3.4K]
The total number of arrangements for all of them to be women is:
C(7, 4) because the order does not matter; we'd still have the same arrangements.

Now, we can simplify this:
C(7, 4) = \frac{7!}{4!(7 - 4)!}
= \frac{5040}{4!3!}
= \frac{5040}{24 \cdot 6}
= \frac{5040}{144} = 35

Now, the total number of arrangements, without restriction, is simply: C(12, 4) because we don't care who we pick.

\text{P(4 women): } \frac{35}{495} = \frac{7}{99}
3 0
3 years ago
The figure below shows the distance between two cities on a map is 1/8 inch to 12 miles. ​
Paul [167]

Answer: A. 38.4

Step-by-step explanation:

Because...

12/3.75 is 3.2; 3.2× 12 is 38.4. do 12÷ 3.75 meaning 3.2 miles every hour multiplied by 12 to get 38.4 miles.

* Hopefully this helps:) Mark me the brainliest:)!!

<em>∞ 234483279c20∞</em>

3 0
3 years ago
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