Mathematics, 26.02.2020 04:32 H7ttaMaan

As a result of friction, the angular speed of a wheel c hanges with time according to d θ d t = ω0 e −σ t , where ω0 and σ are constants. The angular speed changes from an initial angular speed of 4.43 rad/s to 3.63 rad/s in 3.92 s. Determine the magnitude of the angular acceleration after 3.41 s. Answer in units of rad/s 2 .

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Answer from: hhhhffhdhf

The value of angular acceleration after 3.41 s is -0.18925 rad/s^2

Step-by-step explanation:

As per the given data the value is given as

$\frac{d\theta}{dt}=\omega_oe^{-\sigma t}$

Where

$\omega_o$ is given as 4.43 rad/s $\sigma$ is calculated as follows

$3.63=4.43 e^{-\sigma *3.92}\\e^{-\sigma 3.92}=\frac{363}{443}\\-\sigma \cdot \:3.92\ln \left(e\right)=\ln \left(\frac{363}{443}\right)\\\sigma=0.05080$

Now as the acceleration is given as

$\alpha=\frac{d}{dt}(\frac{d\theta}{dt})\\\alpha=\frac{d}{dt}(\omega_oe^{-\sigma t})\\\alpha=\omega_o\frac{d}{dt}(e^{-\sigma t})\\\alpha=-\omega_o \sigma(e^{-\sigma t})$

As values of

$\omega_o$ is given as 4.43 rad/s $\sigma$ is calculated as 0.05080 t is 3.41

thus acceleration is given as

$\alpha=-\omega_o \sigma(e^{-\sigma t})\\\alpha=-4.43*0.05080(e^{-0.05080* 3.41})\\\alpha=-0.18925\, rad/s^2$

So the value of angular acceleration after 3.41 s is -0.18925 rad/s^2

Answer from: Quest

i think the answer is seven, for if i'm being useless °ω°

step-by-step explanation:

Answer from: Quest

Answer: question no. 1 -a. yes, the sides are in the ratio 2 : 5.question no. 2 -b. 59°question no. 3 -c. angles x and y are remote interior angles.question no. 4 -d. 90°, 45° and 45°question no. 5 -b. mn and qrstep-by-step explanation: question no. 1 -rs : xu = 3 : 7.5 = 2 : 5rt : x? = 6.4 : 16 = 2 : 5st : u? = 6 : 15 = 2 : 5as the ratios of all sides are equivalent, the triangles must be congruent and the sides must be proportional.therefore, the answer is: a. yes, the sides are in the ratio 2 : 5.question no. 2 -in the second diagram, angle b is the only letter not shown. therefore, the number must be equivalent to angle b.if we substitute the value of angle b as being 22° in the first diagram, we can now use the angle sum of a triangle to obtain the value of angle a.angle sum of a triangle = 180°therefore: let angle a = aa + 99 + 22 = 180a = 180 - 99 - 22a = 59°therefore, the answer is: b. 59°question no. 3 -angles x and y don't share the vertex of the triangle with the exterior angle w. remote interior angles don't share a vertex of a triangle with an exterior angle. this means that angles x and y are remote interior angles.therefore, the answer is: c. angles x and y are remote interior angles.question no. 4 -the sum of all interior angles of a triangle must be equivalent to 180°.90°, 45° and 45° are the only set of angle measures that are equivalent to 180°.therefore, the answer is: d. 90°, 45° and 45°question no. 5 -the only pair of sides stated in the options which are corresponding are mn and qr.therefore, the answer is: b. mn and qr.

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