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3 years ago

Simplify the following numerical expressions.

Mathematics

1 answer:

Aleksandr-060686 [28]3 years ago

3 0

Answer:

|7| - 7 = 0

2|-7| = 14

(-7)^2 = 49

-7-|-7|= -14

-7-1-71= -79

Step-by-step explanation:

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Solve for m. F=1/2 mr

algol [13]

Answer:

2F /r = m

Step-by-step explanation:

F=1/2 mr

Multiply each side by 2

2F = 2*1/2 mr

2F = mr

Divide each side by r

2F/r = mr/r

2F /r = m

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Answer:

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Step-by-step explanation:

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julsineya [31]

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evaluate the line integral ∫cf⋅dr, where f(x,y,z)=5xi−yj+zk and c is given by the vector function r(t)=⟨sint,cost,t⟩, 0≤t≤3π/2.

meriva

We have

$\displaystyle \int_C \vec f \cdot d\vec r = \int_0^{\frac{3\pi}2} \vec f(\vec r(t)) \cdot \dfrac{d\vec r}{dt} \, dt$

and

$\vec f(\vec r(t)) = 5\sin(t) \, \vec\imath - \cos(t) \, \vec\jmath + t \, \vec k$

$\vec r(t) = \sin(t)\,\vec\imath + \cos(t)\,\vec\jmath + t\,\vec k \implies \dfrac{d\vec r}{dt} = \cos(t) \, \vec\imath - \sin(t) \, \vec\jmath + \vec k$

so the line integral is equilvalent to

$\displaystyle \int_C \vec f \cdot d\vec r = \int_0^{\frac{3\pi}2} (5\sin(t) \cos(t) + \sin(t)\cos(t) + t) \, dt$

$\displaystyle \int_C \vec f \cdot d\vec r = \int_0^{\frac{3\pi}2} (6\sin(t) \cos(t) + t) \, dt$

$\displaystyle \int_C \vec f \cdot d\vec r = \int_0^{\frac{3\pi}2} (3\sin(2t) + t) \, dt$

$\displaystyle \int_C \vec f \cdot d\vec r = \left(-\frac32 \cos(2t) + \frac12 t^2\right) \bigg_0^{\frac{3\pi}2}$

$\displaystyle \int_C \vec f \cdot d\vec r = \left(\frac32 + \frac{9\pi^2}8\right) - \left(-\frac32\right) = \boxed{3 + \frac{9\pi^2}8}$

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2 years ago

3. What is the probability that when a fair coin is flipped 20 times, there will be exactly five tails?

Shkiper50 [21]

Answer: Probability of getting

tails from

tosses is

285

262144

0.0010872

Step-by-step explanation:

When a coin is tossed there are two possibilities.- it is either a head or tail and probability of getting either head or tail is

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