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Ksivusya [100]
4 years ago
5

Hey plz answerit is very urgent​

Mathematics
1 answer:
otez555 [7]4 years ago
7 0

Answer:

1) 1.96

2) 0.36

3) 0.0049

4) 0.0169

5) 0.16

6) 1.21

7) 0.0009

8) 0.0196

Step-by-step explanation:

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In the midpoint rule for triple integrals we use a triple riemann sum to approximate a triple integral over a box b, where f(x,
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<span>The sub-boxes will have dimensions \frac{2-0}{2} \times \frac{2-0}{2} \times \frac{2-0}{2} =1\times1\times1=1 \ cubic \ units

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y sub-intervals are 0 to 1 and 1 to 2. Midpoints are at </span><span>y= \frac{1}{2} and </span><span>y= \frac{3}{4}
z sub-intervals are 0 to 1 and 1 to 2. Midpoints are at </span><span>z= \frac{1}{2} and </span><span><span>z= \frac{3}{4}</span>

Let f(x,y,z)=\cos{(xyz)}

\int\limits  \int\limits  \int\limits {f(x,y,z)} \, dV \approx f\left( \frac{1}{2} , \frac{1}{2} , \frac{1}{2} \right)+f\left( \frac{1}{2} , \frac{1}{2} , \frac{3}{4} \right)+f\left( \frac{1}{2} , \frac{3}{4} , \frac{1}{2} \right)+f\left( \frac{1}{2} , \frac{3}{4} , \frac{3}{4} \right)
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5 0
3 years ago
Expres each complex number in polar form. State the arguments in radians rounded to the nearest thousandth.
Arlecino [84]

Answer:

(a) In polar form complex number will be 5.3851\angle 68.1985^{\circ} and in radian argument is 0.378π

(b) 6.0827\angle -9.46^{\circ}

angle will be 0.05255π

Step-by-step explanation:

We have given

(a) 2+5i

We have to represent in polar form

We know that magnitude is given by \sqrt{(real\ part)^2+(imaginary\ part)^2}=\sqrt{2^2+5^2}=\sqrt{29}

Argument is given by tan^{-1}\frac{imaginary\ part}{real\ part}=tan^{-1}\frac{5}{2}=68.198

So in polar form complex number will be 5.3851\angle 68.1985^{\circ}

In radian argument will be 68.1985\times \frac{\pi }{180}=0.378\pi

(b) We have given complex number -6+i

We know that magnitude is given by \sqrt{(real\ part)^2+(imaginary\ part)^2}=\sqrt{(-6)^2+1^2}=\sqrt{37}

Argument is given by tan^{-1}\frac{imaginary\ part}{real\ part}=tan^{-1}\frac{1}{-6}=-9.46

So in polar form complex number will be 6.0827\angle -9.46^{\circ}

In radian argument will be -9.46\times \frac{\pi }{180}=-0.05255\pi

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