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2 years ago

Express 5.555... in the form of a geometric series.

Mathematics

1 answer:

Evgesh-ka [11]2 years ago

4 0

5.555 = 5.1 + 0.05 + 0.005

= 5.5 + 0.05 + 0.05(.1)

= 5.5 + 0.05/(1-.1)

=5.5+0.05/.9

=5.5 + 5/90

= 5.5+1/18

=55/10 + 1/18

= 495/90 + 5/90

=500/90

= 50/9

= 5 5/9

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Two forces, F1 and F2, are represented by vectors with initial points that are at the origin. The first force has a magnitude of

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Answer:

Step-by-step explanation:

The two force F1 and F2 are represented by vectors with initial points that are at the origin.

the terminal point of the vector is point P(1, 1, 0)

Therefore, the direction of the vector force is

$v_1=(1-0)\hat i+(1-0)\hat j +(0-0)\hat k\\\\=1\hat i+1\hat j+0\hat k\\\\=\hat i + \hat j$

The unit vector in the direction of force will be

$\frac{v_1}{|v_1|} =\frac{\hat i+ \hat j}{\sqrt{1^2+1^2+0^2} } \\\\=\frac{1}{\sqrt{2} (\hat i +\hat j)}$

The magnitude of the force is 40lb, so the force will be

$F_1=40\times \frac{1}{\sqrt{2} } (\hat i+\hat j)\\\\=20\sqrt{2} (\hat i+\hat j)$

The terminal point of its vector is point Q(0, 1, 1)

Therefore, the direction of the vector force is

$v_2=(0-0)\hat i+(1-0)\hat j +(1-0)\hat k\\\\=0\hat i+1\hat j+1\hat k\\\\=\hat j + \hat k$

$\frac{v_2}{|v_2|} =\frac{\hat j+ \hat k}{\sqrt{0^2+1^2+1^2} } \\\\=\frac{1}{\sqrt{2} (\hat j +\hat k)}$

The magnitude of the force is 60lb, so the force will be

$F_2=60\times \frac{1}{\sqrt{2} } (\hat j+\hat k)\\\\=30\sqrt{2} (\hat j+\hat k)$

The resultant of the two forces is

$F=F_1+F_2\\\\=[20\sqrt{2} (\hat i+\hat j)]+[30\sqrt{2} (\hat j +\hat k)]\\\\=20\sqrt{2} \hat i+20\sqrt{2} \hat j +30\sqrt{2} \hat j+30\sqrt{2} \hat k\\\\=20\sqrt{2} \hat i+50\sqrt{2} \hat j+30\sqrt{2} \hat k$

The magnitude force will be

$|F|=\sqrt{(20\sqrt{2} )^2+(50\sqrt{2} )^2+(30\sqrt{2} )^2} \\\\=\sqrt{800+5000+1800} \\\\=\sqrt{3100} \\\\=55.68$

to (1 decimal place)=55.7lb

b) The direction angle of force F

The angle formed by F and x axis

$\alpha=\cos^{-1}(\frac{20\sqrt{2} }{\sqrt{3100} } )\\\\=\cos^{-1}(0.5080)\\\\=59.469$

The angle formed by F and y axis

$\alpha=\cos^{-1}(\frac{50\sqrt{2} }{\sqrt{3100} } )\\\\=\cos^{-1}(1.270)\\\\=$

The angle formed by F and z axis

$\alpha=\cos^{-1}(\frac{30\sqrt{2} }{\sqrt{3100} } )\\\\=\cos^{-1}(0.7620)\\\\=40.359$

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Answer:

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Step-by-step explanation:

The total amount paid on a 35 year loan was $98,000 at the rate of interest 4.1%

We will calculate Principal amount by this formula

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Where A = amount (98,000)

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r = rate of interest 4.1% (0.041)

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t = time (35 years)

$98,000=P(1+\frac{0.041}{12})^{(12)(35)}$

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$98,000=P(1.003416)^{(420)}$

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To remove proportionality, introduce a constant (k).

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So,

40 = k ×√25

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k = 8

Now,

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10.4 / 8 = √C

( 10.4 / 8 ) ^ 2 = C

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Answer:

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Step-by-step explanation:

A confidence interval of 95% means that there is a 95% certainty that for a given sample, the population mean will be within the confidence interval estimated.

This is the same as saying that if he sampling procedure were repeated many times, 95% of the time the population mean would be contained in the resulting confidence interval.

Therefore, the answer is B)

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