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2 years ago

The two triangles below are similar. Solve for x:

Mathematics

1 answer:

Nataliya [291]2 years ago

3 0

Answer:

Explanation:

given the two triangles are similar

x = 5(27/9)

x = 135/9

x = 15

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4. Using the geometric sum formulas, evaluate each of the following sums and express your answer in Cartesian form.

nikitadnepr [17]

Answer:

$\sum_{n=0}^9cos(\frac{\pi n}{2})=1$

$\sum_{k=0}^{N-1}e^{\frac{i2\pi kk}{2}}=0$

$\sum_{n=0}^\infty (\frac{1}{2})^n cos(\frac{\pi n}{2})=\frac{1}{2}$

Step-by-step explanation:

$\sum_{n=0}^9cos(\frac{\pi n}{2})=\frac{1}{2}(\sum_{n=0}^9 (e^{\frac{i\pi n}{2}}+ e^{\frac{i\pi n}{2}}))$

$=\frac{1}{2}(\frac{1-e^{\frac{10i\pi}{2}}}{1-e^{\frac{i\pi}{2}}}+\frac{1-e^{-\frac{10i\pi}{2}}}{1-e^{-\frac{i\pi}{2}}})$

$=\frac{1}{2}(\frac{1+1}{1-i}+\frac{1+1}{1+i})=1$

2nd

$\sum_{k=0}^{N-1}e^{\frac{i2\pi kk}{2}}=\frac{1-e^{\frac{i2\pi N}{N}}}{1-e^{\frac{i2\pi}{N}}}$

$=\frac{1-1}{1-e^{\frac{i2\pi}{N}}}=0$

3th

$\sum_{n=0}^\infty (\frac{1}{2})^n cos(\frac{\pi n}{2})==\frac{1}{2}(\sum_{n=0}^\infty ((\frac{e^{\frac{i\pi n}{2}}}{2})^n+ (\frac{e^{-\frac{i\pi n}{2}}}{2})^n))$

$=\frac{1}{2}(\frac{1-0}{1-i}+\frac{1-0}{1+i})=\frac{1}{2}$

What we use?

We use that

$e^{i\pi n}=cos(\pi n)+i sin(\pi n)$

and

$\sum_{n=0}^k r^k=\frac{1-r^{k+1}}{1-r}$

6 0

3 years ago

Two numbers are in the ratio 3:7

lbvjy [14]

Answer:

98 And 18 i think

Step-by-step explanation:

8 0

3 years ago

Find the median, first quartile, third quartile, and interquartile range of the data.

jasenka [17]

Answer:

Median: 55

First quartile: 26.5

Third quartile: 93

Interquartile range: 66.5

5 0

2 years ago

Read 2 more answers

Geometry pls halp... I have been asking this single question for over half an hour

irina [24]

Answer:

first one is SAS

Step-by-step explanation:

3 0

3 years ago

A random sample of 85 group leaders, supervisors, and similar personnel revealed that a person spent an average 6.5 years on the

strojnjashka [21]

Answer:

95% of confidence interval for the Population

( 6.1386 , 6.8614)

Step-by-step explanation:

Step( i ):-

Given random sample size 'n' =85

Mean of the sample size x⁻ = 6.5 years

Standard deviation of Population = 1.7 years

Level of significance = 0.95 or 0.05

Step(ii):-

95% of confidence interval for the Population is determined by

$(x^{-} - Z_{0.05} \frac{S.D}{\sqrt{n} } , x^{-} + Z_{0.05} \frac{S.D}{\sqrt{n} })$

$(6.5 - 1.96\frac{1.7}{\sqrt{85} } , 6.5 + 1.96 \frac{1.7}{\sqrt{85} })$

( 6.5 - 0.3614 , 6.5 + 0.3614 )

( 6.1386 , 6.8614)

Conclusion:-

95% of confidence interval for the Population

( 6.1386 , 6.8614)

8 0

3 years ago