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1 year ago

Identify the following series as arithmetic, geometric, both, or neither.

Mathematics

2 answers:

morpeh [17]1 year ago

8 0

Answer:

Option 2 - Geometric series

Step-by-step explanation:

Given : Series $3a+3a^2+3a^3+.....+3a^n$

To identify : The following series as arithmetic, geometric, both, or neither.

Solution :

According to the series,

$3a+3a^2+3a^3+.....+3a^n$

If we take 3 common,

$=3(a+a^2+a^3+.....+a^n)$

the above series make is a geometric series as 3 is a constant.

Geometric series is $\sum_k a_k$ where ratio of two terms is $\frac{a_{k+1}}{a_k}$

In the above given series, the common ratio is a.

As the series satisfy all conditions of geometric series.

Therefore, Option 2 is correct.

pychu [463]1 year ago

3 0

The expression <span>3a + 3a² + 3a³ + . . . + 3an is a geometric expression, because 3 is constant. </span>

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You are considering buying one of two brands of barbecue grills. Brand F costs $650 and will last for about fifteen year

melamori03 [73]

Answer:

the anser is b

Step-by-step explanation:

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1 year ago

Find the cube roots of 27(cos 330Á + i sin 330Á). Please help c:

Mashcka [7]

Use formula
$e^{ix}=\cos{x}+\sin{x}$

$\sqrt[3]{27(\cos{330^o}+i\sin{330^o})} 
\\\sqrt[3]{27e^{i330^o} }
\\ \sqrt[3]{27} \sqrt[3]{e^{i330^o}} 
\\ \sqrt[3]{3^3} \sqrt[3]{e^{i110^o\times 3}} 
\\ \sqrt[3]{3^3} \sqrt[3]{(e^{i110^o})^ 3}} 
\\ 3e^{i110^o}
\\3(\cos{110^o}+i\sin{110^o})$

Since $330^o=360^o+330^o=690^o
$ and $330^o=2\times 360^o+330^o=1050^o$ there are two more solutions:
1. $3(\cos{230^o}+i\sin{230^o})$
2. $3(\cos{350^o}+i\sin{350^o})$

4 0

1 year ago

Read 2 more answers

A point x is 34m due to east of a point Y . The bearing of a flagpole from x and Y are N18°W And N40°E respectively .

Murljashka [212]

Answer:

The distance of flag post from Y is 38.13 m

Step-by-step explanation:

Consider point Y at the intersection of both lines as shown below. Now the point X lies 34 meter from point Y in east direction.

Now flag pole at point X lies at a bearing of N18°W. That is at point X from north, flag post makes an angle of 18° towards west.

Similarly flag pole at point Y lies at a bearing of N40°E. That is at point Y from north, flag post makes an angle of 40° towards east.

Consider ∆ AXY as right angle triangle. Therefore measure of angle FXY is,

$\angle AXY=\angle AXF+\angle FXY$

$\therefore 90 \degree=18\degree+\angle FXY$

$\angle FXY=72\degree$

Consider ∆ BYX as right angle triangle. Therefore measure of angle FYX is,

$\angle BYX=\angle BYF+\angle FYX$

$\therefore 90 \degree=40\degree+\angle FYX$

$\angle FYX=50\degree$

Refer attachment 1.

From diagram consider the triangle FYX. To find the third angle that is ∠YFX can be calculated by using angle sum property of triangle.

∠YFX+∠FYX+∠FXY=180°

∠YFX+50°+72°=180°

∠YFX=58°

Refer attachment 2.

Now the distance FY can be calculated using sin rule as follows,

$\frac{\sin X}{FY}=\frac{\sin F}{YX}=\frac{\sin Y}{FX}$

Substituting the values,

$\frac{\sin 72}{FY}=\frac{\sin 58}{34}=\frac{\sin 50}{FX}$

Simplifying first two terms,

$\frac{\sin 72}{FY}=\frac{\sin 58}{34}$

Cross multiplying,

$34\times\sin 72=FY\times \sin 58$

$\dfrac{34\times\sin 72}{\sin 58}=FY$

$FY=38.13$ m

7 0

1 year ago

A water tank leaks 5 gallons of water each day. What integer represents the change in the number of gallons of water in the tank

andrey2020 [161]

Answer:

35 is the integer that represents the change in number of gallons of water in the tank after 7 days

Step-by-step explanation:

The water tank leaks 5 gallons in one day.

So if there is leakage of 5 gallons a day, then after 7 days the total leakage will be:

Total Leakage = Leakage per day * Total number of days

= 5 Gal/day * 7 day

= 35 Gallons

So, 35 is the integer that represents the change in number of gallons of water in the tank after 7 days ..

5 0

1 year ago

Of 1,050 randomly selected adults, 360 identified themselves as manual laborers, 280 identified themselves as non-manual wage ea

garik1379 [7]

Answer:

We can claim with 95% confidence that the proportion of executives that prefer trucks is between 19.2% and 32.8%.

Step-by-step explanation:

We have a sample of executives, of size n=160, and the proportion that prefer trucks is 26%.

We have to calculate a 95% confidence interval for the proportion.

The sample proportion is p=0.26.

The standard error of the proportion is:

$\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.26*0.74}{160}}\\\\\\ \sigma_p=\sqrt{0.0012}=0.0347$

The critical z-value for a 95% confidence interval is z=1.96.

The margin of error (MOE) can be calculated as:

$MOE=z\cdot \sigma_p=1.96 \cdot 0.0347=0.068$

Then, the lower and upper bounds of the confidence interval are:

$LL=p-z \cdot \sigma_p = 0.26-0.068=0.192\\\\UL=p+z \cdot \sigma_p = 0.26+0.068=0.328$

The 95% confidence interval for the population proportion is (0.192, 0.328).

We can claim with 95% confidence that the proportion of executives that prefer trucks is between 19.2% and 32.8%.

3 0

2 years ago