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3 years ago

PLEASE can someone explain why The exact value of sec ( π/6) is 2 /√ 3 ??

1 answer:

3 0

$\bf sec\left( \frac{\pi }{6} \right)\qquad recall\to sec(\theta)=\cfrac{1}{cos(\theta)}\qquad thus
\\\\
sec\left( \frac{\pi }{6}\right)\iff \cfrac{1}{cos\left( \frac{\pi }{6}\right)}
\\\\\\
\textit{check your Unit Circle for what the }cos\left( \frac{\pi }{6}\right)\ is
\\\\\\
\cfrac{1}{\frac{\sqrt{3}}{2}}\implies \cfrac{\frac{1}{1}}{\frac{\sqrt{3}}{2}}\implies 
\cfrac{1}{1}\cdot \cfrac{2}{\sqrt{3}}\implies \cfrac{2}{\sqrt{3}}$

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Find the 10th partial sum of the arithmetic sequence defined by

Evgesh-ka [11]

Answer:

22.5

Step-by-step explanation:

If you expand the series, you can see the first few terms of the series:

Putting 1 in $n$ , $\frac{1}{2}(1)-\frac{1}{2}=0$
Putting 2 in $n$ , $\frac{1}{2}(2)-\frac{1}{2}=0.5$
Putting 3 in $n$ , $\frac{1}{2}(3)-\frac{1}{2}=1$
Putting 4 in $n$ , $\frac{1}{2}(4)-\frac{1}{2}=1.5$

We can see the series is 0, 0.5, 1, 1.5, ....

This is an arithmetic series with common difference (the difference in 2 terms) 0.5 and first term 0.

We know formula for sum of arithmetic series:

$s_{n}=\frac{n}{2}(2a+(n-1)d)$

Where,

$S_{n}$ denotes the nth partial sum
$a$ is the first term (in our case it is 0)
$n$ is the term (in our case it is 10 since we want to find 10th partial sum -- sum until first 10 terms)
$d$ is the common difference (difference in term and the previous term) (in our case it is 0.5)

Substituting these into the formula, we get the 10th partial sum to be:

$s_{10}=\frac{10}{2}(2(0)+(10-1)(0.5))\\s_{10}=5(0+(9)(0.5))\\s_{10}=5(0+4.5)\\s_{10}=5(4.5)\\s_{10}=22.5$

So the sum of the first 10 terms is 22.5. Third answer choice is right.

8 0

3 years ago

Read 2 more answers

ULLIVLY/1/2/3/assessment

zvonat [6]

<h3>The worth after 4 years is $ 680.24</h3>

Solution:

The formula for compound interest, including principal sum, is:

$A = p(1+\frac{r}{n})^{nt}$

Where,

A = the future value of the investment

P = the principal investment amount

r = the annual interest rate (decimal)

n = the number of times that interest is compounded per unit t

t = the time the money is invested

From given,

n = 1 ( since interest is compounded annually)

p = 500

t = 4

$r = 8 \% = \frac{8}{100} = 0.08$

Substituting the values we get,

$A = 500(1+ \frac{0.08}{1})^{1 \times 4}\\\\A = 500(1.08)^4\\\\A = 500 \times 1.36048896\\\\A = 680.24448 \approx 680.24$

Thus the worth after 4 years is $ 680.24

3 0

3 years ago

Box of cereal contains 23.4 ounces. Cost $5.49. What’s the cost per ounce?

Sedaia [141]

Answer:

it 4.262295082

Step-by-step explanation:

you have to divid the ounces by the cost

6 0

3 years ago

What is the equation of the line that is parallel to the line y =-1\3

PilotLPTM [1.2K]

Hello!

If a you want to find an equation of the line that is parallel to the given line, we must know that if two lines are parallel, then their slope will always have to be equal.

This means that the new equation must have a slope of -1/3.

Also, you would need to substitute the given point (6, 8) into the equation with the slope: -1/3 as well. Following these steps allows you to find the equation of line.

y = -1/3x + b (6, 5)

5 = -1/3(6) + b

5 = -2 + b (add 2 to both sides)

7 = b

Therefore, the equation of the line is y = -1/3x + 7.

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3 years ago

Lars deposited $50 into a savings account for which interest is compounded quarterly. According to the rule of 72, what interest

Ivanshal [37]

Answer: C 2.5%

Step-by-step explanation:

The "Rule of 72" is a easy way to calculate how much time an investment will take to double with a given fixed annual rate of interest.

Just we have to divide 72 by the annual rate of return(r), we can get a rough estimate of how many years it will take to double the initial investment .

Now, in given problem: Let 'r' be the rate of interest

Time to double the amount=29 years

Thus by rule 72 ,

$\frac{72}{r}=29\\\Rightarrow\ r=\frac{72}{29}=2.4827\%\approx2.5\%$

Therefore, C is the right option.

3 0

3 years ago

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