All categories

3 years ago

The polygon below is a regular hexagon. What is the approximate length of the apothem? Round to the nearest tenth.

Mathematics

2 answers:

grigory [225]3 years ago

3 0

Answer:

Step-by-step explanation:

Inside the figure is a right triangle with hypotenuse 18 cm. Its height is half the measure of the side length. 18.2 is 9 cm. Using 9 cm and 18 cm, substitute the values into the Pythagorean theorem.

$a^2 + b^2 = c^2\\9^2 + b^2 = 18^2\\81 + b^2 = 324\\b^2 = 243\\b = 15.6$

devlian [24]3 years ago

3 0

Answer:

Step-by-step explanation:

You might be interested in

<img src="https://tex.z-dn.net/?f=%24a%2Ba%20r%2Ba%20r%5E%7B2%7D%2B%5Cldots%20%5Cinfty%3D15%24%24a%5E%7B2%7D%2B%28a%20r%29%5E%7B

riadik2000 [5.3K]

Let

$S_n = \displaystyle \sum_{k=0}^n r^k = 1 + r + r^2 + \cdots + r^n$

where we assume |r| < 1. Multiplying on both sides by r gives

$r S_n = \displaystyle \sum_{k=0}^n r^{k+1} = r + r^2 + r^3 + \cdots + r^{n+1}$

and subtracting this from $S_n$ gives

$(1 - r) S_n = 1 - r^{n+1} \implies S_n = \dfrac{1 - r^{n+1}}{1 - r}$

As n → ∞, the exponential term will converge to 0, and the partial sums $S_n$ will converge to

$\displaystyle \lim_{n\to\infty} S_n = \dfrac1{1-r}$

Now, we're given

$a + ar + ar^2 + \cdots = 15 \implies 1 + r + r^2 + \cdots = \dfrac{15}a$

$a^2 + a^2r^2 + a^2r^4 + \cdots = 150 \implies 1 + r^2 + r^4 + \cdots = \dfrac{150}{a^2}$

We must have |r| < 1 since both sums converge, so

$\dfrac{15}a = \dfrac1{1-r}$

$\dfrac{150}{a^2} = \dfrac1{1-r^2}$

Solving for r by substitution, we have

$\dfrac{15}a = \dfrac1{1-r} \implies a = 15(1-r)$

$\dfrac{150}{225(1-r)^2} = \dfrac1{1-r^2}$

Recalling the difference of squares identity, we have

$\dfrac2{3(1-r)^2} = \dfrac1{(1-r)(1+r)}$

We've already confirmed r ≠ 1, so we can simplify this to

$\dfrac2{3(1-r)} = \dfrac1{1+r} \implies \dfrac{1-r}{1+r} = \dfrac23 \implies r = \dfrac15$

It follows that

$\dfrac a{1-r} = \dfrac a{1-\frac15} = 15 \implies a = 12$

and so the sum we want is

$ar^3 + ar^4 + ar^6 + \cdots = 15 - a - ar - ar^2 = \boxed{\dfrac3{25}}$

which doesn't appear to be either of the given answer choices. Are you sure there isn't a typo somewhere?

7 0

2 years ago

Mark's brother is 5 years older than Mark. Their combined ages add up to 23. How old is Mark?

anygoal [31]

Answer:

Mark would be 9

3 0

3 years ago

Read 2 more answers

SAT Help

posledela

Well, their speeds are ( $V_1$ is Jack's speed, and $V_2$ is Richard's.
$V_1 = \frac{1}{5} houses/day \\ V_2 = \frac{1}{7} houses/day \\ V = V_1 + V_2 = \frac{1}{5}+\frac{1}{7} = \frac{7+5}{35} = \frac{12}{35}$
They, together, can paint 12 houses in 35 days. To get a single house, we only have to calculate $\frac{35}{12}$ which is very close to 3 (a bit below)

5 0

3 years ago

Read 2 more answers

A graph is shown below:

Charra [1.4K]

Answer:

The correct answer is actually B. x - 3y < 5

Step-by-step explanation:

Because you must convert the equation to y-intercept form first.

Which makes it y = 1/3x - 1.6

So y = 1.6 and using the slope of 1/3x you can find that x = 5

3 0