258/300 in decimal form

Matthew is half as old as Alan. If the sum of their ages is 54, find their ages.

kompoz [17]

Answer:

26

Step-by-step explanation:

5 0

3 years ago

kylie has $70 to spend on clothes. she wants to buy a pair of jeans for $ 30 and spend the rest on t-shirts. each t-shirt cost $

lbvjy [14]

Kylie can purchase 32 T-shirt

6 0

3 years ago

If the angle between each blade of the wind turbine is the same, and each blade has a length of 20 meters, find the distance bet

Ket [755]

A typical windmill has three blades. We can envision these blades in a circle, which a circle = 360 degrees. We want to divide up the angles of the blades so they are even or makes up 360 degrees. We have three blades so we have 3 angles to divide by 360 degrees. So, 360 / 3 = 120 degrees. Now that we know the angle of the blades, we can use the Law of Cos to solve the distance between the blade tip.

Law of Cos

$c^2 = a^2 + b^2 - 2(a)(b)(\cos A)$

We know

a = 20

b = 20

A = Angle = 120

We need to solve for c

$c^2 = a^2 + b^2 - 2(a)(b)(\cos A)$

Take the square root of each side of the =

$\sqrt{c^2} = \sqrt{a^2 + b^2 - 2(a)(b)(\cos A)}$

$c = \sqrt{a^2 + b^2 - 2(a)(b)(\cos A)}$

Input the values we know into the formula and solve for c:

$c = \sqrt{a^2 + b^2 - 2(a)(b)(\cos A)}$

$c = \sqrt{20^2 + 20^2 - 2(20)(20)(\cos 120)}$

$c = \sqrt{400 + 400 - 2(20)(20)(\cos 120)}$

$c = \sqrt{800 - 2(20)(20)(\cos 120)}$

$c = \sqrt{800 - 2(400)(\cos 120)}$

$c = \sqrt{800 - 800(\cos 120)}$

$c = \sqrt{800 - (-400)}$

$c = \sqrt{1200}$

$c = 20\sqrt{3}$

$c = 34.641016$

$c = 34.64$

We now have our answer, which is 34.64 and that is C.

3 0

4 years ago

This is on the constant of proportionality from a table...

ZanzabumX [31]

The correct answer is 8.3 repeated.

25 divided by 3 is 8.3 repeated and so is the rest so it is obvious to say that 8.3 repeated is the correct answer.

3 0

3 years ago

(1 point) Each of the following statements is an attempt to show that a given series is convergent or divergent not using the Co

kvv77 [185]

Answer:

I.

CORRECT.

II.

CORRECT.

III.

CORRECT.

IV.

CORRECT.

V.

INCORRECT.

VI.

CORRECT

Step-by-step explanation:

To understand let us restate the comparison test in simple terms.

Comparison test :

Given $\text{Series}_A$ and $\text{Series}_B$ such that $\text{Series}_A < \text{Series}_B$ , then

1. If $\text{Series}_B$ converges then $\text{Series}_A$ converges as well.

2. If $\text{Series}_A$ diverges then $\text{Series}_B$ diverges as well.

Now to give you a more intuitive idea of what is going on, think about it like this. When the series on top converges it is like an "upper bound" for what you have on the bottom, therefore what you have on the bottom has to converge as well.

Similarly if what you have on the bottom explotes, then what you have on top will explote as well.

That's how I like to think about that intuitively.

Now, using those results let us examine the statements.

I.

$\frac{1}{n} < \frac{ln(n)}{n}$

Since the infinite sum of 1/n diverges in fact the infinite sum of ln(n)/n does not converge.

Therefore, CORRECT.

II.

$\frac{\arctan(n)}{n^3} < \frac{\pi}{2}\frac{1}{n^3}$

Since the infinite sum of $\frac{\pi}{2}\frac{1}{n^3}$ is in fact convergent then $\frac{\arctan(n)}{n^3}$ converges as well using the comparison theorem. Therefore