What’s 2 plus 2 Pupil:4 That’s good Good?, that’s perfect!

A rope is tied to the bottom of a hot air balloon as shown below. The rope makes an angle of 35 degrees with the ground distant

Inessa05 [86]

To get the distance of the balloon from the the bottom to the ground we apply the following trigonometric formula:
sin θ=opposite/hypotenuse
θ=35°
opposite=height,h
hypotenuse=75ft
Thus plugging our values in the formula we obtain:
sin 35=h/75
solving for h we get
h=75sin 35
h=43.02~43 ft

7 0

4 years ago

Plss help im bad at math:v 100 points!

KiRa [710]

$\mathbb{MY \: ANSWER}$

A
C
B
D
A

4 0

3 years ago

Read 2 more answers

Consider the sequence {an}={3n+13n−3n3n+1}. Graph this sequence and use your graph to help you answer the following questions.

Fantom [35]

Part 1: You can simplify $a_n$ to

$\dfrac{3n+1}{3n}-\dfrac{3n}{3n+1} = \dfrac1{3n}+\dfrac1{3n+1}$

Presumably, the sequence starts at n = 1. It's easy to see that the sequence is strictly decreasing, since larger values of n make either fraction smaller.

(a) So, the sequence is bounded above by its first value,

$|a_n| \le a_1 = \dfrac13+\dfrac14 = \boxed{\dfrac7{12}}$

(b) And because both fractions in $a_n$ converge to 0, while remaining positive for any natural number n, the sequence is bounded below by 0,

$|a_n| \ge \boxed{0}$

(c) Finally, $a_n$ is bounded above and below, so it is a bounded sequence.

Part 2: Yes, $a_n$ is monotonic and strictly decreasing.

Part 3:

(a) I assume the choices are between convergent and divergent. Any monotonic and bounded sequence is convergent.

(b) Since $a_n$ is decreasing and bounded below by 0, its limit as n goes to infinity is 0.

Part 4:

(a) We have

$\displaystyle \lim_{n\to\infty} \frac{10n^2+1}{n^2+n} = \lim_{n\to\infty}10+\frac1{n^2}}{1+\frac1n} = 10$

and the (-1)ⁿ makes this limit alternate between -10 and 10. So the sequence is bounded but clearly not monotonic, and hence divergent.

(b) Taking the limit gives

$\displaystyle\lim_{n\to\infty}\frac{10n^3+1}{n^2+n} = \lim_{n\to\infty}\frac{10+\frac1{n^3}}{\frac1n+\frac1{n^2}} = \infty$

so the sequence is unbounded and divergent. It should also be easy to see or establish that the sequence is strictly increasing and thus monotonic.

For the next three, I'm guessing the options here are something to the effect of "does", "may", or "does not".

(c) may : the sequence in (a) demonstrates that a bounded sequence need not converge

(d) does not : a monotonic sequence has to be bounded in order to converge, otherwise it grows to ± infinity.

(e) does : this is true and is known as the monotone convergence theorem.

5 0

3 years ago

Olivia goes shopping at the mall and buys a shirt that is on sale for 25% off. She also knows that the sales tax is 5%. If her f

Norma-Jean [14]

Answer: The shirt originally cost 125 dollars.

Step-by-step explanation: The shirt on sale is 25% off. So first multiply 25 by 5 and you get 125. So 125 is the originall price. Her final cost is 25 dollars. Last step: 125 divided by 5 equals 25 dollars.

3 0

4 years ago

Blake has 864 square inches of material with which to create a hollow three-dimensional container. He decides to make either a c

leonid [27]

Answer:

I think it's a cube, because the cube has bigger spaces because of the edges, but I don't know how much...

4 0

3 years ago