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3 years ago

Find the volume of each cylinder in terms of pie

Mathematics

2 answers:

ladessa [460]3 years ago

6 0

A=60 B=36A is greater than B

Tom [10]3 years ago

3 0

Answer:

A=60

B=36

A, is greater

Step-by-step explanation:

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Find the number to which the sequence {(3n+1)/(2n-1)} converges and prove that your answer is correct using the epsilon-N defini

Nat2105 [25]

By inspection, it's clear that the sequence must converge to $\dfrac32$ because

$\dfrac{3n+1}{2n-1}=\dfrac{3+\frac1n}{2-\frac1n}\approx\dfrac32$

when $n$ is arbitrarily large.

Now, for the limit as $n\to\infty$ to be equal to $\dfrac32$ is to say that for any $\varepsilon>0$ , there exists some $N$ such that whenever $n>N$ , it follows that

$\left|\dfrac{3n+1}{2n-1}-\dfrac32\right|$

From this inequality, we get

$\left|\dfrac{3n+1}{2n-1}-\dfrac32\right|=\left|\dfrac{(6n+2)-(6n-3)}{2(2n-1)}\right|=\dfrac52\dfrac1{|2n-1|}$
$\implies|2n-1|>\dfrac5{2\varepsilon}$
$\implies2n-1\dfrac5{2\varepsilon}$
$\implies n\dfrac12+\dfrac5{4\varepsilon}$

As we're considering $n\to\infty$ , we can omit the first inequality.

We can then see that choosing $N=\left\lceil\dfrac12+\dfrac5{4\varepsilon}\right\rceil$ will guarantee the condition for the limit to exist. We take the ceiling (least integer larger than the given bound) just so that $N\in\mathbb N$ .

6 0

3 years ago

A milk carton is 20cm long, 5cm wide and 40cm high. What volume of milk can it hold (in cubic cm)? *

Marina CMI [18]

Answer:

30 times 10 is 300. 300 times 50 is 15,000.

Step-by-step explanation:

bc i know

6 0

3 years ago

Read 2 more answers

Label five places in the photo that have a slope.

Naya [18.7K]

Step-by-step explanation

The orange machine, the very end of the shovel part. That line is a slope. The middle part of the scooper could also be a slope. The very beginng part of the scooper is also a slope. The bottom part of the scooper is also a slope. The bottom part at the end of the scooper could also be slope.

3 0

3 years ago

Trees are planted at intervals of 5 m along side of a 140 m straight path. The first tree is planted at the start of the path an

Luden [163]

<h3>Solution :</h3>

Distance between first tree and last tree is 140m .

And distance between each tree (d) = 5 m

let's solve for number of trees (n) :

$\hookrightarrow \: (n - 1)d = 140$