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3 years ago

Robert and Elena usually order a pizza for $10.00. the large pizza costs 40% more. what does the large pizza cost

Mathematics

2 answers:

Julli [10]3 years ago

6 0

30 Bc that's was a question

AfilCa [17]3 years ago

3 0

Sierra 10.00(.40%) and then times 10.00 to .40

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The area of a circle is 153.86 square meters. What is the diameter of the circle? Use 3.14 for π

Sav [38]

Answer: √ 4A /π or 13.996450848446

Step-by-step explanation:

D = 2R

C = 2πR

A = πR2

where:

R: Radius

D: Diameter

C: Circumference

A: Area

π: 3.14159

3 0

3 years ago

Read 2 more answers

Lim (n/3n-1)^(n-1) n → ∞

n200080 [17]

Looks like the given limit is

$\displaystyle \lim_{n\to\infty} \left(\frac n{3n-1}\right)^{n-1}$

With some simple algebra, we can rewrite

$\dfrac n{3n-1} = \dfrac13 \cdot \dfrac n{n-9} = \dfrac13 \cdot \dfrac{(n-9)+9}{n-9} = \dfrac13 \cdot \left(1 + \dfrac9{n-9}\right)$

then distribute the limit over the product,

$\displaystyle \lim_{n\to\infty} \left(\frac n{3n-1}\right)^{n-1} = \lim_{n\to\infty}\left(\dfrac13\right)^{n-1} \cdot \lim_{n\to\infty}\left(1+\dfrac9{n-9}\right)^{n-1}$

The first limit is 0, since 1/3ⁿ is a positive, decreasing sequence. But before claiming the overall limit is also 0, we need to show that the second limit is also finite.

For the second limit, recall the definition of the constant, e :

$\displaystyle e = \lim_{n\to\infty} \left(1+\frac1n\right)^n$

To make our limit resemble this one more closely, make a substitution; replace 9/(n - 9) with 1/m, so that

$\dfrac{9}{n-9} = \dfrac1m \implies 9m = n-9 \implies 9m+8 = n-1$

From the relation 9m = n - 9, we see that m also approaches infinity as n approaches infinity. So, the second limit is rewritten as

$\displaystyle\lim_{n\to\infty}\left(1+\dfrac9{n-9}\right)^{n-1} = \lim_{m\to\infty}\left(1+\dfrac1m\right)^{9m+8}$

Now we apply some more properties of multiplication and limits:

$\displaystyle \lim_{m\to\infty}\left(1+\dfrac1m\right)^{9m+8} = \lim_{m\to\infty}\left(1+\dfrac1m\right)^{9m} \cdot \lim_{m\to\infty}\left(1+\dfrac1m\right)^8 \\\\ = \lim_{m\to\infty}\left(\left(1+\dfrac1m\right)^m\right)^9 \cdot \left(\lim_{m\to\infty}\left(1+\dfrac1m\right)\right)^8 \\\\ = \left(\lim_{m\to\infty}\left(1+\dfrac1m\right)^m\right)^9 \cdot \left(\lim_{m\to\infty}\left(1+\dfrac1m\right)\right)^8 \\\\ = e^9 \cdot 1^8 = e^9$

So, the overall limit is indeed 0:

$\displaystyle \lim_{n\to\infty} \left(\frac n{3n-1}\right)^{n-1} = \underbrace{\lim_{n\to\infty}\left(\dfrac13\right)^{n-1}}_0 \cdot \underbrace{\lim_{n\to\infty}\left(1+\dfrac9{n-9}\right)^{n-1}}_{e^9} = \boxed{0}$

7 0

3 years ago

An ice cream shop offers 3 ice cream flavors 3 types of syrup and 2 toppings for sundaes

babymother [125]

Answer: 18

Step-by-step explanation:

3 0

3 years ago

How old were the twins who played in the recital?

inna [77]

To find out how old the twins were that were in the recital you need to be able to interpret a stem and leaf plot. The number of the left gets placed with each number on the right to create a number in the data set. See the key for an example. This means there were 2 people that were 5 years old making them the twins!

3 0

3 years ago

Solve for y: 3(2y + 4) = 4(2y – 1/2). The solution is y =

tatyana61 [14]

Answer:

Answer y=7

Step-by-step explanation:

6 0

3 years ago