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2 years ago

Teresa received $80 for her birthday. At what rate would she have to invest to have $90 at the end of the year

Mathematics

1 answer:

DiKsa [7]2 years ago

4 0

Saving I don’t know but please let me know :)

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The area of a circle is 9π m². What is the circumference, in meters? Express answer in terms of π

ad-work [718]

Answer:

20.25 pi

Step-by-step explanation:

The circumference of a circle is given by

C = 2 * pi *r

9 pi = 2 * pi *r

Divide each side by 2pi

9pi / 2 pi = 2 pi r / 2 pi

4.5 = r

Now we can find area

A = pi r^2

= pi ( 4.5)^2

20.25 pi

8 0

1 year ago

What is 44.2 rounded to the nearest whole number?

tatuchka [14]

44 is the number rounded

5 0

2 years ago

Read 2 more answers

Of the following sets, which numbers in {1, 2, 3, 4, 5} make the inequality 5x + 2 > 12 true?

kicyunya [14]

Answer:

3,4,5

Step-by-step explanation:

try every one

4 0

3 years ago

I need help with question

Sergeu [11.5K]

Answer:

y = x² + 2

Step-by-step explanation:

Given

x = $\sqrt{y-2}$ ( square both sides )

x² = y - 2 ( add 2 to both sides )

x² + 2 = y

8 0

2 years ago

Evaluate the infinite sum:

satela [25.4K]

Consider the k-th partial sum,

$S_k = 1 + \dfrac2\pi + \dfrac3{\pi^2} + \cdots + \dfrac k{\pi^{k-1}}$

More compactly,

$\displaystyle S_k = \sum_{i=1}^k \frac i{\pi^{i-1}} = \frac{(1-\pi)k+\pi^{k+1}-\pi}{(1-\pi)^2\pi^{k-1}}$

(this is just another case of a similar sum you asked about a while ago [24494877])

The infinite sum is the limit of the partial sum as k goes to infinity. We have

$\displaystyle \lim_{k\to\infty} \frac{(1-\pi)k+\pi^{k+1}-\pi}{(1-\pi)^2\pi^{k-1}} = \frac\pi{(1-\pi)^2} \lim_{k\to\infty} \left(\frac{(1-\pi)k}{\pi^k} + \pi - \frac1{\pi^{k-1}} \right) = \boxed{\frac{\pi^2}{(1-\pi)^2}}$

since the non-constant terms in the limit converge to 0.

Alternatively, recall that for |x| < 1, we have

$\dfrac1{1-x} = \displaystyle \sum_{n=0}^\infty x^n$

Differentiating both sides gives

$\dfrac1{(1-x)^2} = \displaystyle \sum_{n=0}^\infty nx^{n-1} = \sum_{n=1}^\infty nx^{n-1}$

also valid for |x| < 1. Take x = 1/π and you get the sum you want to compute.

5 0

2 years ago