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3 years ago

PLEASE HELPPP MEHHHHHHHHHHHH

Mathematics

1 answer:

Yuliya22 [10]3 years ago

8 0

Answer:

Ummm... I'm not sure if this'll help

Step-by-step explanation:

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<img src="https://tex.z-dn.net/?f=%24a%2Ba%20r%2Ba%20r%5E%7B2%7D%2B%5Cldots%20%5Cinfty%3D15%24%24a%5E%7B2%7D%2B%28a%20r%29%5E%7B

riadik2000 [5.3K]

Let

$S_n = \displaystyle \sum_{k=0}^n r^k = 1 + r + r^2 + \cdots + r^n$

where we assume |r| < 1. Multiplying on both sides by r gives

$r S_n = \displaystyle \sum_{k=0}^n r^{k+1} = r + r^2 + r^3 + \cdots + r^{n+1}$

and subtracting this from $S_n$ gives

$(1 - r) S_n = 1 - r^{n+1} \implies S_n = \dfrac{1 - r^{n+1}}{1 - r}$

As n → ∞, the exponential term will converge to 0, and the partial sums $S_n$ will converge to

$\displaystyle \lim_{n\to\infty} S_n = \dfrac1{1-r}$

Now, we're given

$a + ar + ar^2 + \cdots = 15 \implies 1 + r + r^2 + \cdots = \dfrac{15}a$

$a^2 + a^2r^2 + a^2r^4 + \cdots = 150 \implies 1 + r^2 + r^4 + \cdots = \dfrac{150}{a^2}$

We must have |r| < 1 since both sums converge, so

$\dfrac{15}a = \dfrac1{1-r}$

$\dfrac{150}{a^2} = \dfrac1{1-r^2}$

Solving for r by substitution, we have

$\dfrac{15}a = \dfrac1{1-r} \implies a = 15(1-r)$

$\dfrac{150}{225(1-r)^2} = \dfrac1{1-r^2}$

Recalling the difference of squares identity, we have

$\dfrac2{3(1-r)^2} = \dfrac1{(1-r)(1+r)}$

We've already confirmed r ≠ 1, so we can simplify this to

$\dfrac2{3(1-r)} = \dfrac1{1+r} \implies \dfrac{1-r}{1+r} = \dfrac23 \implies r = \dfrac15$

It follows that

$\dfrac a{1-r} = \dfrac a{1-\frac15} = 15 \implies a = 12$

and so the sum we want is

$ar^3 + ar^4 + ar^6 + \cdots = 15 - a - ar - ar^2 = \boxed{\dfrac3{25}}$

which doesn't appear to be either of the given answer choices. Are you sure there isn't a typo somewhere?

7 0

3 years ago

Cereal. A dietician obtains the amounts of sugar (incentigrams) from 100 centigrams (or 1 gram) in each of 10 differentcereals,

nadezda [96]

Answer:

Range is 44

mean is 29.7

variance is 289.56

standard deviation is 17.016

Step-by-step explanation:

The data given as follows

3, 24, 30, 47, 43, 7, 47,13, 44, 39

Range = maximum - minimum

= 47 -3 = 44

mean = $\frac{3+24+30+47+43+7+47+13+44+39}{10}$ = 297/10 = 29.7

variance = $\frac{sum xi^2 }{N} - mean^2 }$

= 289.56

SD = $\sqrt{variance}$ = 17.016

The standard deviation of the given data is not a good measure as the range and standard deviation are far apart. The standard deviation gives how the given data is dispersed from the mean or expected value, while the range gives a rough idea of variability of the data.

3 0

3 years ago

MUST HELP!!!! (25 POINTS) +BRAINLEST +5 STARS +THANKS ON PROLFILE!!!!

MrMuchimi

Answer:

Enlargement Areas

Step-by-step explanation:

if you enlarge the little one, they will intersect each other perfectly because those triangles are similar and the same. they are just different sizes

hope this helps!

3 0

3 years ago

What is the value of an investment of $650 invested at an annual interest rate of 1.5% compounded monthly for 16 years?

diamong [38]

Answer:

it should be 650

1.5

0.015

Step-by-step explanation:

6 0

3 years ago

What is the solution to the inequliaty below?

Mandarinka [93]

The answer is A because the sign changes

3 0

3 years ago