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2 years ago

What is this called, like whats the name of this thing?? {18 ≤ y ≤ 30}

Mathematics

1 answer:

Tpy6a [65]2 years ago

3 0

Answer:

An inequality.

Step-by-step explanation:

This gives the range of values that y can take.

It can equal 18 or be greater than eighteen but it also could be 30 or less than thirty.

WE read the signs starting from y to the left and to the right.

So y is greater or equal to 18 and less than or equal to 30.

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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

2 years ago

Sammy is conducting a science experiment were he has to mix 8. 25 ounces and 4

aleksley [76]

430 oz + 8.25 oz = 438.25 oz

6 0

3 years ago

Find the sum of the interior angle measures of the green polygon,

Radda [10]

Answer:

The sum of interior angles of given polygon is 900°

Step-by-step explanation:

A regular polygon is a n-sided figure with n sides and the length of all sides is same.

In the diagram, we have a polygon with 7 sides.

The formula given is used to calculate the sum of interior angles of a polygon

$Sum\ of\ interior\ angles = (n-2)*180$

Here n is the number of sides of polygon

In the given polygon

n = 7

So,

$Sum = (7-2)*180 = 5*180 = 900$

Hence,

The sum of interior angles of given polygon is 900°

7 0

3 years ago

The number of students in a school increased by 25%between last year and this year. Last year there were 250 students in the sch

Ber [7]

I believe that is 275 because percent is just out of one hundred

8 0

3 years ago

Based on the graph, which inequality is correct for a number that is to the right of -4

Anon25 [30]

2 > -4

2 is greater than -4

3 0

3 years ago