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4 years ago

Please help me!!!!!!!

Mathematics

1 answer:

scZoUnD [109]4 years ago

8 0

Step-by-step explanation:

Write all numerators above the common denominator 7w-5w+6 (w+4)=0 Multiply parenthesis by 6 collect terms 7w-5w+6 (w+4) Wx (w+4) =0 set numerator equal to 0 8w=-24 divide both sides by 8 w=-3

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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

HELP does anyone get these three questions?

Tom [10]

Step-by-step explanation:

since we have the relation (inches/dollars)

4.3 inches down per dollar

per 10 dollars 43 inches down

per half a dollar 2.15 inches down

per 63.60 dollars 273.48 inches down

8 0

3 years ago

Geometry

Mademuasel [1]

DB is a median (given). It goes from vertex point D to midpoint B.

The point B is the midpoint of segment AC. So B cuts AC into two equal halves: AB and AC
Meaning AB = AC

AC = AB+BC ... segment addition postulate
AC = AB+AB ... substitution; replace BC with AB (valid because AB = AC)
AC = 2*AB
2*AB = AC
2*AB = 50 ... substitution; replace AC with 50
2*AB/2 = 50/2 ... divide both sides by 2
AB = 25 which is the answer

6 0

3 years ago

Determine the 15th term of the sequence -2, 4,...

Thepotemich [5.8K]

Mot enough information given.
The rule might be

-- add 6
or
-- double and add 8
or
-- square
or
-- multiply by -2 .

We need one more term to determine what the rule is for calculating the next term from the previous one.

The

7 0

3 years ago

Read 2 more answers

Does anyone know the coordinates for this if i graphed it?

zavuch27 [327]

Answer:

I have no idea

Step-by-step explanation:

5xt789v

6 0

3 years ago

Please help me!!!!!!!​

Please help me!!!!!!!