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choli [55]
3 years ago
11

The balance in Petra's account is -$32.50. The balance in John's

Mathematics
1 answer:
Firlakuza [10]3 years ago
7 0

Answer:

Petra

Step-by-step explanation:

Petra's acc has $32.50,while John's balance acc has $34.60 so,petra has less balance money

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3x+3(x+y) what is equivalent
NNADVOKAT [17]

Answer:

6x+3y

Step-by-step explanation:

6 0
3 years ago
<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
FRÉD AND ETHEL WACHED TV FOR SEVERAL HOURS ONE AFTERNOON. THEY BEGAN AT 1:30 P.M AND CONTINUED WACHING TV FOR 3 HOURS AND 45 MIN
QveST [7]

30 + 45 =75
3 + 1 = 4
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4 + 1 = 5
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7 0
3 years ago
If 1/2x+1/3=4 What is the value of 3x+2y
ivolga24 [154]

Answer:

x=3/22 ; y=-9/44

Step-by-step explanation:

1/2x+1/3=4

=>1/2x=4-1/3

=>1/2x=(12-1)/3

=>1/2x=11/3

=>22x=3

=>x=3/22....(1)

then,

3x+2y

2y=-3 . (3/22)

y=-9/44

6 0
4 years ago
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How many inches are in 200 meters?
4vir4ik [10]
200×39.37=7874
the answer is 7874 in
3 0
3 years ago
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