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Anettt [7]
3 years ago
6

(3a - b)(a + b) - (3a - b)²

Mathematics
1 answer:
natali 33 [55]3 years ago
5 0
The answer is 13a -2b
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Find S^20 if the series 1 + 1.1 ..... is a (a) arithmetic (b) geometric
quester [9]
I'm guessing S^20 is actually referring to the 20th partial sum S_{20}, with

S_{20}=1+(1+1\times0.1)+(1+2\times0.1)+\cdots+(1+18\times0.1)+(1+19\times0.1)

in the arithmetic case, and

S_{20}=1+1.1+1.1^2+\cdots+1.1^{18}+1.1^{19}

in the geometric case.

(a) Combining like terms, we have

S_{20}=20+0.1(1+2+\cdots+18+19)

and invoking the formula

1+2+\cdots+(n-1)+n=\dfrac{n(n+1)}2

we end up with

S_{20}=20+0.1\dfrac{19\times20}2=39

(b) Multiply S_{20} by 1.1, then subtract this from S_{20}:

1.1S_{20}=1.1+1.1^2+1.1^3+\cdots+1.1^{19}+1.1^{20}

S_{20}-1.1S_{20}=-0.1S_{20}=1-1.1^{20}
\implies S_{20}=\dfrac{1.1^{20}-1}{0.1}\approx57.275
7 0
3 years ago
V5. Suppose you invest $5,000 at 9% interest, compounded annually, for 10 years. Determine the future value of your investment,
Elanso [62]

Answer: $11836.8

Step-by-step explanation:

Given. That :

Amount invested = $5000

Interest rate = 9% = 0.09

Period = 10 years, compounded annually

Using the compound interest formula :

A = p(1 + r/n)^nt

A = final amount

P = principal or invested amount

r = rate of interest

n = number of times interest Is applied per period

t = period

A = 5000(1 + 0.09/1)^(1*10)

A = 5000(1.09)^10

A = 5000 * 2.36736367459211723401

A = 11836.81837296058617005

= $11836.8

4 0
3 years ago
If you spin a spinner with 3 equal parts, how many possible outcomes are there? A. 1 B. 2 C. 3 D. 4
kakasveta [241]
The answer is c. 3 possible outcomes
6 0
4 years ago
Read 2 more answers
kali bought 6 books for a total of $154. math books cost $27 and English books cost $23. how many of each type of book did she b
kipiarov [429]
She bought 4 English books and 2 math books

27 x 4 = 108
23 x 2 = 46
108+46=154
5 0
3 years ago
Plssss do this!!!!! thanks
lisabon 2012 [21]

Answer:

4) SU = TU                    definition of a midpoint

5) ΔSVU ≅ ΔTWU        Side-Side-Side

6) ∠SVU ≅ ∠TWU        corresponding parts of congruent triangles are congruent

Step-by-step explanation:

7 0
3 years ago
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