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3 years ago

If the dimensions of a square are increased 10%, by what percent is the area increased?

1 answer:

6 0

Increasing the length by 10% means we multiply the old length x by 1.1 since
100% + 10% = 1+0.1 = 1.1

Old length = x
New length = 1.1x
Old area = x*x = x^2
New area = (1.1x)*(1.1x) = (1.1*1.1)*(x*x) = 1.21x^2

So the area increases by 21%
1.21 = 1+0.21 = 100% + 21%

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What is the length of each piece????PLEASE HELP!!!!

Alex787 [66]

The last one because its a side length if 26 inches so you spit in half

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3 years ago

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Identify the cylinder with the smallest surface area

vovikov84 [41]

Answer:

Step-by-step explanation:

It has the smallest surface with an increase in height

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2 years ago

Determine formula of the nth term 2, 6, 12 20 30,42

nalin [4]

Check the forward differences of the sequence.

If $\{a_n\} = \{2,6,12,20,30,42,\ldots\}$ , then let $\{b_n\}$ be the sequence of first-order differences of $\{a_n\}$ . That is, for n ≥ 1,

$b_n = a_{n+1} - a_n$

so that $\{b_n\} = \{4, 6, 8, 10, 12, \ldots\}$ .

Let $\{c_n\}$ be the sequence of differences of $\{b_n\}$ ,

$c_n = b_{n+1} - b_n$

and we see that this is a constant sequence, $\{c_n\} = \{2, 2, 2, 2, \ldots\}$ . In other words, $\{b_n\}$ is an arithmetic sequence with common difference between terms of 2. That is,

$2 = b_{n+1} - b_n \implies b_{n+1} = b_n + 2$

and we can solve for $b_n$ in terms of $b_1=4$ :

$b_{n+1} = b_n + 2$

$b_{n+1} = (b_{n-1}+2) + 2 = b_{n-1} + 2\times2$

$b_{n+1} = (b_{n-2}+2) + 2\times2 = b_{n-2} + 3\times2$

and so on down to

$b_{n+1} = b_1 + 2n \implies b_{n+1} = 2n + 4 \implies b_n = 2(n-1)+4 = 2(n + 1)$

We solve for $a_n$ in the same way.

$2(n+1) = a_{n+1} - a_n \implies a_{n+1} = a_n + 2(n + 1)$

Then

$a_{n+1} = (a_{n-1} + 2n) + 2(n+1) \\ ~~~~~~~= a_{n-1} + 2 ((n+1) + n)$

$a_{n+1} = (a_{n-2} + 2(n-1)) + 2((n+1)+n) \\ ~~~~~~~ = a_{n-2} + 2 ((n+1) + n + (n-1))$

$a_{n+1} = (a_{n-3} + 2(n-2)) + 2((n+1)+n+(n-1)) \\ ~~~~~~~= a_{n-3} + 2 ((n+1) + n + (n-1) + (n-2))$

and so on down to

$a_{n+1} = a_1 + 2 \displaystyle \sum_{k=2}^{n+1} k = 2 + 2 \times \frac{n(n+3)}2$

$\implies a_{n+1} = n^2 + 3n + 2 \implies \boxed{a_n = n^2 + n}$

6 0

2 years ago

How are the functions f(x)=16^x and g(x)=16^(1/2)x related? The output values of g(x) are one-half the output values of f(x) for

Goshia [24]

F(x) =16ˣ and g(x) = 16⁽ˣ/₂⁾

Since 16 = 2⁴, then we can write:

f(x) =2⁽⁴ˣ⁾ and g(x) = 2⁽⁴ˣ/₂⁾ = 2²ˣ

for x = 1 f(x) = 2⁴ = 16
for x = 1 g(x) = 2² = 4
(√16 = 4)

for x = 2 f(x) = 2⁸ = 256
for x = 2 g(x) = 2⁴ =16
(√256) = 16

for x = 3 f(x) = 2¹² = 4096
for x = 1 g(x) = 2⁶ = 64
(√4096 = 64)

We notice that:
The output values of g(x) are the square root of the output values of f(x) for the same value of x.

6 0

3 years ago

Read 2 more answers

I NEED THIS TO BE CORRECT, I WILL GIVE ANYTHING!!

Andrew [12]

Answer:

a) 105 degrees

b) 75

c) 105

Step-by-step explanation:

a) 180-75 is 105 (supplementary angles)

b) same angle as kings ave and 4th street. (supplementary angles)

c) 180-75 is 105 (also vertical angle rule)

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3 years ago