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2 years ago

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The altitude of Object B is 27 times the altitude of Object A. The altitude of Object A is $3^3$ feet. What is the altitude of O

bject B? Write your answer as a power.
ft

1 answer:

Andrej [43]2 years ago

3 0

Answer:

3^6

Step-by-step explanation:

We know that A is 3^3 and B is 27 times that.

3•3•3=27

So B is 3•3•3• of 3^3 which is 3•3•3•3•3•3

Write the answer to the exponents which will be 3^6

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How can i prove this property to be true for all values of n, using mathematical induction.

chubhunter [2.5K]

Proof -

So, in the first part we'll verify by taking n = 1.

$\implies \: 1 = {1}^{2} = \frac{1(1 + 1)(2 + 1)}{6}$

$\implies{ \frac{1(2)(3)}{6} }$

$\implies{ 1}$

Therefore, it is true for the first part.

In the second part we will assume that,

$\: { {1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} = \frac{k(k + 1)(2k + 1)}{6} }$

and we will prove that,

$\sf{ \: { {1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{(k + 1)(k + 1 + 1) \{2(k + 1) + 1\}}{6}}}$

$\: {{1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{(k + 1)(k + 2) (2k + 3)}{6}}$

${1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{k (k + 1) (2k + 1) }{6} + \frac{(k + 1) ^{2} }{6}$

${1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{k(k+1)(2k+1)+6(k+1)^ 2 }{6}$

${1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{(k+1)\{k(2k+1)+6(k+1)\} }{6}$

${1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{(k+1)(2k^2 +k+6k+6) }{6}$

${1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{(k+1)(2k^2+7k+6) }{6}$

${1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{(k+1)(k+2)(2k+3) }{6}$

<u>Henceforth, by </u><u>using </u><u>the </u><u>principle </u><u>of </u><u> mathematical induction 1²+2² +3²+....+n² = n(n+1)(2n+1)/ 6 for all positive integers n</u>.

_______________________________

<em>Please scroll left - right to view the full solution.</em>

8 0

1 year ago

What is the average of 11, 13, 18 and 22?

kirill [66]

Answer:

16

Step-by-step explanation:

To find the average, add up all the number and divide by the number of terms

(11+ 13+ 18 + 22)/4

64/4

16

5 0

3 years ago

Read 2 more answers

What’s the answer ASAP will give brainlist

disa [49]

It’s 1, looks like you got it lol

7 0

3 years ago

HELPPPPPP QUICKKKKKHELPPPPPP QUICKKKKKHELPPPPPP QUICKKKKK

Lilit [14]

Answer:A

Step-by-step explanation: The first few square numbers are:

1

,

4

,

9

,

16

,

25

,

36

,

49

,

√

1

=

1

√

4

=

2

√

9

=

3

√

16

=

4

√

25

=

5

√

36

=

6

w

w

w

w

w

w

←

√

40

lies here

√

49

=

7

Therefore

√

40

is between

6

and

7

8 0

2 years ago

Read 2 more answers

What is the measure of angle A?

fgiga [73]

Answer:

∠A=65º

Step-by-step explanation:

A angle of a line is 180º, so we can say that angle ABC=(180-6x)º
The interior angkes of a triangle is 180º, so (x+40)º+(3x+10)º+(180-6x)º=180º
Remove parenthesis, x+40+3x+10+180-6x=180
Combine like terms, -2x+230=180
Subtract 180, -2x=-50
Divide by -2, so x=25

Now:

∠CAB=(25+40)º=65º
∠ABC=[180-6(25)]º=30º
∠BCA=[3(25)+10]=85º

5 0

2 years ago