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2 years ago

9. What is the area of the largest square? A=? A = 36 units A = 64 units.

Mathematics

2 answers:

lisov135 [29]2 years ago

4 0

The answer is A=64 but I’m not pretty sure

Studentka2010 [4]2 years ago

3 0

The answer is A hope that works

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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,

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

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

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

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

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

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

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

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

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

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1 year ago

the new basketball team playoff shirts are $42.52 plus $7.05 sales tax what is the amount and what's the cost of the t-shirts

baherus [9]

The total would be $49.57

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2 years ago

Write the perimeter of the triangle as a simplified expression

ioda

Answer: 10y + 1

Step-by-step explanation:

The perimeter is the total distance round the figure.

Now, in this case it is going to be

Perimeter = 3y + 5 + 6y + y - 4

= 3y + 6y + y + 5 - 4

= 10y + 1

3 0

3 years ago

name a factor pair for a rectangle that has an area of 50 sq. cm.and a perimeter greater than 100 cm.

ioda

a rectangle of dimensions 1 cm * 50 cm has a perimeter of 102 cm.

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2 years ago

Help a sis out ??

REY [17]

Answer:

Step-by-step explanation:

let base be b then height h = 2b + 4

The area (A) of a triangle is calculated as

A = $\frac{1}{2}$ bh ( b is the base and h the height ) , then

A = $\frac{1}{2}$ b(2b + 4) ← distribute parenthesis

A = b² + 2b

When b = 16 , then

A = 16² + 2(16) = 256 + 32 = 288 in²

7 0

1 year ago