All categories

4 years ago

Solve the following Problems

Mathematics

1 answer:

harkovskaia [24]4 years ago

7 0

Answer:

Number of pens that can be put in each box is 4

Step-by-step explanation:

You might be interested in

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.

_______________________________

Please scroll left - right to view the full solution.

8 0

2 years ago

What's the slope intercept form

dybincka [34]

Y=-1/4x+3 should be the correct answer

7 0

3 years ago

Keenan gives tisha half of his strawberries. tisha keeps 4 of the strawberries she got from keenan and gives the rest to suvi. w

Ilya [14]

At start Keenan has x strawberries. He gives Tisha x/2. Then Tisha keeps 4 strawberries and gives Suvi the rest. If y is the number of strawberries that Suvi gets:
y = x/2 - 4.
For example: Keenan has 20 strawberries. He gives Tisha 10 and Tisha gives Suvi 6:
6 = 20/2 - 4
6 = 10 - 4

3 0

3 years ago

Solve each equation for the indicated variable

Korolek [52]

G = 4x + 1, solve for x
Start by isolating the x, subtract 1 from both sides:
g - 1 = 4x
Then, divide both sides by 4:
g/4 - 1/4 = x

Hope this helps! :)

7 0

3 years ago

Read 2 more answers

The amount of energy it takes to run a race is most likely to be a function of

Lana71 [14]

The amount of energy it takes to run a race is most likely to be a function of the; D: Length of the Race

<h3>How to find amount of energy?</h3>

We want to basically find the factor that influences the amount of energy expended by a sprinter.

Now, formula for potential energy is;

P = mgd

where;

m is mass

g is acceleration due to gravity

d is distance covered

Now, the only option that falls into the input that affects energy expended is the distance covered. This is true because the more the distance covered, the higher the energy expended.

Read more about Amount of Energy at; brainly.com/question/13439286

#SPJ1

7 0

2 years ago