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2 years ago

Car A travels 105 miles on 3 gallons of petrol.

Mathematics

1 answer:

Aloiza [94]2 years ago

7 0

Answer:

Car B

Step-by-step explanation:

Car A: 105 miles/3 gallons

= 35miles/gallon

1 gallon = 4.5 litres

So 9 litres = 2 gallons

Car B: 80 miles/2 gallons

= 40 miles/gallon

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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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8 0

1 year ago

N employee earns $175 for 15 hours work. assuming he is paid by the hour, how much will this employee earn in 18 hours?

alekssr [168]

First you would divide 175 by 15 and get 11.6666666667, you would then multiply that by 18 amd get 210.0000000001

7 0

2 years ago

The graph below shows the height of a projectile t seconds after it is launched. If acceleration due to gravity is –16 ft/s2, wh

nika2105 [10]

Answer:

see attached

Step-by-step explanation:

The x-coordinate of the vertex is given by ...

x = -b/(2a)

for f(x) = ax^2 +bx +c.

We see that the vertex is at x = 1, and we are given a = -16. Then we can find "b" from ...

1 = -b/(2(-16))

32 = b

We know the y-intercept of the equation is 5 (the starting height), so the equation must be ...

h(t) = -16t^2 +32t +5 . . . . . matches the last choice

5 0

3 years ago

Identify the coefficients and variables in rst-12v

BigorU [14]

Coefficients are the numbers in a equation variables are the letter

6 0

2 years ago

Read 2 more answers

A carpenter has a wooden that measures 1/4 meter long. He must cut the board into 6 pieces of equal length. How long in meters s

DanielleElmas [232]

Answer:

1/26 meter

Step-by-step explanation:

You would start by dividing 1/4 by 6. You'd have to multiply 1/4 by the reciprocal of 6 (the reciprocal of 6 would be 1/6). Then you get (1/4) * (1/6), which is equal to 1/24.

8 0

2 years ago