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3 years ago

How many six-digit odd numbers are possible if the leftmost digit cannot be zero

Mathematics

1 answer:

Romashka [77]3 years ago

4 0

For the leftmost digit there are 9 possibilities!

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Determine whether the series is convergent or divergent by expressing sn as a telescoping sum (as in Example 8). [infinity] 6 n2

vekshin1

Answer:

Step-by-step explanation:

given

$\sum\limits^\infty_{n=3}\frac{6}{n^2-1}=\sum\limits^\infty_{n=3}\frac{6}{(n-1)(n+1)}\\\\=\sum\limits^\infty_{n=3}\frac{6}{2}(\frac{1}{n-1}-\frac{1}{n+1})\\\\=\frac{6}{2}\sum\limits^\infty_{n=3}(\frac{1}{n-1}-\frac{1}{n+1})\\\\=3[(\frac{1}{2}-\frac{1}{4})+(\frac{1}{3}-\frac{1}{5})+(\frac{1}{4}-\frac{1}{6})+(\frac{1}{5}-\frac{1}{7})+...]\\\\=3[\frac{1}{2}+\frac{1}{3}]=3[\frac{3+2}{6}]=3[\frac{5}{6}]\\\\=\frac{15}{6}=\frac{5}{3}$

5 0

3 years ago

What is the measurement of this angle

mafiozo [28]

Answer:

28°

Step-by-step explanation:

62° + 90° = 152°

180° - 152° = 28°

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6 0

3 years ago

Read 2 more answers

You have 800 feet of fencing and you want to make two fenced in enclosures by splitting one enclosure in half. What are the larg

katovenus [111]

Problema Solution

You have 800 feet of fencing and you want to make two fenced in enclosures by splitting one enclosure in half. What are the largest dimensions of this enclosure that you could build?

Answer provided by our tutors

Make a drawing and denote:

x = half of the length of the enclosure

2x = the length of the enclosure

y = the width of the enclosure

P = 800 ft the perimeter

The perimeter of the two enclosures can be expressed P = 4x + 2y thus

4x + 3y = 800

Solving for y:

........

click here to see all the equation solution steps

........

y = 800/3 - 4x/3

The area of the two enclosure is A = 2xy.

Substituting y = 800/3 - 4x/3 in A = 2xy we get

A = 2x(800/3 - 4x/3)

A =1600x/3 - 8x^2/3

We need to find the x for which the parabolic function A = (- 8/3)x^2 + (1600/3)x has maximum:

x max = -b/2a, a = (-8/3), b = 1600/3

x max = (-1600/3)/(2*(-8/3))

x max = 100 ft

y = 800/3 - 4*100/3

y = 133.33 ft

2x = 2*100

2x = 200 ft

3 0

3 years ago

What is the slope of ( 5,1 ) and ( 2,-7 )

PolarNik [594]

Answer:

8/3 is the slope

3 0

3 years ago

Julio bought a fish tank shaped like a rectangular prism. The inside of the tank measures 24 inches in length, 10 inches in widt

Rudik [331]

Answer:

$Volume = 960in^3$

Step-by-step explanation:

Given

Empty Tank

$Length = 24in; Width=10in; Height = 12in$

When filled with water, the height is:

$Height = 8in$

Required

Determine how many more cubic inches needed

First, we calculate the difference between the height of the tank and the height of the water.

$H = 12in - 8in$

$H = 4in$

The volume of water to full the tank is then calculated as:

$Volume = Length * Width * H$

$Volume = 24in * 10in * 4in$

$Volume = 960in^3$

7 0

2 years ago