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2 years ago

What's the sum of an infinite geometric series if the first term is 156 and the common ratio is 2∕3?

Mathematics

1 answer:

DENIUS [597]2 years ago

4 0

Answer:

468

Step-by-step explanation:

Formula for infinite sum of geometric series is;

S_∞ = a1/(1 - r)

Where;

a1 is first term

r is common ratio

We are given;

a1 = 156

r = ⅔

Thus;

S_∞ = 156/(1 - ⅔)

S_∞ = 156/(⅓)

S_∞ = 468

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Prove that√P is irrational for any prime number P

Luda [366]

Answer:

Step-by-step explanation:

I’m not sure if this is super accurate, but since P is prime, the only factors it has is 1 and itself, meaning that the square root of it will be irrational

3 0

3 years ago

Thomas needs to buy a cardboard sheet that will allow him to make his 224 in 3 box. To help construct the box, he decided to cut

Slav-nsk [51]

Answer:

Part 1; The volume of the box Thomas wants to make is 224 = 2·w² + 12·w

Part 2; The zeros for the equation of the function, are w = -14, or w = 8

Part 3

The width of the box is 8 inch

The length of the box, is 14 inches

The height of the box, is given as 2 inches

Part 4

Please find attached the graph of the function

Step-by-step explanation:

Part 1

The volume of the box Thomas wants to make, V = 224 in.³

The dimensions he cuts out from the length and width = 2 in² each

The length of the box = 6 inches + The width of the box

Let l represent the length of the box and let w represent the width of the box, we have;

l = 6 + w

The height of the box, h = The length of the cut out square = 2 inches

The volume of the box, V = Length, l × Width, w × Height, h

∴ V = l × w × h

l = 6 + w, h = 2

∴ V = (6 + w) × w × 2

V = 2·w² + 12·w,

The equation of the volume of the box, V = 2·w² + 12·w, where, V = 224

∴ 224 = 2·w² + 12·w

Part 2

The zeros of the equation for the volume of the box, V = 2·w² + 12·w, where, V = 224 are found as follows;

V = 224 = 2·w² + 12·w

∴ 2·w² + 12·w - 224 = 0

Dividing by 2 gives;

(2·w² + 12·w - 224)/2 = w² + 6·w - 112 = 0

∴ (w + 14) × (w - 8) = 0

The zeros for the equation of the function, are w = -14, or w = 8

Part 3

We reject the value, w = -14, therefore, the width of the box, w = 8 inch

The length of the box, l = 6 + w

∴ l = 6 + 8 = 14

The length of the box, l = 8 inches

The height of the box, h, is given as h = 2 inches

Part 4

The graph of the function created with MS Excel is attached

4 0

2 years ago

Find the 4th term Thank you in advance

shepuryov [24]

B1 = 2
b2 = (b1)^2 + 1 = 2^2 + 1 = 5
b3 = (b2)^2 + 1 = 5^2 + 1 = 26

b4 = (b3)^2 + 1 = 26^2 + 1 = 676+1=677

7 0

3 years ago

Read 2 more answers

Just the answer Please hurry

kaheart [24]

Answer:

We have been given that a car can travel 476 miles on 14 gallons of gas and we are asked to write an equation relating the distance d to the number of gallons g.

We can set an equation as distance traveled is directly proportional to number of gallons used in travelling that distance.

Now we will find out K(number of miles traveled in one gallon of gas) by substituting our given values in this equation.

Therefore, we can see that car travels 34 miles in one gallon of gas.

Now we can use this information to find out how many gallons of gas does this car need to travel 578 miles.

Let us divide number of miles to be traveled by number of miles traveled in one gallon of gas to find out number of gallons of gas needed.

Therefore, car need 17 gallons of gas to travel 578 miles.

Step-by-step explanation:

5 0

2 years ago

Read 2 more answers

Yeah thanks m8 for this

nikitadnepr [17]

Step-by-step explanation:

the process is shown in the picture.

4 0

2 years ago