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Roman55 [17]
3 years ago
8

What is the factorization of 729x^15 + 1000?

Mathematics
1 answer:
Tcecarenko [31]3 years ago
8 0

Answer:

729x¹⁵ + 1000

This is a case of a sum of cubes.

729 is the cube of 9

1000 is the cube of 10

x¹⁵ is the cube of x⁵

A sum of perfect cubes can be factored into 

(a + b) (a² - ab + b²)

(9x⁵+ 10) ((9x⁵)²-(9x⁵)(10) + 10²)

(9x⁵ + 10) (81x¹⁰ - 90x⁵ + 100) THIS IS THE FACTORIZATION

9x⁵ (81x¹⁰ - 90x⁵ + 100) + 10(81x¹⁰ - 90x⁵ + 100)

729x¹⁵ - 810x¹⁰ + 900x⁵ + 810x¹⁰ - 900x⁵ + 1000

729x¹⁵ - 810x¹⁰ + 810x¹⁰ + 900x⁵ - 900x⁵ + 1000

729x¹⁵ + 1000

Step-by-step explanation:

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Can someone help me please !
elena55 [62]
The reference angle is
pi/3.

At 180 it would be 9pi/3 so going past that is 10pi/3.

7 0
3 years ago
The sum of 5 consecutive even numbers is 20
vladimir2022 [97]

Step-by-step explanation:

Let the 1st number be x

2nd number = x + 2

3rd number = x + 4

4th number = x + 6

5th number = x + 8

x + x + 2 + x + 4 + x + 6 + x + 8 = 20

5x + 20 = 20

5x = 20 - 20

5x = 0

x = 0 ÷ 5

x = 0

The 5 consecutive integers are

0, 2, 4, 6, 8

8 0
3 years ago
The monthly utility bills in a city at e normally distributed, with a mean $100 and a standard deviation of $13. find the probab
dmitriy555 [2]

Answer:

how's your day

Step-by-step explanation:

how's your day

5 0
2 years ago
0.0007716049 as a fraction
elena55 [62]

To write 0.0007716049 as a fraction you have to write 0.0007716049 as numerator and put 1 as the denominator. Now you multiply numerator and denominator by 10 as long as you get in numerator the whole number.

0.0007716049 = 0.0007716049/1 = 0.007716049/10 = 0.07716049/100 = 0.7716049/1000 = 7.716049/10000 = 77.16049/100000 = 771.6049/1000000 = 7716.049/10000000 = 77160.49/100000000 = 771604.9/1000000000 = 7716049/10000000000

so your answer is: 7716049/10000000000

7 0
3 years ago
The two pyramids are similar. Find the volume of the smaller pyramid. Round your answer to the nearest hundredth.
mihalych1998 [28]

Answer:

A) 5.12mm³

Step-by-step explanation:

Step 1

Find the volume of the bigger pyramid

This is a triangular based pyramid.

The formula to use is given as Volume of Pyramid =

1/3 × Area of the triangle × Height

Area of the triangle = 1/2 × 3 mm × 4mm = 6mm²

Volume of the large pyramid = 1/3 × 6mm² × 5mm

= 10mm³

We are given the length of the small pyramid as 4mm

We would be using was is known as scale factor to find the volume of the small pyramid

The scale factor k = (Height of the small pyramid)³/ (Height of the Large pyramid)³

k = 4³/5³

k = Volume of small pyramid/ Volume of large pyramid

Volume of small pyramid = X

Volume of large pyramid = 10mm³

Hence,

4³/5³ = X/10

Cross Multiply

= 4³ × 10 = 5³ × X

X = (4³ × 10)/ 5³

X = 5.12mm³

5 0
3 years ago
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