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2 years ago

A large 32x+1 square units

Mathematics

1 answer:

Sauron [17]2 years ago

8 0

Answer:

Step-by-step explanation:

L:3x+x=4x

W:8

4x*8=32x

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Type the correct answer in each box. (____)

trapecia [35]

Answer:

1. -16; 2. +64; 3. 16

Step-by-step explanation:

The formula for the volume of a cylinder is

V = πr²x

Data:

r = (x - 8) mm

V = 1024π mm³

Calculations:

1. Find the cubic equation

V = πr²h

1024π = π(x - 8)² × x

Divide each side by π

1024 = x(x - 8)²

1024 = x(x² - 16x + 64)

1024 = x³ - 16x² + 64x

x³ - 16x² + 64x - 1024 = 0

2. Solve the cubic equation

The general formula for a third-degree polynomial is

f(x) = ax³ + bx² + cx + d

Your polynomial is

f(x) = x³ - 16x² + 64x - 1024

a = 1; d = -1024

According to the rational roots theorem, the possible roots are

factors of d/factors of a

Factors of d = ±1, ±2, ±4, ±8, ±16, ± 32, ± 64, ±128, ±256, ±512, ±1024

Factors of a = ±1

Potential roots are x = ±1, ±2, ±4, ±8, ±16, ± 32, ± 64, ±128, ±256, ±512, ±1024

That's a lot of possibilities to check by trial and error. I will just use the one that works.

Try x = 16 by synthetic division.

16|1 -16 64 -1024

| 16 0 1024

1 0 64 0

So,

(x³ - 16x² + 64x - 1024)/(x – 16) = x² + 64

and

(x - 16)(x² + 64) = 0

x - 16 = 0 x² + 64 = 0

x = 16 x² = -64

x = ±8i

There is only one real root: x = 16 mm

6 0

3 years ago

An unknown number y is 20 more than an unknown number x. The number y is also x less than 2. The equations to find x and y are s

Scorpion4ik [409]

Add the equations to eliminate x.

4 0

3 years ago

Read 2 more answers

Jace invested $65,000 in an account paying an interest rate of 2.5% compounded continuously. Assuming no deposits or withdrawals

Tomtit [17]

Answer:

15 years

Step-by-step explanation:

93400=65000*e^(.025x)

x=14.5 which rounds to 15

7 0

3 years ago

Whats is 3/5 as a percent

likoan [24]

60%; Since 1/5 is .2 or 20% and then multiply that by 3.

6 0

3 years ago

Read 2 more answers

Jared has 12 more comic books than Zoe. If they have 28 comic books

ZanzabumX [31]

Answer:

20 comic books

Step-by-step explanation:

Let us first set up a variable, x, for the number of books that Zoe has. If Jared has 12 more comics than Zoe, he would have x+12 books.

Given that Zoe and Jared have a total of 28 comic books, let us write an equation and solve for x:

$x+x+12=28\\2x+12=28$

Now that we have a simplified version of the equation, let us solve for x by isolating the variable on the left side:

$2x=28-12\\2x=16\\x=8$

We now know that x=8, and also that Jared has x+12 books. To find the number of comic books Jared has, let us add 12 to x:

$x+12=\\8+12=\\20\\$

Therefore, Jared has 20 comic books.

I hope this helps! Please let me know if you have any further questions :)

4 0

3 years ago