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4 years ago

Which shows how to best estimate the product of 4.73 x 8.92?

Mathematics

2 answers:

Alexandra [31]4 years ago

7 0

Answer:

Step-by-step explanation:multiply them

Anettt [7]4 years ago

6 0

Answer:

5 x 9 = 45

Step-by-step explanation:

A good way to estimate this would be rounding to the nearest whole number.

First we'll look at 4.73. If we're rounding to the nearest whole number, then that means we'll look at the digit one place to the right of 4. The digit to the right of 4 is 7. 7 is greater than 5 so we round up. We get 5. If we do the same for the other number we see that it also gets rounded up to 9. So our new equation is: 5 x 9. That is a simple multiplication equation and when we multiply we get 45.

Hope this helped!

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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 <em>rational roots theorem</em>, 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

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

A manufacturer is designing a flashlight. For the flashlight to emit a focused beam, the bulb needs to be on the central axis of

aalyn [17]

From the problem, the vertex = (0, 0) and the focus = (0, 3)
From the attached graphic, the equation can be expressed as:
(x -h)^2 = 4p (y -k)
where (h, k) are the (x, y) values of the vertex (0, 0)
The "p" value is the difference between the "y" value of the focus and the "y" value of the vertex.
p = 3 -0
p = 3
So, we form the equation
(x -0)^2 = 4 * 3 (y -0)
x^2 = 12y
To put this in proper quadratic equation form, we divide both sides by 12
y = x^2 / 12

Source:
http://www.1728.org/quadr4.htm