All categories

3 years ago

Identify the polynomial x^3-y^3+z

Mathematics

1 answer:

Vaselesa [24]3 years ago

5 0

Answer:

Hi there!

The answer to this question is:

Standard: y= x- (cube root) z

the leading coefficient: 1

Step-by-step explanation:

when identifying a polynomial you always need to know the standard equation, and leading coefficient.

-you first need to know what "y" so you move y to the other side by adding it on both sides

-then you need to get y by itself and cube root it on both sides resulting in x^3 becoming x and z becoming (cube root) z

You might be interested in

How to prove this???

swat32

$\cos^3 2A + 3 \cos 2A \\
\Rightarrow \cos 2A (\cos^2 2A + 3) \\
\Rightarrow (\cos^2 A - \sin^2 A) (\cos^2 2A + 3) \\
\Rightarrow (\cos^2 A - \sin^2 A) (1 - \sin^2 2A + 3) \\
\Rightarrow (\cos^2 A - \sin^2 A) (4 - \sin^2 2A) \\
\Rightarrow (\cos^2 A - \sin^2 A) (4 - (2\sin A \cos A)(2\sin A \cos A)) \\
\Rightarrow (\cos^2 A - \sin^2 A) (4 - 4\sin^2 A \cos^2 A) \\ 
\Rightarrow 4(\cos^2 A - \sin^2 A) (1 - \sin^2 A \cos^2 A) 
$

go to right side now

$4( \cos^6 A - \sin^6 A)\\
\Rightarrow 4( \cos^3 A - \sin^3 A)(\cos^3 A + \sin^3 A)$

use $x^3 - y^3 = (x-y)(x^2 + xy + y^2)$ and $x^3 + y^3 = x^2 - xy + y^2$

$4( \cos^6 A - \sin^6 A)\\ \Rightarrow 4( \cos^3 A - \sin^3 A)(\cos^3 A + \sin^3 A) \\
\Rightarrow 4(\cos A - \sin A)(\cos^2 A + \cos A \sin A + \sin^2 A) \\
~\quad \quad\cdot ( \cos A + \sin A)(\cos^2 A - \cos A \sin A + \cos^2 A)$

so $\sin^2 A + \cos^2 A = 1$

$4( \cos^6 A - \sin^6 A)\\ \Rightarrow 4(\cos A - \sin A)(\cos^2 A + \cos A \sin A + \sin^2 A) \\ ~\quad \quad\cdot ( \cos A + \sin A)(\cos^2 A - \cos A \sin A + \cos^2 A) \\ \Rightarrow 4(\cos^2 A - \sin^2 A)(1 + \cos A \sin A )(1- \cos A \sin A ) \\ \Rightarrow 4(\cos^2 A - \sin^2 A)(1 - \cos^2 A \sin^2 A )\\ \Rightarrow 4(\cos^2 A - \sin^2 A)(1 - \sin^2 A \cos^2 A ) \\
 \Rightarrow Left hand side$

4 0

2 years ago

What is the simplified form of 15 times x to the fifth power over 20 times y to the sixth power times the fraction 6 times y to

VARVARA [1.3K]

Answer:

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

What type of number is 302.14

kondor19780726 [428]

302.14 is a decimal number

Explanation:

302.14 is a decimal type of number.

A decimal number can be defined as a number whose whole number part and the fractional part is separated by a decimal point. The dot in a decimal number is called a decimal point. The digits following the decimal point show a value smaller than one.

Decimals are based on the preceding powers of 10. Thus, as we move from left to right, the place value of digits gets divided by 10, meaning the decimal place value determines the tenths, hundredths and thousandths. A tenth means one tenth or 1/10. In decimal form, it is 0.1. Hundredth means 1/100. In decimal form, it is 0.01.

Similarly, 302.14 has a decimal place value of hundred.

3 0

3 years ago

Samantha’s rectangular gift is 10 inches. by 12 inches and is framed with a ribbon. She wants to use the same length of ribbon t

yanalaym [24]

Answer:

7 inches

Step-by-step explanation:

The dimension of the rectangular gift is 10 by 12 inches so let us find the perimeter of this rectangle.

Perimeter of rectangular gift = 2 (L+ W) = 2 (10 +12) = 44 inches

Since we are to use the same length of ribbon to wrap a circular clock so the perimeter or circumference of the clock should be no more than 44 inches.

$2\pi r=44$

$r=\frac{44}{2\pi }$

$r=7.003$

Therefore, the maximum radius of the circular clock is 7 inches.

7 0

2 years ago

Read 2 more answers

Suppose the equation of the axis of symmetry for a quadratic function is x = 3 and one of the x-intercepts is 8. What is the oth

soldi70 [24.7K]

Answer:

-2

Step-by-step explanation:

The axis of symmetry divides the quadratic exactly in half. If one x-intercept is 8, then the other will be the same distance on the other side of it. 8 is 5 from 3 where the axis of symmetry is. So 3-5 = -2. -2 will be the other intercept.

8 0

3 years ago