I need help please can’t seem to understand this

Which expression is a difference of cubes? 9w^33-y^12 18p^15-q^21 36a^22-b^16 64c^15- a^26

LiRa [457]

we know that

A polynomial in the form $a^{3}-b^{3}$ is called adifference of cubes. Both terms must be a perfect cubes

Let's verify each case to determine the solution to the problem

case A) $9w^{33} -y^{12}$

we know that

$9=3^{2}$ ------> the term is not a perfect cube

$w^{33}=(w^{11})^{3}$ ------> the term is a perfect cube

$y^{12}=(y^{4})^{3}$ ------> the term is a perfect cube

therefore

The expression $9w^{33} -y^{12}$ is not a difference of cubes because the term $9$ is not a perfect cube

case B) $18p^{15} -q^{21}$

we know that

$18=2*3^{2}$ ------> the term is not a perfect cube

$p^{15}=(p^{5})^{3}$ ------> the term is a perfect cube

$q^{21}=(q^{7})^{3}$ ------> the term is a perfect cube

therefore

The expression $18p^{15} -q^{21}$ is not a difference of cubes because the term $18$ is not a perfect cube

case C) $36a^{22} -b^{16}$

we know that

$36=2^{2}*3^{2}$ ------> the term is not a perfect cube

$a^{22}$ ------> the term is not a perfect cube

$b^{16}$ ------> the term is not a perfect cube

therefore

The expression $36a^{22} -b^{16}$ is not a difference of cubes because all terms are not perfect cubes

case D) $64c^{15} -a^{26}$

we know that

$64=2^{6}=(2^{2})^{3}$ ------> the term is a perfect cube

$c^{15}=(c^{5})^{3}$ ------> the term is a perfect cube

$a^{26}$ ------> the term is not a perfect cube

therefore

The expression $64c^{15} -a^{26}$ is not a difference of cubes because the term $a^{26}$ is not a perfect cube

I'm adding a new case so I can better explain the problem

case E) $64c^{15} -d^{27}$

we know that

$64=2^{6}=(2^{2})^{3}$ ------> the term is a perfect cube

$c^{15}=(c^{5})^{3}$ ------> the term is a perfect cube

$d^{27}=(d^{9})^{3}$ ------> the term is a perfect cube

Substitute

$64c^{15} -d^{27}=((2^{2})(c^{5}))^{3}-(d^{9})^{3}$

therefore

The expression $64c^{15} -d^{27}$ is a difference of cubes because all terms are perfect cubes

5 0

3 years ago

Read 2 more answers

I need help with this

zhenek [66]

Answer:

6 1/5 = 31/5 and 2 3/4 = 11/4 as improper fractions, hope this helps!

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

The sum of the length l and 17

Sladkaya [172]

Answer:

18 is the sum of 17 and 1

Step-by-step explanation:

17+1=18

5 0

2 years ago

find the equation of a cubic function whose graph passes through points (3,0) and (1,4) and is tangent to x-axis at the origin

Tomtit [17]

Answer:

y = -2x^2(x - 3)

Step-by-step explanation:

Preliminary Remark

If a cubic is tangent to the x axis at 0,0

Then the equation must be related to y = a*x^2(x - h)

(3,0)

If the cubic goes through the point (3,0), then the equation will become

0 = a*3^2(3 - h)

0 = 9a (3 - h)

0 = 27a - 9ah

from which h = 3

From the second point, we get

4 = ax^2(x - 3)

4 = a(1)^2(1 - 3)

4 = a(-2)

a = 4 / - 2

a = -2

Answer

y = -2x^2(x - 3)

3 0

3 years ago

PLEASE HELP, WRONG/ABSURD ANSWERS GET REPORTED GOOD ANSWERS GET 25 POINTS AND BRAINLIEST!!

cestrela7 [59]

2. Find the derivative of f (x) = 5x + 9 at x = 2.
A) 9
B) 5
C) 0
D) 10
f (x) = 5x + 9
The first thing we should do in this case is to derive the function.
We have then:
f '(x) = 5
We now evaluate the function for the value of x = 2.
We have then:
 f '(2) = 5
Answer:
 the derivative of f (x) = 5x + 9 at x = 2 is:
B) 5

3. Find the derivative of f (x) = 8 divided by x at x = -1.

4
0
8
 -8

f (x) = 8 / x
The first thing we should do in this case is to derive the function.
We have then:
f '(x) = ((0 * x) - (1 * 8)) / (x ^ 2)
 Rewriting we have:
 f '(x) = -8 / (x ^ 2)
We now evaluate the function for the value of x = -1.
 We have then:
f '(- 1) = -8 / ((- 1) ^ 2)
f '(- 1) = -8
Answer:
The derivative of f (x) = 8 divided by x at x = -1 is:
-8

 4. Find the derivative of f (x) = negative 11 divided by x at x = 9.
 A) 11 divided by 9
B) 81 divided by 11
C) 9 divided by 11
 D) 11 divided by 81

 f (x) = -11 / x
The first thing we should do in this case is to derive the function.
 We have then:
f '(x) = ((0 * x) - (1 * (- 11))) / (x ^ 2)
Rewriting we have:
 f '(x) = 11 / (x ^ 2)
We now evaluate the function for the value of x = 9.
We have then:
 f '(9) = 11 / ((9) ^ 2)
 f '(9) = 11/81
Answer:
the derivative of f (x) = negative 11 divided by x at x = 9 is:
D) 11 divided by 81

5. The position of an object at time is given by s (t) = 3 - 4t. Find the instantaneous velocity at t = 8 by finding the derivative.
s (t) = 3 - 4t
For this case, the first thing we must do is derive the given expression.
We have then:
s' (t) = - 4
We evaluate now for t = 8
 s' (8) = - 4
Answer:
 the instantaneous velocity at t = 8 by finding the derivative is:
s' (8) = - 4

6 0

3 years ago