Can you solve 64x³+y³ by factoring?

Answers

Answer 1

Answer: $64x^3+y^3=(4x)^3+y^3\n\n=(4x+y)[(4x)^2-4xy+y^2]=(4x+y)(16x^2-4xy+y^2)$

Answer 2

Answer: $a^3+b^3=(a+b)(a^2-ab+b^2)\n-----------------\n64x^3+y^3=(4x)^3+y^3=(4x+y)[(4x)^2-4x\cdot y+y^2]=\n\n=(4x+y)(16x^2-4xy+y^2)$

Related Questions

A jewelry designer is making a pendant. The pendant will be a circular dis (center O) with a circular hold cut out of it, as shown. The radius of the disc is 35 millimeters. Find the area of the pendant. Use 3.14 for π and round to the nearest tenth
Determine whether or not a regular polygon can have an interior angle of 100
What is the volume of the cylinder below? A. 72π units³ B. 36π units³ C. 45π units³ D. 90π units³
Subtract.(x + 1) - (-2x - 5) A) 6 –x B) -x - 4 C) 3x - 4 D) 3x + 6
Write the pair of fractions as a pair of fractions with a common denominator with 2/3 and 5/12

K³-4j+12 when k=8, j=2

Answers

k³-4j+12 = (8)³ - 4(2) + 12
= 512 - 8 + 12
= 516

Therefore, the value of the expression k³-4j+12 when k=8 and j=2 is 516.

6 is 12% of what number

Answers

6 is 12% 50

Change the percentage into a decimal by dividing the percentage (12) by 100:
$(12)/(100) = 0.12$

Divide 6 by the decimal (0.12):
$6 / 0.12 = 50$

When you do these problems, just divide the part value by the percentage (converted into a decimal value, of course).
6/0.12 = 50.
So 6 is 12% of 50.
Hope that helped you.

Complex numbers kkkkkkkkkkkkk

Answers

Answer:

1-7i

17i

Step-by-step explanation:

7-5i-6-2i=1-7i

1+9i-1+8i=17i

3i+14-3i=14

Suppose that the equation of motion for a particle (where s is in meters and t in seconds) is s = 5 t^2 - 8 t + 3
find the acceleration at the instant when the velocity is at 0

Answers

Differentiate equation
v = 10t - 8
Differerentiate again
a = 10

Accelleration will always be 10m/s^-2

Select the graph that represents the volume of a cube as a function of the length of an edge.

Answers

Answer:

The Graph D) is correct

Step-by-step explanation:

Let, x be length of cube and y is volume of cube

The volume of cube is given by

Volume = $(\textrm{Length of one side of cube})^(3)$

Such that, all the sides of cube are equal

We can write as y= $x^(3)$

Thus, The Graph D) is correct

Find the equation of all tangent lines having slope of -1 that are tangent to the curve y=(9)/(x+1)

Answers

Answer: y = -x + 5 and y = -x - 7 (see attached graph)

Step-by-step explanation:

y = $(9)/(x + 1)$

= 9(x + 1)⁻¹

Use the product rule to find the derivative

a = 9 a' = 0

b = (x + 1)⁻¹ b' = -(x + 1)⁻²

ab' + a'b

= 9[-(x + 1)⁻²] + 0[(x + 1)⁻¹ ]

= $(-9)/((x + 1)^(2))$

Set the derivative equal to the desired slope of -1 to solve for x

-1 = $(-9)/((x + 1)^(2))$

-(x + 1)² = -9

(x + 1)² = 9

√(x + 1)² = √9

x + 1 = +/- 3

x + 1 = 3 x + 1 = -3

x = 2 x = -4

Plug those values into the original equation to solve for y:

y = $(9)/(x + 1)$

= $(9)/(2 + 1)$

= 3

(2, 3)

y = $(9)/(x + 1)$

= $(9)/(-4 + 1)$

= -3

(-4, -3)

Next, plug in the given slope (-1) and the coordinates above into the Point-Slope formula y - y₁ = m(x - x₁) to find the equations:

m = -1, (x₁ y₁) = (2, 3) m = -1, (x₁ y₁) = (-4, -3)

y - 3 = -1(x - 2) y + 3 = -1(x + 4)

y - 3 = -x + 2 y + 3 = -x - 4

y = -x + 5 y = -x - 7

Answer:

$f(x)=\frac9{x+1}\n f'(x)=-\frac9{(x+1)^2}\n f'(x)=-1\ \iff\ -\frac9{(x+1)^2}=-1\ \to \ \frac9{(x+1)^2}=1\ \to \ (x+1)^2=9\n |x+1|=3\ \to \ x+1=3\ \vee\ x+1=-3\n x_1=2\ \vee\ x_2=-4\n f(x_1)=f(2)=\frac9{2+1}=3\n f(x_2)=f(-4)=\frac9{-4+1}=-3$

First tangent line:

$y=f'(x_1)\cdot (x-x_1)+f(x_1)\ \to \ y=-1(x-2)+3\ \to \ y=-x+5$

Second tangent line:

$y=f'(x_2)\cdot (x-x_2)+f(x_2)\ \to \ y=-1(x+4)-3\ \to \ y=-x-7$

Notice: slope of -1 means that both $f'(x_1), \ f'(x_2)$ are equal to -1, so $f'(x_1)=-1 \ and \ f'(x_2)=-1$

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