All categories

3 years ago

Factor:

Mathematics

1 answer:

Naddik [55]3 years ago

3 0

Answer:

D) (5x - 3) (25x^2+ 15x + 9)

Step-by-step explanation:

$125 {x}^{3} - 27 \\ \\ = ( {5x)}^{3} - {(3)}^{3} \\ \\ = (5x - 3) \{(5x) ^{2} + 5x \times 3 + ( {3})^{2} \}\\ \\ = (5x - 3) \{25 {x}^{2} + 15x + 9\}$

You might be interested in

20 times 1/2 I don't know what th8s means can you help

Natalka [10]

Multiplying 20×1/2 is the same as dividing 20 by 2. Which means the answer is 10.

5 0

3 years ago

Read 2 more answers

Find the x-coordinates of any relative extrema and inflection point(s) for the function f(x)= 6x^1/3 + 3x^4/3. You must justify

irina [24]

Answer:

x-coordinates of relative extrema = $\frac{-1}{2}$

x-coordinates of the inflexion points are 0, 1

Step-by-step explanation:

$f(x)=6x^{\frac{1}{3}}+3x^{\frac{4}{3}}$

Differentiate with respect to x

$f'(x)=6\left ( \frac{1}{3} \right )x^{\frac{-2}{3}}+3\left ( \frac{4}{3} \right )x^{\frac{1}{3}}=\frac{2}{x^{\frac{2}{3}}}+4x^{\frac{1}{3}}$

$f'(x)=0\Rightarrow \frac{2}{x^{\frac{2}{3}}}+4x^{\frac{1}{3}}=0\Rightarrow x=\frac{-1}{2}$

Differentiate f'(x) with respect to x

$f''(x)=2\left ( \frac{-2}{3} \right )x^{\frac{-5}{3}}+\frac{4}{3}x^{\frac{-2}{3}}=\frac{-4x^{\frac{2}{3}}+4x^{\frac{5}{3}}}{3x^{\frac{2}{3}}x^{\frac{5}{3}}}\\f''(x)=0\Rightarrow \frac{-4x^{\frac{2}{3}}+4x^{\frac{5}{3}}}{3x^{\frac{2}{3}}x^{\frac{5}{3}}}=0\Rightarrow x=1$

At x = $\frac{-1}{2}$ ,

$f''\left ( \frac{-1}{2} \right )=\frac{4\left ( -1+4\left ( \frac{-1}{2} \right ) \right )}{3\left ( \frac{-1}{2} \right )^{\frac{5}{3}}}>0$

We know that if $f''(a)>0$ then x = a is a point of minima.

So, $x=\frac{-1}{2}$ is a point of minima.

For inflexion points:

Inflexion points are the points at which f''(x) = 0 or f''(x) is not defined.

So, x-coordinates of the inflexion points are 0, 1

7 0

3 years ago

Can anyone please help me with this RSM question? I have literally posted this like four times!

Ostrovityanka [42]

Answer:

Angles in a triangle add up to 180.

ABG - x + 90 + ANGLE AGB = 180

Angles on a straight add up to 180.

CDE - 8x + ANGLE D + 3x = 180

Alterate angles - ATTACHMENT

ANGLE D = x

8x + x + 3x = 180

12x = 180

x = 180/12

5 0

3 years ago

Read 2 more answers

The volume V of a cube with sides of length x inches is changing with respect to time t (in seconds). When the sides of the cube

goldfiish [28.3K]

Answer:

dV/dt = 3×10^2 × 0.5 = 150 in^3/sec

the volume of the cube is increasing at 150in^3/sec

Step-by-step explanation:

Volume V = length l^3

V = x^3

Differentiating both sides;

dV/dt = 3x^2 dv/dt

Given;

x = 10 in

dx/dt = 0.5 in/sec

dV/dt = 3×10^2 × 0.5 = 150 in^3/sec

the volume of the cube is increasing at 150in^3/sec

5 0

3 years ago

Mrs. O'Malley is setting up for a party. Each adult will get 2 glasses, and each child will get 1 glasses. There are 8 Adult and

malfutka [58]

1 adult=2

1 child=1

multiply 2*8=16 adult glasses

multiply 1*5=5 child glasses

in total she needs 21 glasses

hope I was helpful

5 0

3 years ago