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4 years ago

What is the cube root of 64x^12

Mathematics

2 answers:

dimulka [17.4K]4 years ago

6 0

<span>64x^12 = 4^3 x^12
cube root </span>64x^12 = 4x^4

answer 4x^4

Dvinal [7]4 years ago

4 0

Answer: The required cube root of the given expression is $4x^4.$

Step-by-step explanation: We are given to find the cube root of the following expression :

$E=64x^{12}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~``(i)$

We will be using the following property :

$\sqrt[n]{a}=a^\frac{1}{n}.$

Taking cube root on both sides of equation (i), we get

$\sqrt[3]E\\\\=\sqrt[3]{64x^{12}}\\\\=(64x^{12})^\frac{1}{3}\\\\=(4^3x^{12})^\frac{1}{3}\\\\=4^{3\times\frac{1}{3}}x^{12\times\frac{1}{3}}}\\\\=4x^4.$

Thus, the required cube root of the given expression is $4x^4.$

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Compare the values of the underline 6,300 and 530

alisha [4.7K]

The value of 3 in 6,300 is 10 times the value of 3 in 530. And your welcome.

7 0

3 years ago

Read 2 more answers

Translate and simply: subtract 18 from -11

navik [9.2K]

Answer: -29

Subtract 18 FROM -11.
That means that 18 would go after -11.

-11 - 18 = -29

4 0

3 years ago

A ladder 16 feet long is leaning against the wall of a tall building. The base of the ladder is moving away from the wall at a r

svet-max [94.6K]

Answer:

a. 0.588

b. 0.0722

c. 4.576 sqft/sec

Step-by-step explanation:

Let b and h denote the base and height as indicated in the diagram. By pythagoras theorem, $h^2 + b^2 = 16^2 = 256 \dotsc\;(1)$ because it is a right angle triangle.

It is given that $\frac{db}{dt} = 1$

Now differentiate (1) with respect to t (time) :

$\displaystyle{2h\frac{dh}{dt} + 2b\frac{db}{dt} = 0 \implies \frac{dh}{dt} = -\frac{b}{h} \frac{db}{dt}}$

$\displaystyle{=-\frac{b}{\sqrt{256 - b^2}} \frac{db}{dt} = -\frac{8}{13.856} \times 1 = -0.588}$

The minus sign indicates that the value of h is actually decreasing. The required answer is 0.588.

b. From the diagram, infer that $16 \sin{\theta} = b$ . When b = 8, then $\theta = \arcsin{0.5} = \ang{30}$ .

Differentiate the above equation w.r.t t

$\displaystyle{16 \cos{\theta} \frac{d\theta}{dt} = \frac{db}{dt} \implies \frac{d\theta}{dt} = \frac{1}{16 \cos{\theta}} = \frac{1}{13.856} = \mathbf{0.0722}}$

c. The area of the triangle is given by $A = 0.5\times h \times b$ . Differentiating w.r.t t,

$\displatstyle{\frac{dA}{dt} = 0.5 b \frac{dh}{dt} + 0.5 h \frac{db}{dt}}$

Plugging in b = 8, h = 13.856, $\frac{dh}{dt} = -0.588$ ,

$\frac{dA}{dt} = -2.352 + 6.928 = \mathbf{4.576 ft^2/sec}$

8 0

4 years ago

Please help me asap ty ty :)

Zanzabum

Answer:

x-intercept = (-9,0)

y-intercept = (0,27)

Step-by-step explanation:

So first we will convert 9x - 3y = -81 into slope intercept form (y=mx+b).

Subtract 9x on both sides to get -3y = -9x -81. Next divide -3 on both sides to get y = 3x + 27.

Since b is the y-intercept, in y=mx+b and 27 is in the position of b, we can already tell that 27 is the y-intercept. So we will write it as (0,27) because coordinates are supposed to be written as (x,y).

Now in order to find the x-intercept, we will have to plug in 0 for y, in the original equation, so we can solve for x.

So we have: 9x -3(0) = -81

Since 3 × 0 = 0, we now have 9x - 0 = -81. So next we add 0 on both sides to get 9x = -81, and then we divide by 9 to get x = -9. So we will write this as (-9,0).

Hope this helps you :)

8 0

2 years ago

The graph of y = x^2 is translated 3 units to the left. The equation for this new graph is:

EastWind [94]

The answer is:
C. Y=(x+3)^2

7 0

3 years ago