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3 years ago

Find the cube root of 19683 by prime factorization method. Show steps.

Mathematics

2 answers:

ANTONII [103]3 years ago

3 0

Answer:

Step-by-step explanation:

Given number:

19683

Prime factors of 19683:

19683 = 3 × 3 × 3 × 3 × 3 × 3 × 3 × 3 × 3 = 3^9

Cube root:

∛19683 = ∛3^9 = 3^3 = 27

SVEN [57.7K]3 years ago

3 0

Answer:

27 is the cube root

Step-by-step explanation:

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5. What is the slope of the line that passes through (-2, 4) and (7, 1)?

just olya [345]

Answer:

Slope: $-\frac{1}{3}$

Step-by-step explanation:

Step 1: Use slope formula to find the slope

$m = \frac{y2 - y1}{x2- x1}=\frac{4-1}{-2-7}=\frac{3}{-9} =-\frac{1}{3}$

Therefore the slope of a line that passes through (-2, 4) and (7, 1) is $-\frac{1}{3}$

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3 years ago

What is f(5) if f(1)= 3.2 and f(x+1)=5/2(f(x))

Yanka [14]

F(2) = (5/2)f(1) = 8.0
f(3) = (5/2)f(2) = 20
f(4) = (5/2)f(3) = 50
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3 years ago

Read 2 more answers

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

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