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3 years ago

Find the side length of a cube with a volume of 69cm^3. If necessary, round your answer to the nearest tenth

Mathematics

1 answer:

Alex73 [517]3 years ago

3 0

Answer:

4.1 centimeters

Step-by-step explanation:

The volume of a cube can be found using the following formula.

$V=s^3$

We know that the volume of the cube is 69 cm^3, therefore we can substitute 69 cm^3 in for V (volume).

$69 cm^3=s^3$

We want to find out what<em> s</em> (side length) is. Therefore, we must get<em> s </em>by itself.

s is being cubed. The inverse of a cube is the cube root. Take the cubed root of both sides.

$\sqrt[3]{69 cm^3} =\sqrt[3]{s^3}$

$\sqrt[3]{69 cm^3}=s$

$4.10156593 cm=s$

The question tell us to round to the nearest tenth. The 0 in the hundredth place indicates we should leave the 1 in the tenth place.

$4.1 cm=s$

The side length of the cube is 4.1 centimeters.

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IRISSAK [1]

Answer:

80 feet

Step-by-step explanation:

Given:

Initial speed of the car ( $v_0$ ) = 40 ft/sec

Deceleration of the car ( $\frac{dv}{dt}$ ) = -10 ft/sec²

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Let the distance traveled by the car be 'x' at any time 't'. Let 'v' be the velocity at any time 't'.

Now, deceleration means rate of decrease of velocity.

So, $\frac{dv}{dt}=-10\ ft/sec^2$

Negative sign means the velocity is decreasing with time.

Now, $\frac{dv}{dt}=\frac{dv}{dx}(\frac{dx}{dt})$ using chain rule of differentiation. Therefore,

$\frac{dv}{dx}\cdot\frac{dx}{dt}= -10\\\\But\ \frac{dx}{dt}=v.\ So,\\\\v\frac{dv}{dx}=-10\\\\vdv=-10dx$

Integrating both sides under the limit 40 to 0 for 'v' and 0 to 'x' for 'x'. This gives,

$\int\limits^0_{40} {v} \, dv=\int\limits^x_0 {-10} \, dx\\\\\left [ \frac{v^2}{2} \right ]_{40}^{0}=-10x\\\\-10x=\frac{0}{2}-\frac{1600}{2}\\\\10x=800\\\\x=\frac{800}{10}=80\ ft$

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gulaghasi [49]

The question is essentially asking for the least common multiple of 20 and 25. There are several ways you can find the LCM. One easy way is to divide the product by the GCD (greatest common divisor).

GCD(20, 25) = 5 . . . . . see below for a way to find this, if you don't already know

LCM(20, 25) = 20×25/GCD(20, 25)

... = 500/5 = 100

The buses will be there together again after ...

... B. 100 minutes

_____

You can also look at the factors of the numbers:

... 20 = 2²×5

... 25 = 5²

The least common multiple must have factors that include all of these*, so must be ...

... 2²×5² = 100

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* you can describe the LCM as the product of the unique factors to their highest powers. 20 has 2 raised to the 2nd power. 25 has 5 raised to the 2nd power, which is a higher power of 5 than is present in the factorization of 20. Hence the LCM must have 2² and 5² as factors.

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You can also look at the factorization of 20 and 25 to see that 5 is the only factor they have in common. That is the GCD, sometimes called the GCF (greatest common factor).

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