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3 years ago

is 3240 a perfect cube? if not then by which smallest number should 3240 be multiplied so that the product is a perfect cube?

Mathematics

1 answer:

Debora [2.8K]3 years ago

5 0

Answer:

<h2>3240 it's not a perfect cube.</h2><h2>The smallest number should 3240 be multiplied so that the product is a perfect cube is 15² = 225.</h2>

Step-by-step explanation:

3240 is a perfect cube if 3240 = n³ (n ∈ N).

Use the Prime Factorization:

$\begin{array}{c|c}3240&2\\1620&2\\810&2\\405&5\\81&3\\27&3\\9&3\\3&3\\1\end{array}\\\\3240=2\cdot2\cdot2\cdot5\cdot3\cdot3\cdot3\cdot3=2^3\cdot3^3\cdot5\cdot3=(2\cdot3)^3\cdot5\cdot3=6^3\cdot5\cdot3$

$3240=6^3\cdot15\qquad\text{multiply both sides by}\ 15^2\\\\3240\cdot15^2=6^3\cdot15^3=3240\cdot15^2=(6\cdot15)^3=90^3$

Used:

$a^n\cdot a^m=a^{n+m}\\\\(ab)^n=a^nb^m$

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Three towns divided highway repair costs equally.

OLEGan [10]

Answer:

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Step-by-step explanation:

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3 0

3 years ago

A submarine started at the surface of the water and was moving at -15 meters per minute. The submarine traveled at this rate for

velikii [3]

Given :

A submarine started at the surface of the water and was moving at -15 meters per minute.

The submarine traveled at this rate for 48 minutes before coming to rest on the ocean floor.

To Find :

The change in the submarine position.

Solution :

We need to find the position of submarine position from the surface of water.

Distance travelled = Speed × Time

Distance travelled = -15 m/min × 48 min

Distance travelled = 720 m

Therefore, the position of submarine is 720 m below the surface of ocean.

5 0

3 years ago

How do i figure out these problems ?

Andreyy89

Given two vectors

$v=(a,b),\quad w=(c,d)$

they are parallel if they are a multiple of each other:

$c=ka,\quad d=kb$

You can easily test this by checking if

$\dfrac{c}{a}=\dfrac{d}{b}$

they are orthogonal if their dot product is null:

$v\cdot w=ac+bd=0$

For example, in the first case, we have

$\dfrac{10}{3}\div 2 \neq \dfrac{4}{3}\div 5$

So, they aren't parallel. Similarly, you have

$2\cdot \dfrac{10}{3}+5\cdot \dfrac{4}{3}\neq 0$

So, they aren't orthogonal.

In the second case, we have

$\dfrac{5}{-12}\neq \dfrac{-6}{-10}$

So, they aren't parallel, and

$5(-12)+(-6)(-10)=-60+60=0$

So, they are orthogonal.

Finally, we have

$\dfrac{2}{-4}=\dfrac{-7}{14}=-\dfrac{1}{2}$

So, they are parallel (and thus can't be orthogonal)

7 0

3 years ago

35.

babunello [35]

Hi there! :)

Answer:

$\huge\boxed{y = 4x - 2}$

Given line with an equation of y = 4x + 3

Parallel lines contain equivalent slopes, so a parallel line to the given equation would contain a slope of m = 4.

Plug in the coordinates of the point given, along with the slope into the equation y = mx + b where:

m = slope

y = y-coordinate of point

x = x-coordinate of point

Solve for the 'b' value, or y-intercept:

y = mx + b

6 = 4(2) + b

6 = 8 + b

b = -2

Rewrite the equation as slope-intercept form:

y = 4x - 2

4 0

3 years ago

Read 2 more answers

A rectangle is removed from a right triangle to create the shaded region shown below. Find the area of the shaded region.

irina [24]

Answer:

I can't tell what the triangle is

Step-by-step explanation:

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3 years ago

is 3240 a perfect cube? if not then by which smallest number should 3240 be multiplied so that the product is a perfect cube?​

is 3240 a perfect cube? if not then by which smallest number should 3240 be multiplied so that the product is a perfect cube?