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2 years ago

Find the smallest positive integer k such that 360k is a cube number.

Mathematics

2 answers:

MAXImum [283]2 years ago

8 0

Answer: k = 75

<u>Step-by-step explanation:</u>

360

∧

36 10

∧ ∧

6 6 2 5

∧ ∧

2 3 2 3

Prime factorization of 360 is: 2³ · 3² · 5

Since we want a perfect cube, every number must be to the power of 3.

That means we need a 3 and 2 more 5s to make a cube

k = 3 × 5 × 5

= 75

Luden [163]2 years ago

5 0

Answer:

k = 75

Step-by-step explanation:

Factorize 360

360 = 36 * 10

= 2 * 2 * 3 * 3 * 2 * 5

As 360k is cube number, k = 3 * 5 * 5

k = 75

360k = 360 * 75 = 27000 is a perfect cube

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The given matrix is the augmented matrix for a linear system. Use technology to perform the row operations needed to transform t

shtirl [24]

Answer:

$x_{1} = \frac{176}{127} + \frac{71}{127}x_{4}\\\\ x_{2} = \frac{284}{127} + \frac{131}{254}x_{4}\\\\x_{3} = \frac{845}{127} + \frac{663}{254}x_{4}\\$

Step-by-step explanation:

As the given Augmented matrix is

$\left[\begin{array}{ccccc}9&-2&0&-4&:8\\0&7&-1&-1&:9\\8&12&-6&5&:-2\end{array}\right]$

Step 1 :

$r_{1}$ ↔ $r_{1} - r_{2}$

$\left[\begin{array}{ccccc}1&-14&6&-9&:10\\0&7&-1&-1&:9\\8&12&-6&5&:-2\end{array}\right]$

Step 2 :

$r_{3}$ ↔ $r_{3} - 8r_{1}$

$\left[\begin{array}{ccccc}1&-14&6&-9&:10\\0&7&-1&-1&:9\\0&124&-54&77&:-82\end{array}\right]$

Step 3 :

$r_{2}$ ↔ $\frac{r_{2}}{7}$

$\left[\begin{array}{ccccc}1&-14&6&-9&:10\\0&1&-\frac{1}{7} &-\frac{1}{7} &:\frac{9}{7} \\0&124&-54&77&:-82\end{array}\right]$

Step 4 :

$r_{1}$ ↔ $r_{1} + 14r_{2}$ , $r_{3}$ ↔ $r_{3} - 124r_{2}$

$\left[\begin{array}{ccccc}1&0&4&-11&:-8\\0&1&-\frac{1}{7} &-\frac{1}{7} &:\frac{9}{7} \\0&0&- \frac{254}{7} &\frac{663}{7} &:-\frac{1690}{7} \end{array}\right]$

Step 5 :

$r_{3}$ ↔ $\frac{r_{3}. 7}{254}$

$\left[\begin{array}{ccccc}1&0&4&-11&:-8\\0&1&-\frac{1}{7} &-\frac{1}{7} &:\frac{9}{7} \\0&0&1&-\frac{663}{254} &:-\frac{1690}{254} \end{array}\right]$

Step 6 :

$r_{1}$ ↔ $r_{1} - 4r_{3}$ , $r_{2}$ ↔ $r_{2} + \frac{1}{7} r_{3}$

$\left[\begin{array}{ccccc}1&0&0&-\frac{71}{127} &:\frac{176}{127} \\0&1&0&-\frac{131}{254} &:\frac{284}{127} \\0&0&1&-\frac{663}{254} &:\frac{845}{127} \end{array}\right]$

∴ we get

$x_{1} = \frac{176}{127} + \frac{71}{127}x_{4}\\\\ x_{2} = \frac{284}{127} + \frac{131}{254}x_{4}\\\\x_{3} = \frac{845}{127} + \frac{663}{254}x_{4}\\$

6 0

2 years ago

What is the measure of

stepan [7]

Answer:

Angle A is 37 degrees, Angle B is 82 degrees, Angle C is 61 degrees

Step-by-step explanation:

Exterior angles are the supplement of interior angles, so subtract 143 from 180 to find Angle A.

180 - 143 = 37

All angles add up to 180.

37 + 61 = 98

180 - 98 = 82

Angle B is 82 degrees.

Hope this helped. :)

7 0

2 years ago

Tony is trying to find the solution of the system 2x - 4y +12 using elimination 3x + 4y = 48 He wrote these steps to solve the p

kobusy [5.1K]

Answer: Solution: (12, 3)

Step-by-step explanation:

2x - 4y = 12

3x + 4y = 48

Add both equations

5x = 60

Divide both sides by 5

x = 12

We can use the value of x to find y

3x + 4y = 48

3 (12) + 4y = 48

36 + 4y = 48

Subtract 36 from both sides

4y = 12

Divide both sides by 4

y = 3

Solution: (12, 3)

7 0

2 years ago

Any help, please! <br> I dont understand

frutty [35]

The answer would be 40% :)

3 0

3 years ago

Help geometry what I m jlf <br> Picture provided

Zolol [24]

Answer:

$\angle\,JLF = 114^o$ which agrees with option"B" of the possible answers listed

Step-by-step explanation:

Notice that in order to solve this problem (find angle JLF) , we need to find the value of the angle defined by JLG and subtract it from $180^o$ , since they are supplementary angles. So we focus on such, and start by drawing the radii that connects the center of the circle (point "O") to points G and H, in order to observe the central angles that are given to us as $90^o$ and $138^o$ . (see attached image)

We put our efforts into solving the right angle triangle denoted with green borders.

Notice as well, that the triangle JOH that is formed with the two radii and the segment that joins point J to point G, is an isosceles triangle, and therefore the two angles opposite to these equal radius sides, must be equal. We see that angle JOH can be calculated by : $360^o-90^o-138^o=132^o$

Therefore, the two equal acute angles in the triangle JOH should add to:

$180^o-132^o=48^o$ resulting then in each small acute angle of measure $24^o$ .

Now referring to the green sided right angle triangle we can find find angle JLG, using: $180^o-24^o-90^o=66^o$

Finally, the requested measure of angle JLF is obtained via: $180^o-66^o=114^o$

4 0

3 years ago