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2 years ago

What is the smallest positive perfect cube that is a multiple of 180?

Mathematics

1 answer:

Lelechka [254]2 years ago

5 0

Answer:Factor it into its prime factors:

180 / 2 = 90

90 / 2 = 45

45 / 3 = 15

15 / 3 = 5

5 / 5 = 1

2 x 2 x 3 x 3 x 5

All of those factors pair should pair up in 3 members to make cube

2 x 2 x 2 x 3 x3 x 3 x 5 x 5 x 5 = (30)^3 = 27000

Smallest no. = 2 x 3 x 5 x 5 = 150

Step-by-step explanation:

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I keep believing the answer is either 18,000 or 1,800 but im incorrect. Can someone please help me?? I use the formula A^2 *2*A*

Yuri [45]

The base is a square, so the area of the square is (10 cm)² = 100 cm²

To find the area of each triangle use the formula

base • height

10 cm • 9 cm = 90 cm²

now multiply by the number of triangles

90 cm • 4 = 360 cm²

Add the area of the square:

100 cm² + 360 cm² = 460 cm²

I hope it's correct

4 0

2 years ago

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Pairs of expressions are given. Select the pairs that are equivalent .

mafiozo [28]

Answer:

All the options are correct

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2 years ago

Hi! The question is in the is in the picture :) (worth 50 points)

Reika [66]

Answer:

53.2

Step-by-step explanation:

5 0

2 years ago

A car is being driven at a rate of 40 ft/sec when the brakes are applied. The car decelerates at a constant rate of 10 ft/sec2.

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

Final speed of the car ( $v_x$ ) = 0 ft/sec

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,

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

Therefore, the car travels a distance of 80 feet before stopping.

4 0

2 years ago

Angie and Kenny play online video games. Angie buys 1 software package and 2 months of game play. Kenny buys 1 software package

GalinKa [24]

Answer:

The cost of one month of game play is $12.

Step-by-step explanation:

We are given the following in the question:

Cost of software package = $30

Let y dollars be the cost of one month of game play.

Angie buys 1 software package and 2 months of game play.

Angie's cost =

$1(30) + 2y = 2y + 30$

Kenny buys 1 software package and 4 months of game play.

Kenny's cost =

$1(30) + 4y = 4y + 30$

Total cost = $132

Thus, we can write the equation:

$(2y+30)+(4y+30) = 132\\6y + 60 = 132\\6y = 132-60\\6y = 72\\\Rightarrow y = 12$

Thus, the cost of one month of game play is $12.

7 0

2 years ago