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2 years ago

a cube with a volume of 64 cubic meters is scaled by a factor of 5, what is the volume of this modified cube in cubic meters?

Mathematics

2 answers:

mixer [17]2 years ago

8 0

Answer :

8,000

Step-by-step explanation:

When the sides of the cube are scaled by a factor of k, the volume increases by a factor of k3. Here, the new volume is 64 cubic meters × 53 = 8,000 cubic meters.

IceJOKER [234]2 years ago

4 0

Answer:

8000 m^3.

Step-by-step explanation:

Volume of cube: 64 m^3

Let's say x is the sides of cube.

Volume: x^3= 64

Length is scaled up by a factor of 5.

Side of the cube will be 5x.

New volume would be: (5x)^3 = 125 x 64 = 8000 m^3

Hope this helps & good luck.

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(5) Find the Laplace transform of the following time functions: (a) f(t) = 20.5 + 10t + t 2 + δ(t), where δ(t) is the unit impul

Aloiza [94]

Answer

(a) $F(s) = \frac{20.5}{s} - \frac{10}{s^2} - \frac{2}{s^3}$

(b) $F(s) = \frac{-1}{s + 1} - \frac{4}{s + 4} - \frac{4}{9(s + 1)^2}$

Step-by-step explanation:

(a) $f(t) = 20.5 + 10t + t^2 +$ δ(t)

where δ(t) = unit impulse function

The Laplace transform of function f(t) is given as:

$F(s) = \int\limits^a_0 f(s)e^{-st} \, dt$

where a = ∞

=> $F(s) = \int\limits^a_0 {(20.5 + 10t + t^2 + d(t))e^{-st} \, dt$

where d(t) = δ(t)

=> $F(s) = \int\limits^a_0 {(20.5e^{-st} + 10te^{-st} + t^2e^{-st} + d(t)e^{-st}) \, dt$

Integrating, we have:

=> $F(s) = (20.5\frac{e^{-st}}{s} - 10\frac{(t + 1)e^{-st}}{s^2} - \frac{(st(st + 2) + 2)e^{-st}}{s^3} )\left \{ {{a} \atop {0}} \right.$

Inputting the boundary conditions t = a = ∞, t = 0:

$F(s) = \frac{20.5}{s} - \frac{10}{s^2} - \frac{2}{s^3}$

(b) $f(t) = e^{-t} + 4e^{-4t} + te^{-3t}$

The Laplace transform of function f(t) is given as:

$F(s) = \int\limits^a_0 (e^{-t} + 4e^{-4t} + te^{-3t} )e^{-st} \, dt$

$F(s) = \int\limits^a_0 (e^{-t}e^{-st} + 4e^{-4t}e^{-st} + te^{-3t}e^{-st} ) \, dt$

$F(s) = \int\limits^a_0 (e^{-t(1 + s)} + 4e^{-t(4 + s)} + te^{-t(3 + s)} ) \, dt$

Integrating, we have:

$F(s) = [\frac{-e^{-(s + 1)t}} {s + 1} - \frac{4e^{-(s + 4)}}{s + 4} - \frac{(3(s + 1)t + 1)e^{-3(s + 1)t})}{9(s + 1)^2}] \left \{ {{a} \atop {0}} \right.$

Inputting the boundary condition, t = a = ∞, t = 0:

$F(s) = \frac{-1}{s + 1} - \frac{4}{s + 4} - \frac{4}{9(s + 1)^2}$

3 0

3 years ago

The first 4 terms of a geometric sequence are 2, 6, 18, 54. Part A: Find the common ratio. Remember the common ratio is the numb

ra1l [238]

Answer:

Common ratio is 3

The three terms are 162, 486, 1458

Step-by-step explanation:

Given: The first 4 terms of a sequence are $2,6,18,54$

To find:

A. the common ratio

B. the next 3 values in the geometric sequence

Solution:

Geometric sequence is a sequence in which each of the terms is obtained by multiplying the previous term by a fixed number.

$\frac{6}{2}=3\\\\\frac{18}{6}=3\\\\\frac{54}{18}=3$

So, the common ratio is $3$

The next three values are as follows:

$54(3)=162\\162(3)=486\\486(3)=1458$

8 0

2 years ago

If the revenue for the week is $2000 and the labor cost consists of two workers earning eight dollars per hour who work 40 hours

arsen [322]

To find the cost of labor for one worker, you multiply the wage by the number of hours worked.

40 * 8 = 320

Because there are two workers, now you double it.

320 * 2 = 640

To find the percentage of the revenue that this is, you do the labor cost divided by the revenue.

640 / 2000 = 0.32

Move the decimal two places to the right to get the percentage.

0.32 = 32%

The labor cost is 32% of the revenue.

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3 years ago

Please help me and give explanation on how you got your answer if not that’s fine

Sladkaya [172]

D

The reason is because well first of the plotted dot is filled in with means that x needs to be less then or equal too so to represent that you put the line under the less then symbol and none of the other options have that exact symbol

The arrow is going to the left this is stating that x needs to be less than -2

If it’s wrong then I apologize because I don’t really remember this

8 0

2 years ago

2<br> Carrots<br> €1.80 per kg<br> How much does 250 g of carrots<br> cost?

igomit [66]

Answer:

The cost of 250 g carrots is €0.45.

Step-by-step explanation:

Given that,

Cost of carrots is €1.80 per kg

We need to find the cost of 250 g of carrots.

1 kg cost = €1.80

We know that, 250 gram = 0.25 kg

0.25 kg cost = €1.80 × 0.25

= €0.45

So, the cost of 250 g carrots is €0.45.

3 0

3 years ago