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3 years ago

5

A particle moves with velocity function v(t) =

^{2} " alt=" 3t^{2} " align="absmiddle" class="latex-formula"> − 4t + 1, with v measured in feet per second and t measured in seconds. Find the acceleration of the particle at time t = 3 seconds.
2 divided by 3 feet per second^2
7 feet per second^2
14 feet per second^2
21 feet per second^2

2 answers:

geniusboy [140]3 years ago

7 0

V'(t)=a(t)

deriviive of the velocity is the acceleration

easy peasy
dy/dx v(t)=6t-4
v'(t)=a(t)=6t-4

at=t=3
a(3)=6(3)-4
a(3)=18-4
a(3)=14 ft per second squared

3rd answer

Ivahew [28]3 years ago

6 0

Acceleration is the rate of change of velocity.
So take the derivative of the velocity which would be a =6t-4. When t=3, a=14 ft/sec^2

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Lagrange multipliers have a definite meaning in load balancing for electric network problems. Consider the generators that can o

Ivahew [28]

Answer:

The load balance $(x_1,x_2,x_3)=(545.5,272.7,181.8)$ Mw minimizes the total cost

Step-by-step explanation:

<u>Optimizing With Lagrange Multipliers</u>

When a multivariable function f is to be maximized or minimized, the Lagrange multipliers method is a pretty common and easy tool to apply when the restrictions are in the form of equalities.

Consider three generators that can output xi megawatts, with i ranging from 1 to 3. The set of unknown variables is x1, x2, x3.

The cost of each generator is given by the formula

$\displaystyle C_i=3x_i+\frac{i}{40}x_i^2$

It means the cost for each generator is expanded as

$\displaystyle C_1=3x_1+\frac{1}{40}x_1^2$

$\displaystyle C_2=3x_2+\frac{2}{40}x_2^2$

$\displaystyle C_3=3x_3+\frac{3}{40}x_3^2$

The total cost of production is

$\displaystyle C(x_1,x_2,x_3)=3x_1+\frac{1}{40}x_1^2+3x_2+\frac{2}{40}x_2^2+3x_3+\frac{3}{40}x_3^2$

Simplifying and rearranging, we have the objective function to minimize:

$\displaystyle C(x_1,x_2,x_3)=3(x_1+x_2+x_3)+\frac{1}{40}(x_1^2+2x_2^2+3x_3^2)$

The restriction can be modeled as a function g(x)=0:

$g: x_1+x_2+x_3=1000$

Or

$g(x_1,x_2,x_3)= x_1+x_2+x_3-1000$

We now construct the auxiliary function

$f(x_1,x_2,x_3)=C(x_1,x_2,x_3)-\lambda g(x_1,x_2,x_3)$

$\displaystyle f(x_1,x_2,x_3)=3(x_1+x_2+x_3)+\frac{1}{40}(x_1^2+2x_2^2+3x_3^2)-\lambda (x_1+x_2+x_3-1000)$

We find all the partial derivatives of f and equate them to 0

$\displaystyle f_{x1}=3+\frac{2}{40}x_1-\lambda=0$

$\displaystyle f_{x2}=3+\frac{4}{40}x_2-\lambda=0$

$\displaystyle f_{x3}=3+\frac{6}{40}x_3-\lambda=0$

$f_\lambda=x_1+x_2+x_3-1000=0$

Solving for \lambda in the three first equations, we have

$\displaystyle \lambda=3+\frac{2}{40}x_1$

$\displaystyle \lambda=3+\frac{4}{40}x_2$

$\displaystyle \lambda=3+\frac{6}{40}x_3$

Equating them, we find:

$x_1=3x_3$

$\displaystyle x_2=\frac{3}{2}x_3$

Replacing into the restriction (or the fourth derivative)

$x_1+x_2+x_3-1000=0$

$\displaystyle 3x_3+\frac{3}{2}x_3+x_3-1000=0$

$\displaystyle \frac{11}{2}x_3=1000$

$x_3=181.8\ MW$

And also

$x_1=545.5\ MW$

$x_2=272.7\ MW$

The load balance $(x_1,x_2,x_3)=(545.5,272.7,181.8)$ Mw minimizes the total cost

5 0

3 years ago

What is the volume of this rectangular prism?

ollegr [7]

Answer:

$57,600cm {}^{2}$

<em><u>Solving steps:</u></em>

To find the volume of a rectangular prism, multiply its 3 dimensions: length x width x height. The volume is expressed in cubic units.

=> 40 cm ${}^{2}$ × 30cm ${}^{2}$ × 48 cm ${}^{2}$

multiply all the numbers

=> 57,600cm ${}^{2}$

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2 years ago

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Point A is shown on the the number line below.(The picture I attached)

Lina20 [59]

Answer:

b

Step-by-step explanation:

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2 years ago

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What number makes the expressions equivalent? Enter your answer in the box. 1/2(–1.4m + 0.4) =__m + 0.2A) -1.4B) 1.4C) -0.7D) 0.

Snowcat [4.5K]

Answer:

C. -0.7

Explanation:

Given the equation:

$\frac{1}{2}(-1.4m+0.4)=\boxed{\square}_{}m+0.2$

First, distribute the bracket on the left-hand side:

$\begin{gathered} \frac{1}{2}(-1.4m)+\frac{1}{2}(0.4) \\ =-0.7m+0.2 \end{gathered}$

The number that makes the given expressions equivalent is -0.7.

The correct choice is C.

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1 year ago

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Tcecarenko [31]

Answer:

356.53

Step-by-step explanation:

Calculate the semicircle and square areas separately. For the semicircle, A = πr²/2, so 100.53

And for the square, A = a², so 256

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3 years ago