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3 years ago

A particle is moving with the given data. Find the position of the particle. a(t) = t2 − 2t + 9, s(0) = 0, s(1) = 20

Mathematics

1 answer:

lozanna [386]3 years ago

6 0

Answer:

Position of the particle is 20.

Step-by-step explanation:

Position function is integration of velocity function.

Velocity function is integration of acceleration function.

So, let's integrate the given a(t) to get v(t)

If we integrate v(t) then we get s(t)

It is given the values of s(0) =0 and s(1)=20

So, position of the particle is difference of 20, 0. That's 20-0 =20.

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A farmer finds that if she plants 50 trees per acre, each tree will yield 80 bushels of fruit. She estimates that for each addit

pashok25 [27]

Answer:

Step-by-step explanation:

From the given information:

Let x be the number of trees.

F(x) = (50 +x) (20 - 3x)

F(x) = 1000 - 150x + 20x - 3x²)

F(x) = -3x² - 130x + 1000

Differentiating F(x) with respect to x;

$F'(x) = \dfrac{d}{dx}( -3x^2- 130x + 1000)$

$F'(x) = ( -3(2x)- 130(1) +0)$

F'(x) = -6x -130

Now; we set F'(x) to be equal to zero to determine the critical value;

-6x - 130 = 0

x = - 130/6

Differentiating F''(x) with respect to x

$F''(x) = \dfrac{d}{dx}( -6x- 130)$

$F''(x) = ( -6(1))$

F''(x) = -6 (<0)

Thus; by the second derivative, the revenue function F(x) is maximum when x = -130/6

Therefore, the number of trees she should plant per acre to maximize her harvest is:

50 + x = 50 - 130/6

= 85/3

$\simeq$ 28

Therefore, the number of trees per acre to maximize the harvest is 28

6 0

3 years ago

A to 4. 14 - 213p + 1) = 6/4 + p)

frutty [35]

Answer:

Step-by-step explanation:

Figure it out yourself

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3 years ago

3x+4y+6z=15 Solve for x.

aalyn [17]

Answer:

Step-by-step explanation:

<h3>Question:-</h3>

To solve for x

<h3>Equation:-</h3>

3x + 4y + 6z = 15

<h3>Solution:-</h3>

=> 3x + 4y + 6z = 15

[On subtracting both sides with 4y]

=> 3x + 4y + 6z - 4y = 15 - 4y

[On Simplification]

=> 3x + 6z = 15 - 4y

[On subtracting both sides with 6z]

=> 3x + 6z - 6z = 15 - 4y - 6z

[On Simplification]

=> 3x = 15 - 4y - 6z

[On dividing both sides with 3]

$= > \frac{3x}{3} = \frac{15 - 4y - 6z}{3}$

[On Simplification]

$= > x = 5 - \frac{4}{3} y - 2z \: (ans)$

3 0

2 years ago

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The table represents the cost for oranges in Mr. Nguyen's store. Image In this situation, cost is a function of the number of or

xxMikexx [17]

Answer:

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3 years ago

What is the value of the determinant?

Contact [7]

Answer:

The value of the determinant is 0.

Step-by-step explanation:

Since it is a 3 x 3 determinant, we can calculate its value by the Law of Sarrus:

$Det = (11)\cdot (98)\cdot (26\cdot y) + (97)\cdot (24\cdot y) \cdot (13) + (22\cdot y) \cdot (12) \cdot (99) - (22\cdot y) \cdot (98) \cdot (13) - (97)\cdot (12) \cdot (26\cdot y) - (11) \cdot (24\cdot y) \cdot (99)$

$Det = 28028\cdot y + 30264\cdot y + 26136\cdot y - 28028\cdot y - 30264\cdot y - 26136\cdot y$

$Det = 0$

The value of the determinant is 0.

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3 years ago