(3,-8), (3, 2), (6, -1), (2, 2)) (-6, 3), (2,-2), (0, 8), (1, 1))

290 pennies are equal to how many dimes

ExtremeBDS [4]

29 dimes
............

6 0

3 years ago

Read 2 more answers

Inverse laplace of [(1/s^2)-(48/s^5)]

Katen [24]

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I am not familiar with Laplace transforms, so my explanation probably won't help, but given that for two Laplace transform $F(s)$ and $G(s)$ , then $\mathcal{L}^{-1}\{aF(s)+bG(s)\} = a\mathcal{L}^{-1}\{F(s)\}+b\mathcal{L}^{-1}\{G(s)\}$

Given that $\dfrac{1}{s^2} = \dfrac{1!}{s^2}$ and $-\dfrac{48}{s^5} = -2\cdot\dfrac{4!}{s^5}$

So you have $\mathcal{L}^{-1}\left\{\dfrac{1}{s^2} - 2\cdot\dfrac{4!}{s^5}\right\} = \mathcal{L}^{-1}\left\{\dfrac{1}{s^2}\right\} - 2\mathcal{L}^{-1}\left\{\dfrac{4!}{s^5}\right\}$

From Table of Laplace Transform, you have $\mathcal{L}\{t^n\} = \dfrac{n!}{s^{n+1}}$ and hence $\mathcal{L}^{-1}\left\{\dfrac{n!}{s^{n+1}}\right\} = t^n$

So you have $\mathcal{L}^{-1}\left\{\dfrac{1}{s^2}\right\} - 2\mathcal{L}^{-1}\left\{\dfrac{4!}{s^5}\right\} = \boxed{t-2t^4}$ .

Hope this helps...

7 0

3 years ago

Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. 2x −

zloy xaker [14]

Answer:

Only one solution
(x, y) = (-0.8, -3.6)

Step-by-step explanation:

You know there is only one solution because the ratio of x- and y-coefficients is different in the two equations. That means the lines will have different slopes, so must intersect in exactly one point.

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The y-coefficients are opposites, so you can eliminate the y-variable by adding the equations:

(2x -y) + (3x +y) = (2) + (-6)

5x = -4

x = -4/5 = -0.8

Substituting this into the second equation, we have ...

3(-0.8) +y = -6

y = -3.6 . . . . . . . add 2.4 to both sides

The solution is (x, y) = (-0.8, -3.6).

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You can also find the solution by graphing (or using a graphing calculator).

5 0

3 years ago

What is the circumference of circle P?<br> Express your answer in terms of pi.<br><br> PC= 17 cm.

Sedbober [7]

I am assuming that PC is a radius.

d = 2 * PC = 2 * 17 = 34

C = pi * d
C = pi * 34 = 34pi cm

if PC is a diameter, the change the 34 into 17.

3 0

4 years ago

Read 2 more answers

2 1/3 fills 3 1/2 dispensers how many fill one

Y_Kistochka [10]

2/3 (0.666) quantities fills one dispenser.

Step-by-step explanation:

Step 1; It is given that 2 1/3 amount of some liquid fills up 3 1/2 dispensers. First, we must convert the mixed fractions into improper fractions. To do that we multiply the number with the denominator and add with it the numerator whereas the denominator remains the same. To convert the fraction

2 1/3 we multiply the 2 with the 3 and add it with 1 while denominator remains 3, so 2 1/3 becomes 7/3. Similarly the fraction 3 1/2 converts into 7/2.

Step 2; So we have 7/3 quantities of liquid fills 7/2 dispensers. We multiply both sides by 2/7 so that the right side of the equation becomes 1 and the left side of the equation indicates the amount of liquid in 1 dispenser.

7/3 * 2/7 = 7/2 * 2/7 , 14/21 = 1 dispenser. So 14/21 = 2/3. So 2/3 or 0.666 quantity of liquid fills one dispenser.

8 0

3 years ago