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4 years ago

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List all rational roots that are possible according to the rational zero theorem. x^3-5x^2-9x+45=0

1 answer:

Lina20 [59]4 years ago

8 0

-3, 3, 5.

https://www.wolframalpha.com/input/?i=%28x%5E3%29-%285x%5E2%29-9x%2B45%3D0

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Consider the graph of Bx + Cy = A where A, B, and C are all positive constants. Find the coordinates of the x-intercept. Use upp

timofeeve [1]

That is where the line crosses the x axis or where y=0
set y=0
Bx=A
find x value
divie both sides by B
x=A/B
the x intercept is x=A/B

3 0

3 years ago

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Melissa lives 5/6 of a mile from the bus stop. pete lives 2/3 of a mile from the bus stop. how much closer to the bus stop does

valina [46]

Melissa lives 5/6 of a mile from the bus stop 5/6 of a mile is 0.83
Peter lives 2/3 of a mile from the bus stop, 2/3 of a mile is 0.66 miles
Pete does not live close to the bus stop than Melissa.
Melissa lives 0.83 - 0.66 = 0.17 miles closer to the bus stop

8 0

3 years ago

What is the area of the composite figure?<br> (Attached picture)<br><br> __cm²

lara31 [8.8K]

Answer:

59.5

Step-by-step explanation:

area of the triangle is (7 x 3)/2=21/2=10.5

area of the square 7x7=49

7 0

3 years ago

What is 68.52 rounded to the nearest whole number?

4vir4ik [10]

Answer:

it would be 69 because you would round .5 to 1 then 1 plus the 68 from the 68.52 making it 69

Step-by-step explanation:

6 0

3 years ago

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Solve these linear equations in the form y=yn+yp with yn=y(0)e^at.

WINSTONCH [101]

Answer:

a) $y(t) = y_{0}e^{4t} + 2$ . It does not have a steady state

b) $y(t) = y_{0}e^{-4t} + 2$ . It has a steady state.

Step-by-step explanation:

a) $y' -4y = -8$

The first step is finding $y_{n}(t)$ . So:

$y' - 4y = 0$

We have to find the eigenvalues of this differential equation, which are the roots of this equation:

$r - 4 = 0$

$r = 4$

So:

$y_{n}(t) = y_{0}e^{4t}$

Since this differential equation has a positive eigenvalue, it does not have a steady state.

Now as for the particular solution.

Since the differential equation is equaled to a constant, the particular solution is going to have the following format:

$y_{p}(t) = C$

So

$(y_{p})' -4(y_{p}) = -8$

$(C)' - 4C = -8$

C is a constant, so (C)' = 0.

$-4C = -8$

$4C = 8$

$C = 2$

The solution in the form is

$y(t) = y_{n}(t) + y_{p}(t)$

$y(t) = y_{0}e^{4t} + 2$

b) $y' +4y = 8$

The first step is finding $y_{n}(t)$ . So:

$y' + 4y = 0$

We have to find the eigenvalues of this differential equation, which are the roots of this equation:

$r + 4 =$

$r = -4$

So:

$y_{n}(t) = y_{0}e^{-4t}$

Since this differential equation does not have a positive eigenvalue, it has a steady state.

Now as for the particular solution.

Since the differential equation is equaled to a constant, the particular solution is going to have the following format:

$y_{p}(t) = C$

So

$(y_{p})' +4(y_{p}) = 8$

$(C)' + 4C = 8$

C is a constant, so (C)' = 0.

$4C = 8$

$C = 2$

The solution in the form is

$y(t) = y_{n}(t) + y_{p}(t)$

$y(t) = y_{0}e^{-4t} + 2$

6 0

4 years ago