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3 years ago

Solve the equation. Check your answer. 6y - 10 - 4y + 9 = 0

Mathematics

1 answer:

Kaylis [27]3 years ago

3 0

$6y-10-4y+9=0\\\\(6y-4y)+(-10+9)=0\\\\2y-1=0\ \ \ |+1\\\\2y=1\ \ \ \ |:2\\\\\boxed{y=0.5}$

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Determine the exact solution to the following in radians.

Sloan [31]

3sinx+1=sinx
2sinx+1=0
2sinx=-1
sinx=-1/2
x=sin^-1 (1/2) = 30 = $\pi$ /6 (when finding the inverse, always take the positive value, ignore the negative sign)
x is therefore negative in 3rd and 4th quadrant
Therefore values of x are:
180+30=210 = 7 $\pi$ /6
360-3=330 = 11 $\pi$ /6

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3 years ago

Name three pairs that have 5 as there greatest common factor

Hitman42 [59]

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3 years ago

Read 2 more answers

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:

$y_{p}(t) = C$

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

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

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:

$y_{p}(t) = C$

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

$(C)' + 4C = 8$

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

3 years ago

You bought a magazine for $5 and four erasers. You spend a total of $25. How much did each eraser cost?

Lesechka [4]

Subtract magazine from total:

25 -5 = 20

Divide by number of erasers:

20/4 = 5

Each eraser cost $5

5 0

3 years ago

Read 2 more answers

Leah has a 22 ounce coffee. she drinks 7 ounces. enter the percentage of ounces Leah has left of her coffee. round your answer t

Mademuasel [1]

Answer:

The percentage of ounces Leah has left of her coffee is 68.18%.

Step-by-step explanation:

The decrease percentage is computed using the formula:

$\text{Decrease}\%=\frac{\text{Original amount - Decrease}}{\text{Original amount}}\times 100$

It is provided that Leah originally had 22 ounce coffee.

Then she drinks 7 ounces of coffee.

Decrease = 7 ounces

Original = 22 ounces

Compute the percentage of ounces Leah has left of her coffee as follows:

$\text{Decrease}\%=\frac{\text{Original amount - Decrease}}{\text{Original amount}}\times 100$

$=\frac{22-7}{22}\times 100\\\\=\frac{15}{22}\times 100\\\\=68.1818182\%\\\\\approx 68.18\%$

Thus, the percentage of ounces Leah has left of her coffee is 68.18%.

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3 years ago