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2 years ago

M5-3/2x less than or equal to 1/3

Mathematics

1 answer:

Zepler [3.9K]2 years ago

8 0

Answer: choice A

Step-by-step explanation:

by rearranging the initial inequality you’ll get

$\frac{3}{2} x\leq 5-\frac{1}{3}$

which equals

$\frac{3}{2} x\leq\frac{14}{3}$

then multiply both sides by 2/3

$x\leq \frac{28}{9}$

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5. Find the general solution to y'''-y''+4y'-4y = 0

CaHeK987 [17]

For any equation,

$a_ny^(n)+\dots+a_1y'+a_0y=0$

assume solution of a form, $e^{yt}$

Which leads to,

$(e^{yt})'''-(e^{yt})''+4(e^{yt})'-4e^{yt}=0$

Simplify to,

$e^{yt}(y^3-y^2+4y-4)=0$

Then find solutions,

$\underline{y_1=1}, \underline{y_2=2i}, \underline{y_3=-2i}$

For non repeated real root y, we have a form of,

$y_1=c_1e^t$

Following up,

For two non repeated complex roots $y_2\neq y_3$ where,

$y_2=a+bi$

and,

$y_3=a-bi$

the general solution has a form of,

$y=e^{at}(c_2\cos(bt)+c_3\sin(bt))$

Or in this case,

$y=e^0(c_2\cos(2t)+c_3\sin(2t))$

Now we just refine and get,

$\boxed{y=c_1e^t+c_2\cos(2t)+c_3\sin(2t)}$

Hope this helps.

r3t40

5 0

3 years ago

What is the greatest common factor of 60x4y?, 45xy, and 75xºy?

Scrat [10]

Answer:

15x^3y

Step-by-step explanation:

60, 45 & 75 are all divisible by 15

3 0

1 year ago

What, in degrees, is the measure of the largest angle in $\triangle PQR?$

irina1246 [14]

Answer:

108 degrees

Step-by-step explanation:

3x+x+6x=10x, 180/10=18 and 18x6 is 108

3 0

2 years ago

ind the present value that will grow to $4000 if the annual interest rate is 8.5% compounded quarterly for 9 yr.

frozen [14]

Answer:

$1876.31

Step-by-step explanation:

The present value can be found using the compound interest formula.

<h3>Present value</h3>

The formula for the future value of an investment of P earning annual interest rate r compounded n times per year for t years is ...

FV = P(1 +r/n)^(nt)

Filling in the known values gives ...

4000 = P(1 +0.085/4)^(4·9) = P(1.02125^36)

Then the amount to be invested is ...

P = 4000/1.02125^36 ≈ 1876.31

The present value is $1876.31.

4 0

1 year ago

A model railway train is designed using a scale factor of 1:87. If the model train is 4 inches , how many feet long is the actua

goblinko [34]

Answer:

The actual length of the train is 79 3/4 feet

Step-by-step explanation:

5 0

2 years ago