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2 years ago

10

A regular pentagon has a perimeter of 15x+35 What is the length of one side of the pentagon?

1 answer:

valentinak56 [21]2 years ago

8 0

Answer:

-3.5 or -7/2

Step-by-step explanation:

Pentagons have five sides, so 15x+35

15x+35=5

subtract 35

15x+35-35=5x-35

simplify

15x=5x-35

subtract 5x

15x-5x=5x-35-5x

simplify

10x=-35

divide by 10

$\frac{10x}{10}=\frac{-35}{10}$

simplify

$x=-\frac{7}{2}$ or also -3.5

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Morgarella [4.7K]

$\text{mass of freight train} = 9.98 \times {10}^{6} kg$

$\text{mass of aircraft carrier} = 7.3 \times {10}^{7} \: kg$

$\text{difference of masses of aircraft and train: } \\ \\ 7.3 \times {10}^{7} - 9.98 \times {10}^{6} \\ \\ = 73 \times {10}^{6} - 9.98 \times {10}^{6}$

$= (73 - 9.98 )\times {10}^{6} \\ \\ = 63.02 \times {10}^{6} \\ \\ = 6.302 \times {10}^{6} \: kg \\ \\ \approx 6.3 \times {10}^{6} \: kg$

Approximately, aircraft carrier is 6.3 × 10^6 kg heavier than the freight train.

7 0

3 years ago

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,

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

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r3t40

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3 years ago

For the function F defined by F(x) = x2 – 2x + 4, find F(b+3).

Ivanshal [37]

Answer:

$\displaystyle F(b + 3) = b^2 + 4b + 7$

Step-by-step explanation:

We are given the function:

$\displaystlye F(x) = x^2 - 2x + 4$

And we want to find F(<em>b</em> + 3).

We can substitute:

$\displaystyle F(b + 3) = (b + 3)^2 - 2(b+3) + 4$

Expand:

$\displaystyle = (b^2 + 6b + 9) + (-2b -6) + 4$

Rearrange:

$\displaystyle = (b^2) + (6b-2b) + (9 - 6 + 4)$

Combine like terms. Hence:

$\displaystyle = b^2 +4b + 7$

In conclusion:

$\displaystyle F(b + 3) = b^2 + 4b + 7$

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3 years ago

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lesantik [10]

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Step-by-step explanation:

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3 years ago

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