What angle turns through non-degree angles?

Two sides of a triangle are 8 m and 9 m in length and the angle between them is increasing at a rate of 0.06 rad/s. Find the rat

Lelechka [254]

<h2>Rate at which area is increasing is 1.08 m²/s.</h2>

Step-by-step explanation:

Area of triangle is with side a and b and angle C between them is given by

A = 0.5 ab SinC

Here we need to find how area changes with a and b fixed and C is changing,

$\frac{dA}{dt}=\frac{d}{dt}\left (0.5 absinC\right )\\\\\frac{dA}{dt}=0.5ab\frac{d}{dt}\left (sinC\right )\\\\\frac{dA}{dt}=0.5abcosC\frac{dC}{dt}$

We have

a = 8 m

b = 9 m

$C=\frac{\pi}{3}rad\\\\\frac{dC}{dt}=0.06rad/s$

Substituting

$\frac{dA}{dt}=0.5\times 8\times 9\times cos\left ( \frac{\pi}{3}\right )\times 0.06\\\\\frac{dA}{dt}=1.08m^2/s$

Rate at which area is increasing is 1.08 m²/s.

4 0

4 years ago

What is <br><img src="https://tex.z-dn.net/?f=%20%5Cfrac%7B4%7D%7B8%7D%20%20-%20%20%5Cfrac%7B1%7D%7B4%7D%20" id="TexFormula1" ti

marysya [2.9K]

Hello there, and thank you for posting your question here on brainly.

Something I noticed right away is that 4/8 can be simplified.

4/8 ===> 2/4

So now we have 2/4 - 1/4

Just subtract the numerators only.

2/4 - 1/4 = 1/4

1/4 cannot be simplified, so 1/4 is your final answer.

Hope this helped!! ☺♥

5 0

3 years ago

1) Use power series to find the series solution to the differential equation y'+2y = 0 PLEASE SHOW ALL YOUR WORK, OR RISK LOSING

iogann1982 [59]

If

$y=\displaystyle\sum_{n=0}^\infty a_nx^n$

then

$y'=\displaystyle\sum_{n=1}^\infty na_nx^{n-1}=\sum_{n=0}^\infty(n+1)a_{n+1}x^n$

The ODE in terms of these series is

$\displaystyle\sum_{n=0}^\infty(n+1)a_{n+1}x^n+2\sum_{n=0}^\infty a_nx^n=0$

$\displaystyle\sum_{n=0}^\infty\bigg(a_{n+1}+2a_n\bigg)x^n=0$

$\implies\begin{cases}a_0=y(0)\\(n+1)a_{n+1}=-2a_n&\text{for }n\ge0\end{cases}$

We can solve the recurrence exactly by substitution:

$a_{n+1}=-\dfrac2{n+1}a_n=\dfrac{2^2}{(n+1)n}a_{n-1}=-\dfrac{2^3}{(n+1)n(n-1)}a_{n-2}=\cdots=\dfrac{(-2)^{n+1}}{(n+1)!}a_0$

$\implies a_n=\dfrac{(-2)^n}{n!}a_0$

So the ODE has solution

$y(x)=\displaystyle a_0\sum_{n=0}^\infty\frac{(-2x)^n}{n!}$

which you may recognize as the power series of the exponential function. Then

$\boxed{y(x)=a_0e^{-2x}}$

7 0

3 years ago

Write the next whole number after 4444 in the base-five system.

svet-max [94.6K]

<h3>Answer: 10000 in base 5</h3>

====================================================

Explanation:

4+1 = 5 in base 10

But in base 5, the digit "5" does not exist.

The only digits in base five are: 0, 1, 2, 3, 4

This is similar to how in base ten, the digits span from 0 to 9 with the digit "10" not being a thing (rather it's the combination of the digits "1" and "0" put together).

----------------

Anyways let's go back to base 5.

Instead of writing 4+1 = 5, we'd write 4+1 = 10 in base 5. The first digit rolls back to a 0 and we involve a second digit of 1.

Think how 9+1 = 10 in base 10.

Similarly,

44+1 = 100 in base 5

444+1 = 1000 in base 5

4444+1 = 10000 in base 5

and so on.

----------------

Here are the first few numbers in base 5, when counting up by 1 each time.

0, 1, 2, 3, 4,

10, 11, 12, 13, 14,

20, 21, 22, 23, 24,

30, 31, 32, 33, 34,

40, 41, 42, 43, 44,

100, 101, 102, 103, ...

Notice each new row is when the pattern changes from what someone would expect in base 10. This is solely because the digit "5" isn't available in base 5.

7 0

2 years ago

What is the equation of the line, in standard form, that passes through (4, -3) and is parallel to the line whose equation is 4

Dmitry_Shevchenko [17]

<span>The equation is: 4x + y + a = 0

Point (4, -3) </span>⇒ x = 4 and y = - 3<span>

</span>⇒ 4 · 4 - 3 + a = 0
<span>
16 - 3 +a = 0

13 + a = 0

a = -13

</span>Ansver: equation is: 4x + y - 13 = <span>0 OR 4x + y = 13
</span>

5 0

3 years ago

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