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3 years ago

If two angles are supplement of each other, then one of the angles must be acute

Mathematics

1 answer:

oksian1 [2.3K]3 years ago

7 0

Answer:

this is true

Step-by-step explanation:

a supplementary angle adds up to 180 degrees. two accute angles would equal to around 90 and two obtuse angles would add up to more than 180. two right angles are perpendicular and they could work but since the question asks about acute and obtuse, its true that one angle must be acute and the other must be obtuse for it to add up to 180.

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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]

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

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

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

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3 years ago

the formula for the area of a circle is A pi r^2 what is the radius of a circle with an area of 400 pi cm^2

Bogdan [553]

Answer: 20 cm

Step-by-step explanation: Isolate the variable by dividing each side by factors that don't contain a variable.

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3 years ago

You can just give an answer.

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Step-by-step explanation: 50 x. 10

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3 years ago

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ANEK [815]

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Step-by-step explanation:

When x = x in f(x) and g(x), that means the two functions are equal.

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3 years ago

Use the graph of the function to find, f(-6)

kati45 [8]

Answer:

f(-6) = 3

Step-by-step explanation:

In order to find the value of f(-6), we need to find what y-value appears associated with x = -6 according to the graph resented.

Therefore, go to x = -6 on the horizontal axis (six units to the left of the origin of the coordinate system), and find at what value of the y-axis the vertical grid passing through x = -6 intercepts the graph of the function.

That is indicated by a red dot in the attached image.

We see therefore that for x = -6 the y-value that the graph of the function shows in the vertical scale is "3".

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3 years ago