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2 years ago

In triangle DEF, M angle D equals 44°, M angle E equals 61°, and EF equal 20 Inches. What is DE to the nearest 10th of an inch

Mathematics

1 answer:

Anon25 [30]2 years ago

5 0

The answer is DE = 27.81 in. Explanation: find the missing angle first, and put it into the equation for the law of sin ( sin(A)/a = sin(B)/b). Solve for the missing length, and you have the missing side to the triangle.

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melomori [17]

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scZoUnD [109]

Answer:

Step-by-step explanation:

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iogann1982 [59]

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

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

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

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liraira [26]

The answer is
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3 years ago

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MrRissso [65]

Answer:

Step-by-step explanation:

From the figure attached,

Given: ∠P ≅ ∠S

TQ ≅ RQ

To Prove : ΔQRS ≅ ΔQTP

Statements Reasons

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2). ∠RQS ≅ ∠TQP Reflexive property

3). ΔQRS ≅ ΔQTP AAS

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3 years ago