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3 years ago

7

Can someone pls help

2 answers:

-Dominant- [34]3 years ago

6 0

<u>❒ Required Solution:</u>

We are here to find the three angles with the help of the angle sum property (Sum of the angles of a triangle = 180°). So, using this property we can find all the angles.

<u>❍ According to the question :</u>

$\\ \tt \implies \: 60{}^{ \circ} + 60{}^{ \circ} +(4x - 80) {}^{ \circ} = 180{}^{ \circ} \\ \\ \\ \implies \tt \: 120{}^{ \circ} - 80{}^{ \circ} + 4x = 180{}^{ \circ} \: \: \: \: \: \: \\ \\ \\ \implies \tt 40{}^{ \circ} + 4x = 180{}^{ \circ} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \implies \tt \: 4x = 180{}^{ \circ} - 140{}^{ \circ} \: \: \: \: \: \: \\ \\ \\ \tt \implies \: 4x = 140{}^{ \circ} \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \implies \tt \: x = \frac{140}{4} \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \tt \implies \: { \boxed{ \mathfrak{ \pmb{ \pink{x = 35}}}}} \bigstar \\ \\ \\$

Katyanochek1 [597]3 years ago

3 0

Answer:

x = 35

Step-by-step explanation:

Sum of angles of triangle = 180°

60 + 60 + 4x - 80 = 180
40 + 4x = 180
4x = 140
x = 140/4
x = 35°

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Pls help! will give brainliest to whoever answers first correctly! (70 points)

Nookie1986 [14]

Answer:

#1

Step-by-step explanation:

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2 years ago

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We would like to use the power series method to find the general solution to the differential equation d 2y dx2 − 4x dy dx + 12y

Feliz [49]

$y=\displaystyle\sum_{n\ge0}a_nx^n$

$\dfrac{\mathrm dy}{\mathrm dx}=\displaystyle\sum_{n\ge1}na_nx^{n-1}\implies4x\dfrac{\mathrm dy}{\mathrm dx}=4\sum_{n\ge1}na_nx^n=4\sum_{n\ge0}na_nx^n$

$\dfrac{\mathrm d^2y}{\mathrm dx^2}=\displaystyle\sum_{n\ge2}n(n-1)a_nx^{n-2}=\sum_{n\ge0}(n+2)(n+1)a_{n+2}x^n$

Substituting into the ODE

$\dfrac{\mathrm d^2y}{\mathrm dx^2}-4x\dfrac{\mathrm dy}{\mathrm dx}+12y=0$

gives

$\displaystyle\sum_{n\ge0}\bigg((n+2)(n+1)a_{n+2}-4na_n+12a_n\bigg)x^n=0$

so that the coefficients of the series are given according to

$\begin{cases}a_0=y(0)\\a_1=y'(0)\\a_{n+2}=\dfrac{4(n-3)a_n}{(n+2)(n+1)}&\text{for }n\ge0\end{cases}$

We can shift the index in the recursive part of this definition to get

$a_n=\dfrac{4(n-5)a_{n-2}}{n(n-1)}$

for $n\ge2$ . There's dependency between coefficients that are 2 indices apart, so we can consider 2 cases:

If $n=2k$ , where $k\ge0$ is an integer, then

$k=0\implies n=0\implies a_0=a_0$

but since $y(0)=0$ , we have $a_0=0$ and $a_{2k}=0$ for all $k\ge0$ .

If $n=2k+1$ , then

$k=0\implies n=1\implies a_1=a_1$

$k=1\implies n=3\implies a_3=\dfrac{4(-2)a_1}{3\cdot2}=-\dfrac43a_1$

$k=2\implies n=5\implies a_5=0$

and so $a_{2k+1}=0$ for all $k\ge2$ . If $y'(0)=1$ , we then have $a_1=1$ and $a_3=-\dfrac43$ .

So the ODE has solution

$y(x)=\displaystyle\sum_{k\ge0}(a_{2k}x^{2k}+a_{2k+1}x^{2k+1})\implies\boxed{y(x)=x-\dfrac43x^3}$

8 0

3 years ago

X²-x-12=0<br> Describe the number and types of roots using the discriminant<br> Show steps please

pickupchik [31]

Answer:

2 real roots

Step-by-step explanation:

The discriminant is b^2 -4ac where ax^2 +bx -c

If b^2 -4ac > 0 we have 2 real roots

b^2 -4ac = 0 we have 1 real root

b^2 -4ac < 0 we have 2 complex roots

x²-x-12=0

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(-1)^2 - 4(1)*(-12)

1 +48

49 > 0

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4 years ago

How to solve this question? please help me

Ber [7]

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c^2 = 8425

c = √8425

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4 years ago

What is the slope of the line that passes through the points (26, 7) and (-39, 12)?

Digiron [165]

Answer:

$m=-\frac{1}{13}$

Step-by-step explanation:

we know that

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$m=\frac{y2-y1}{x2-x1}$

we have the points

(26, 7) and (-39, 12)

substitute the values in the formula

$m=\frac{12-7}{-39-26}$

$m=\frac{5}{-65}$

simplify

$m=-\frac{1}{13}$

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3 years ago