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Nezavi [6.7K]
2 years ago
7

Help if you can !! thank you :)

Mathematics
2 answers:
Vsevolod [243]2 years ago
4 0

Answer:

NVM MY BAD

x=19

quadrilateral have the internal degree sum of 360

not 365

aivan3 [116]2 years ago
3 0

Answer:

I'm not sure if you need the value of x or the entire angle measure, so I'll give you both.

x = 19

The angle measure is 46 degrees

Step-by-step explanation:

The sum of a quadrilateral's interior angles is 360 degrees. With that knowledge, we can subtract the angle measures we have from 360. To do that, we must first add 115 + 118 + 81, which equals 314. Now, we do 360 - 314, which gives us the measure of the unknown angle, which is 46 degrees.

Now, we must find x. We write the equation 2x + 8 = 46 since we know what the angle measure is now. Then, we subtract 8 from both sides, which leaves us with 2x=38. Finally, we need to divide 2 on both sides. If your math is correct, you should end up with x = 19. Hope this helps!

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See Below.

Step-by-step explanation:

We want to estimate the definite integral:

\displaystyle \int_1^47\sqrt{\ln(x)}\, dx

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1)

The trapezoidal rule is given by:

\displaystyle \int_{a}^bf(x)\, dx\approx\frac{\Delta x}{2}\Big(f(x_0)+2f(x_1)+...+2f(x_{n-1})+f(x_n)\Big)

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Evaluate:

\displaystyle =\frac{1}{4}(7)(\sqrt{\ln(1)}+2\sqrt{\ln(1.5)}+...+2\sqrt{\ln(3.5)}+\sqrt{\ln(4)})\\\\\approx18.139337

2)

The midpoint rule is given by:

\displaystyle \int_a^bf(x)\, dx\approx\sum_{i=1}^nf\Big(\frac{x_{i-1}+x_i}{2}\Big)\Delta x

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\displaystyle =\frac{1}{2}\Big(f\Big(\frac{1+1.5}{2}\Big)+f\Big(\frac{1.5+2}{2}\Big)+...+f\Big(\frac{3+3.5}{2}\Big)+f\Big(\frac{3.5+4}{2}\Big)\Big)

Simplify:

\displaystyle =\frac{1}{2}(7)\Big(f(1.25)+f(1.75)+...+f(3.25)+f(3.75)\Big)\\\\ =\frac{1}{2}(7) (\sqrt{\ln(1.25)}+\sqrt{\ln(1.75)}+...+\sqrt{\ln(3.25)}+\sqrt{\ln(3.75)})\\\\\approx 18.767319

3)

Simpson's Rule is given by:

\displaystyle \int_a^b f(x)\, dx\approx\frac{\Delta x}{3}\Big(f(x_0)+4f(x_1)+2f(x_2)+4f(x_3)+...+4f(x_{n-1})+f(x_n)\Big)

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\displaystyle =\frac{1/2}{3}\Big((f(1)+4f(1.5)+2f(2)+4f(2.5)+...+4f(3.5)+f(4)\Big)

Simplify:

\displaystyle =\frac{1}{6}(7)(\sqrt{\ln(1)}+4\sqrt{\ln(1.5)}+2\sqrt{\ln(2)}+4\sqrt{\ln(2.5)}+...+4\sqrt{\ln(3.5)}+\sqrt{\ln(4)})\\\\\approx 18.423834

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Answer:

1.2

Step-by-step explanation:

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