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3 years ago

Pls someone help me find the answers

Mathematics

1 answer:

Alecsey [184]3 years ago

7 0

Answer:

x = 145°

Step-by-step explanation:

We know that y = 98°, so we can find ∠DBC:

180°-y = ∠DBC

180°-98° = 82°

We also know that z = 63°, therefore we can apply <u>exterior angle of triangles</u> to find x.

∠DBC + z = x

82°+63° = x

x = 145°

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A rope which is 10.3 centimeters long is cut into 4 pieces of equal length. Write an equation to find the length of

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Answer: x = 10.3 ÷ 4

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Step-by-step explanation:

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x2(3+16x)x2+14

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3 years ago

Which statement is true about the polynomial 3j4k−2jk3+jk3−2j4k+jk3 after it has been fully simplified?

tamaranim1 [39]

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Step-by-step explanation:

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3 years ago

Ah! Okay, need help solving 14, and just checking for 16 and 4.

Allisa [31]

4. Correct. You also could have used the limit test for divergence for the same conclusion (the summand approaches infinity).

- - -

14. I'm guessing the instructions are the same as for 16. Rewrite as

$f(x)=\dfrac4{2x+3}=\dfrac{\frac43}{1-\left(-\frac{2x}3\right)}$

Now recall that for $|x|$ , we have

$\dfrac1{1-x}=\displaystyle\sum_{n\ge0}x^n$

so that for this function, we get

$f(x)=\dfrac43\displaystyle\sum_{n\ge0}\left(-\frac{2x}3\right)^n$

Because this is a geometric sum, this converges when $\left|-\dfrac{2x}3\right|$ , or $|x|$ . This would be the interval of convergence.

Your hunch about checking the endpoints is correct. Checking is easy in this case, because at the endpoints (-3/2 and 3/2) the series obviously diverges.

- - -

16. This one is kind of tricky, and there's more than one way to do it. The standard method would be to take the antiderivative:

$F(x)=\displaystyle\int f(x)\,\mathrm dx=\int\frac{\mathrm dx}{(1+x)^2}=-\frac1{1+x}+C$

We also have

$\displaystyle-\frac1{1+x}=-\frac1{1-(-x)}=-\sum_{n\ge0}(-x)^n\implies F(x)=C-1-\sum_{n\ge1}(-x)^n$

and differentiating this gives

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$\displaystyle\lim_{n\to\infty}\left|\frac{(n+2)(-1)^{n+2}x^{n+1}}{(n+1)(-1)^{n+1}x^n}\right|$

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$\displaystyle|x|\lim_{n\to\infty}\frac{n+2}{n+1}=|x|$

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3 years ago