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3 years ago

Solve for x 2x/3 +1 =3

Mathematics

1 answer:

Bess [88]3 years ago

5 0

Answer:

x=3

Step-by-step explanation:

Hello,

The first thing you do is set up your equation, and we are solving for x so we are going to get x by itself on one side of the = sign.

2x/3+1=3 First thing: subtract 1 from BOTH sides.

-1 -1

----------------------

2x/3=2 Multipliy by 3 on both sides

*3 *3

-----------------------

2x=6 Divide by 2 on both sides

/2 /2

-----------------------

x=3

I hope this helped you!!!

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A)Determine whether the sequence is divergent or convergent. If it is convergent, evaluate its limit. If it diverges to infinity

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b) The lenght of the curve is $\frac{1}{54}(217^{3/2}-37^{3/2})$

Step-by-step explanation:

Consider the sequence $a_n = \frac{-6n^6 + \sin^2(7n)}{n^7+11}$

a) We will prove it using the sandwich lemma. Note that for all n $-1\leq \sin^2(7n)\leq 1$ , then

$\frac{-6n^6 -1}{n^7+11}\leq\frac{-6n^6 + \sin^2(7n)}{n^7+11}\leq \frac{-6n^6 + 1}{n^7+11}$

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So, the sequence converges to 0.

b) The function $f(x) = 4x^{3/2}+7$ the formula of curve lenght is given by

$s = \int_a^b \sqrt[]{1+(f'(x))^2}dx$

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Note that $f'(x) =6x^{{1/2}$ . Then

$s=\int_1^6 \sqrt[]{1+36x}dx$ . Take u = 1+36x. Then du= 36dx (i.e du/36 = dx). If x = 1, then u = 37 and if x = 6 then u = 217. So,

$s=\frac{1}{36}\int_{37}^{217}\sqrt[]{u} du = \frac{2}{36\cdot 3} \left.u^{3/2}\right|_{37}^{217}=\frac{1}{54}(217^{3/2}-37^{3/2})$

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