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3 years ago

Solve eqaution 17-9y=-3+16y

Mathematics

2 answers:

Contact [7]3 years ago

6 0

17 - 9y = -3 + 16y
20 = 25y
20/25 = 4/5 = .8
25/25 = 1 = y
y = .8
Hope this helped!

N76 [4]3 years ago

4 0

Add 9y to both sides:
17= -3 + 25y
add 3 to both sides:
20 = 25y
divide by 25 on both sides:
20/25 = y
then since 5 goes into the numerator and denominator, you can simplify the answer to 4/5.

so the answer is y= 4/5

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Limit (sin4x-4sinx)/x^3 when x close to zero

BartSMP [9]

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Step-by-step explanation:

Hello, please consider the following.

Using Maclaurin series expansion, we can find an equivalent of sin(x) in the neighbourhood of 0.

$sin(x) \sim \left(x-\dfrac{x^3}{3!}\right)\\\\\text{So, in the neighbourhood of 0}\\\\\begin{aligned}(sin(4x)-4sin(x)) &\sim \left( 4x-\dfrac{(4x)^3}{3!}-4x+\dfrac{4x^3}{3!}\right)\\\\&\sim \left(\dfrac{x^3*4*(1-4^2)}{3*2}\right)\\\\&\sim \left(\dfrac{x^3*2*(-15)}{3}\right)\\\\&\sim \left(x^3*2*(-5)\right)\\\\&\sim \left(x^3*(-10)\right)\\\end{aligned}$

Then,

$\displaystyle \lim_{x\rightarrow0} \ {\dfrac{sin(4x)-4sin(x)}{x^3}}\\\\= \lim_{x\rightarrow0} \ {\dfrac{-10*x^3}{x^3}}\\\\=-10$

Thank you

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Answer:

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