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Present the numbers in decimal
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0.25 = 0.25
3/8 = 0.375
5/16 = 0.3125
<span><em>(It is easier to arrange the number using decimals)</em>
</span>
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Arrange the numbers
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0.25 (0.25) , 0.3125 (5/16) , 0.0375 (3/8)
<em>(Put the original numbers given in your final answer)</em>
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Answer: 0.25 , 5/16 , 3/8
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I believe the given limit is
![\displaystyle \lim_{x\to\infty} \bigg(\sqrt[3]{3x^3+3x^2+x-1} - \sqrt[3]{3x^3-x^2+1}\bigg)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clim_%7Bx%5Cto%5Cinfty%7D%20%5Cbigg%28%5Csqrt%5B3%5D%7B3x%5E3%2B3x%5E2%2Bx-1%7D%20-%20%5Csqrt%5B3%5D%7B3x%5E3-x%5E2%2B1%7D%5Cbigg%29)
Let

Now rewrite the expression as a difference of cubes:

Then

The limit is then equivalent to

From each remaining cube root expression, remove the cubic terms:



Now that we see each term in the denominator has a factor of <em>x</em> ², we can eliminate it :


As <em>x</em> goes to infinity, each of the 1/<em>x</em> ⁿ terms converge to 0, leaving us with the overall limit,

Answer:
Sound can travel 12 miles per minute.
Step-by-step explanation:
Speed equation is distance divided by time.
So we have 1 mile per 1/12 of a minute.
Let’s write the equation.
Speed of sound = 1 / 1/12
Multiply by the reciprocal.
1 * 12 = 12.
First, substitute 4 into x
Then multiply 4 times 4
Subtract 2
Then subtract 5 from both sides
Answer:
24 and 66degrees
Step-by-step explanation:
Given the equation
cos(8x+18)=sin(−2x+36)
In trigonometry identity, cos theta = sin (90- theta)
The given expression becomes;
sin (90 - (8x+18)) = sin(−2x+36)
sin will cancel out to have;
90 - (8x+18) = (−2x+36)
90-8x-18 = -2x+36
-8x +72 = -2x+36
-8x + 2x = 36 - 72
-6x = -36
x = 36/6
x = 6
Hence the value of x is 6
cos(8x+18) = cos(8(6)+18)
= cos 66
Also
sin(−2x+36)
= sin(−2(6)+36)
= sin(−12+36)
= sin 24
Hence both angles are 24 and 66degrees