Answer:
See the explanation
Step-by-step explanation:
We know that
f(x) = 2x⁶ + 3x⁴ - 4x³ + (1/x) - sin2x
Lets calculate the derivatives:
f'(x) = 6(2x⁵) + 4(3x³) - 3(4x²) -( 1/x²) - 2(cos2x)
f'(x) = 12x⁵ + 12x³ - 12x² - (1/x²) - 2cos2x
Similarly:
f''(x) = 60x⁴ + 36x² - 24x + (2/x³) + 4sin2x
f'''(x) = 240x³ + 72x - 24 - (6/x⁴) + 8cos2x
Rearrange:
f'''(x) - 240x³ +72x - (6/x⁴) + 8cos2x - 24
f''''(x) = 720x² + 72 + (24/x⁵) - 16sin2x
Rearrange:
f''''(x) = 720x² + (24/x⁵) - 16sin2x +72
Answer: 3y +2
Step-by-step explanation:
By comparing the dimensions above with the dimensions of Taylor's first rectangle, we have the following:
- No, a length of 6 in, width 3/4 in. is not proportional.
- Yes, a length of 1/2 in, width 4 in. is not proportional.
- No, a length of 1 1/8 in, width 9 in. is not proportional.
- No, a length of 3 in, width 5 5/8 in. is not proportional.
<h3>What is a direct proportion?</h3>
Mathematically, a direct proportion (direct variation) can be represented the following mathematical expression:
y = kx
Where:
- y and x are the variables or dimensions.
- k represents the constant of proportionality.
For the dimensions of the rectangular pieces of paper to be proportional, the length and width must remain in a constant ratio.
Next, we would determine the constant of proportionality (k) as follows:
k = y/x
k = (3/8)/3
k = 3/24
k = 1/8
For dimension 1, we have:
k = y/x
k = (6)/(3/4)
k = 24/3
k = 8 (No).
For dimension 2, we have:
k = y/x
k = (1/2)/4
k = 1/2 × 1/4
k = 1/8 (Yes).
For dimension 3, we have:
k = y/x
k = (1 1/8)/9
k = (9/8)/8
k = 9/8 × 1/8
k = 9/64 (No).
For dimension 4, we have:
k = y/x
k = (3)/(5 5/8)
k = 3/(45/8)
k = 3 × 8/45
k = 24/45 (No).
Read more on proportionality here: brainly.com/question/12866878
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Complete Question:
Taylor works on an art project that uses only rectangular pieces of paper. The first rectangle has length 3/8 in. and width 3 in. Determine which dimensions below are proportional to the dimensions of Taylor's first rectangle.
Any percentage can be created into a fraction by taking the number in the percent (56.5) being put over 100, as percentages are out of 100:
56.5/100
This is not in simplest form, as it has a decimal, so try multiplying both the numerator and the denominator by 2:
56.5/100 x 2 = <u><em>113/200
</em></u>Since our numerator, 113, is prime, this cannot be simplified, so this is the final answer.
Hope this helps!
