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Tasya [4]
3 years ago
11

What is the derivative of the following function? f(x) = 4x^6/cos^5(x)

Mathematics
1 answer:
KIM [24]3 years ago
5 0

Answer:

f'(x) = \frac{24x^{5} \cos x + 20x^{6}\sin x}{\cos^{6}x }

Step-by-step explanation:

We have to find the derivative of the following function:

f(x) = \frac{4x^{6} }{\cos^{5} x }

Now, differentiating both sides with respect to x we get,

f'(x) = \frac{\cos^{5}x (24x^{5}) - 4x^{6}(5\cos^{4}x )(- \sin x)}{(\cos^{5}x )^{2}}

⇒ f'(x) = \frac{ 24x^{5} \cos x + 20 x^{6}\sin x}{\cos^{6}x } (Answer)

{Since, we know that, \frac{d(mx^{n} )}{dx} = m \times n x^{(n - 1)} and \frac{d(\cos^{n} x)}{dx} = n \cos^{(n - 1)} x(- \sin x) }

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A rectangular auditorium seats 1564 people. the number of seats in each row exceeds the number of rows by 1212. find the number
yanalaym [24]
<span>We can safely assume that 1212 is a misprint and the number of seats in a row exceeds the number of rows by 12. Let r = # of rows and s = # of seats in a row. Then, the total # of seats is T = r x s = r x ( r + 12), since s is 12 more than the # of rows. Then r x (r + 12) = 1564 or r**2 + 12*r - 1564 = 0, which is a quadratic equation. The general solution of a quadratic equation is: x = (-b +or- square-root( b**2 - 4ac))/2a In our case, a = 1, b = +12 and c = -1564, so x = (-12 +or- square-root( 12*12 - 4*1*(-1564) ) ) / 2*1 = (-12 +or- square-root( 144 + 6256 ) ) / 2 = (-12 +or- square-root( 6400 ) ) / 2 = (-12 +or- 80) / 2 = 34 or - 46 We ignore -46 since negative rows are not possible, and have: rows = 34 and seats per row = 34 + 12 = 46 as a check 34 x 46 = 1564 = total seats</span>
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3 years ago
What is the volume of the prism below?
Triss [41]

Step-by-step explanation:

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Simplify completely quantity x squared plus 4 x minus 45 all over x squared plus 10 x plus 9 and find the restrictions on the va
Brums [2.3K]

Answer:

A) Quantity x minus 5 over quantity x plus 1, where x≠-1 and x≠-9

Step-by-step explanation:

\frac{x^2 + 4x - 45}{x^2 + 10x + 9}

Simplifying the numerator first:

x² + 4x - 45 using the quadratic formula you get;

(x - 5)(x + 9)

Then simplifying the denominator x² + 10x + 9 using a quadratic formula you get;

(x + 1)(x + 9)

Dividing the numerator and denominator now gives;

\frac{(x - 5)(x + 9)}{(x + 1)(x + 9)}

Cancelling (x + 9) throughout leaves you with;

\frac{x - 5}{x + 1}

The only restrictions here is if x = 1 and 9 which will give an undefined answer.

7 0
3 years ago
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The measure of two supplementary angles are in the ratio 4 5 find the degree measures of the angles
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Supplementary angles add to 180
4+5=9

180/9=20

4*20=80
5*20=100
the angles are 80 degrees and 100 degrees
8 0
3 years ago
(5ab-4a-8)-(9ab-5) its an online geometry class,please help!i provided you 10 pts
Bumek [7]
(5ab-4a-8)-(9ab-5)
Ok just remember that the minus sign before the (9ab-5) is like a minus 1 so it changes the sign inside the bracket...
>>5ab-4a-8-9ab+5
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I'm guessing you just have to leave it like that unless there are other parts to the question or whatever but that's that simplified as far as it can be!
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