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castortr0y [4]
3 years ago
9

How would you differentiate this problem using the quotient rule?

Mathematics
1 answer:
ioda3 years ago
6 0
Rewrite the square root of X as X^ 1/2. Then take the derivative. Since 1/3 is a constant with respect to X you can pull that out. So, you should have
1/3 d/dx [ (2x^2-x^5)/3x^1/2].

Then factor x^2 out of 2x^2-x^5.

Then by using the negative exponent rule you should have

1/3 d/dx [ x^2(2-x^3)x^-1/2 ]

Then multiply x^2 by x ^-1/2 by adding the exponents.

1/3 d/dx [ x^3/2 (2-x^3)]

Then differentiate.

You should get x^1/2 - (3x^7/2)/2.

I hope that helps.
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Step-by-step explanation:

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Determine whether the normal sampling distribution can be used. The claim is p < 0.015 and the sample size is n
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Complete Question

Determine whether the normal sampling distribution can be used. The claim is p < 0.015 and the sample size is n=150

Answer:

Normal sampling distribution can not be used

Step-by-step explanation:

From the question we are told that

    The  null hypothesis is  H_o  :  p =  0.015

     The  alternative hypothesis is    H_a  :  p  <  0.015

     

The  sample size is  n= 150

Generally in order to use  normal sampling distribution  

     The value  np  \ge  5

So  

         np =  0.015 * 150

         np =  2.25

Given that  np < 5   normal sampling distribution  can not be used

8 0
3 years ago
Find the values of x on the interval [−π, π] where the tangent line to the graph of y = sin(x) cos(x) is horizontal. (Enter your
Lady_Fox [76]
A trig identity is <span>asinucosu=<span>a/2</span>sin(2u)</span>So you can write your equation as<span>y=sin(x)cos(x)=<span>1/2</span>sin(2x)</span>Use the crain rule here<span><span>y′</span>=<span>d/<span>dx</span></span><span>1/2</span>sin(2x)=<span>1/2</span>cos(2x)<span>d/<span>dx</span></span>2x=cos(2x)</span>The curve will have horizontal tangents when y' = 0.<span><span>y′</span>=0=cos(2x)</span>On the interval [-pi, pi], solution to that is<span><span>x=±<span>π4</span>,±<span><span>3π</span>4</span></span></span>
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3 years ago
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Find the coordinates of the intersection of the diagonals of the parallelogram with the vertices W(−2, 5), X(2, 5), Y(4, 0),
emmasim [6.3K]

Using the midpoint formula, the coordinates of the intersection of the diagonals of the parallelogram is: (1, 2.5).

<h3>What are Diagonals of a Parallelogram?</h3>

The diagonals of a parallelogram bisect each other, therefore, the coordinates of their intersection can be determined using the midpoint formula, which is: M(\frac{x_2 + x_1}{2}, \frac{y_2 + y_1}{2}).

A diagonal is XZ.

X(2, 5) = (x1, y1)

Z(0, 0) = (x2, y2)

Plug in the values

M(\frac{0 + 2}{2}, \frac{0 + 5}{2})

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7 0
1 year ago
What is the coefficient in the expression 7x+14
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Answer:

7

Step-by-step explanation:

The coefficient is the number that comes before the variable

7<u>x</u>+14

In this case, the variable is x.

The number that comes before x is 7, so 7 is the coefficient.

Hope this helps! :)

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