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SpyIntel [72]
3 years ago
12

Differentiating a Logarithmic Function in Exercise, find the derivative of the function. See Examples 1, 2, 3, and 4.

Mathematics
1 answer:
astra-53 [7]3 years ago
7 0

Answer:

\frac{dy}{dx}=\frac{1}{2(x-4)}

Step-by-step explanation:

We are given that a function  

y=ln(x-4)^{\frac{1}{2}}

We have to find the derivative of the function

y=\frac{1}{2}ln(x-4)

By using lna^b=blna

Differentiate w.r.t x

\frac{dy}{dx}=\frac{1}{2}\times \frac{1}{x-4}

By using formula

\frac{d(lnx)}{dx}=\frac{1}{x}

\frac{dy}{dx}=\frac{1}{2(x-4)}

Hence, the derivative of function

\frac{dy}{dx}=\frac{1}{2(x-4)}

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Simplifying an algebra -3(y+2)
Brrunno [24]

Answer: -9y


Step-by-step explanation:

Step1: -3 is multiplied by y = -3y

Step 2: -3 multiplied by 2 = -6

Step 3: -3y + -6

6 0
3 years ago
Given a soda can with a volume of 36 and a diameter of 4, what is the volume of a cone that fits perfectly inside the soda can?
spin [16.1K]
First we need to find the heigh of the soda can be rearanging the volume formula, . We can make that  We know that V is 36 and radius is half of the diameter, so radius is 2. 

h = 2.87

Now, we can use the height to figure out the volume of a cone. The volume of a cone is 
R is 2 again and h is 2.87


12.56*.96 = 12.0576
So a cone with a volume of 12.0576 is the largest that will fit into the soda can
6 0
3 years ago
Read 2 more answers
HELPPPPPP!! ASAPPP!!! PLEASE!! WILL GIVE EXTRA POINTS!<br><br>4.8<br>4<br>8<br>7.2
vivado [14]

Answer:

x = 4

Step-by-step explanation:

180° - 114° = 66°

15x - 6 = 66

15(4) - 6 = 66

60 - 6 = 54      

Statement is wrong because we can see another angle. so...

Final answers: x = 4   while 54 + 114° = 168°  then 180° - 168° = 12°

6 0
3 years ago
Given f(x)=-1/7√16-x^2 find f^-1(x)
Vera_Pavlovna [14]

Answer:

f^{-1}(x)=\pm \sqrt{49x^2-16}

Not a function.

Step-by-step explanation:

The given function is;

f(x)=-\frac{1}{7}\sqrt{16-x^2}

Let y=-\frac{1}{7}\sqrt{16-x^2}

Interchange x and y;

x=-\frac{1}{7}\sqrt{16-y^2}

Solve for y;

-7x=\sqrt{16-y^2}

Square both sides

(-7x)^2=(\sqrt{16-y^2})^2

49x^2^2=16-y^2

49x^2^2-16=y^2

y=\pm \sqrt{49x^2-16}

The inverse is

f^{-1}(x)=\pm \sqrt{49x^2-16}

f^{-1}(x)=\pm \sqrt{49x^2-16} is not a function because one x-value maps onto to different y-values.

6 0
3 years ago
Write the word sentence as a equation. Then solve the equation 13 subtracted from a number w is 15
patriot [66]
W-13=15 add 13 on both sides to isolate variable and you get w=13+15, w=28
7 0
3 years ago
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