Answer:
[tex]\displaystyle \frac{d}{dx}\Big|_{x=3} & = \frac{9(3)-6}{\sqrt{(3(3)-2)^2-4}} = \frac{7\sqrt{5}}{5}[/tex]
Step-by-step explanation:
We are given the two functions:
[tex]\displaystyle f(x) = \sqrt{x^2 -4} \text{ and } g(x) = 3x-2[/tex]
And we want to find:
[tex]\displaystyle \frac{d}{dx}\left[f(g(x))\right] \text{ at } x = 3[/tex]
Recall that from the chain rule:
[tex]\displaystyle \frac{d}{dx}\left[ f(g(x))\right] = f'(g(x)) \cdot g'(x)[/tex]
Hence, find both f'(x) and g'(x).
The derivative of f(x) can be determined using the chain rule:
[tex]\displaystyle \begin{aligned} f'(x) &= \frac{d}{dx}\left[ \sqrt{x^2-4}\right]\\ \\ & = \frac{1}{2\sqrt{(x^2-4)}}\cdot \frac{d}{dx}\left[x^2-4\right] \\ \\ & = \frac{x}{\sqrt{x^2-4}} \end{aligned}[/tex]
Because g(x) is simply a linear function, its derivative will be the slope of the linear function at any point. That is:
[tex]\displaystyle g'(x) = 3[/tex]
Hence:
[tex]\displaystyle \begin{aligned} \frac{d}{dx}\left[f(g(x))\right] & = \frac{(g(x))}{\sqrt{(g(x))^2-4}} \cdot (3) \\ \\ & = \frac{9x-6}{\sqrt{(3x-2)^2-4}} \end{aligned}[/tex]
Then at the point x = 3, the derivative is:
[tex]\displaystyle \frac{d}{dx}\Big|_{x=3} & = \frac{9(3)-6}{\sqrt{(3(3)-2)^2-4}} = \frac{7\sqrt{5}}{5}[/tex]
Every day Sasha spends 45 minutes practicing the oboe. She has already practiced the oboe for 22 minutes today. How much longer must she practice today?
Nelly buy 17 and 1/7 pounds of oranges for $45 from the supermarket how much does 1 pound of oranges cost
2.62 pls give a heart for me please.
use the following formula to solve the following quadratic equation 2x^+7a=15
Answer:
Hope this helps pls mark me Branliest
Step-by-step explanation:
that's my answer
C+3/4= 1 1/3 solve for c
Step-by-step explanation:
your answer is in the picture
5. Mr. Quick bought a new computer system. The regular price was $1580, but he got a 15% discount. How much did he pay?
Answer:
He paid $1343
Step-by-step explanation:
[tex]\frac{x}{1580} =\frac{15}{100}[/tex]
Cross multiply
[tex]x100=23700[/tex]
Divide 100 from both sides
[tex]x=237[/tex]
1580 - 237 = 1343
Hope this is helpful
Answer:
He paid $1343
Step-by-step explanation:
Thanks for the pts
✌️❤️✌️
Can someone help me for 9, 10, 11, 12, and 13 please
Answer:
you have nice handwriting
Step-by-step explanation:
no answer
Two fractions between 2 and 2 1/2
8. Heather purchased an iPad mini on sale 20%
off for $263.20. What was the original price of
the iPad mini?
A. $315.84
B. $329
C. $210.56
D. $400
Answer:
Answer is A.
Step-by-step explanation:
0.2 x 263.20 = 52.64
52.64 + 263.20 = 315.84
PLEASE HELP!! solve for x and y:
Answer:
x=21° ,y=25°
Step-by-step explanation:
when there are 2 equal line, so the degree is mirrowed.
straight line contain 180°. For Triangle there have 180°. You can find the degree in other shape but that shape must be 2D,like kuboid or cube or etc.
find the sum of 3x² + 5x - 1 and x² - 2x -7
Write an equation of the line through the points (-3, 3) and (7, 5) in slope-intercept form. What is the y-intercept?
To amend the U.S. Constitution, 3/4 of the 50 states must approve the amendment. If 35 states approve the amendment will the constitution be amended
bearing in mind that fraction wise we can represent any WHOLE as 1, 5/5 = 1, or 333/333 = 1, so we can say that the whole of the states or namely 50/50 = 1, so we can say that
[tex]\begin{array}{ccll}amount&fraction\\\cline{1-2}50&1\\35&x\end{array}\implies \cfrac{50}{35}=\cfrac{1}{x}\implies 50x=30\implies x=\cfrac{30}{50}\\\\\\\boxed{x = \cfrac{3}{5}\implies 0.7}\\\\[-0.35em]~\dotfill\\\\\cfrac{3}{4}\implies 0.75~\hspace{10em}\stackrel{\textit{since 0.7 is less than 0.75, \underline{nope}}}{0.7 < 0.75}[/tex]
what is the answer for this
Answer:
n = 4/3 or n = 1.3 repeating
Solve for the variable shown
Y=
Answer:
y≈94.31
Step-by-step explanation:
Hi there!
We're given a right triangle (notice the 90 degree angle), the measure of one of the legs (one of the sides that make up the right angle) as 46, the other one as y, and one of the angles as 26°
We want to solve for y
We can use a trigonometric ratio to do that.
First, let's recall the three most-well known ratios:
Sine is [tex]\frac{opposite}{hypotenuse}[/tex]
Cosine is [tex]\frac{adjacent}{hypotenuse}[/tex]
Tangent is [tex]\frac{opposite}{adjacent}[/tex]
Since we are given one of the angles, let's find out which sides are the opposite, adjacent, and hypotenuse, in reference to the given angle (the 26° angle)
In reference to that angle, the side opposite to that angle (also the side known as "opposite) is the side marked as 46, the adjacent side is y, and the hypotenuse is the unmarked side
Since we know the opposite and adjacent, let's use the ratio for tangent
Since we based our labels off of the 26 degree angle, the tangent ratio is the tangent OF 26, or tan(26)
tan(26)=[tex]\frac{46}{y}[/tex]
Now we need to solve the equation
Start by multiplying both sides by y
tan(26)*y=46
Divide both sides by tan(26)
y=[tex]\frac{46}{tan(26)}[/tex]
Plug [tex]\frac{46}{tan(26)}[/tex] into your calculator, and remember to have the calculator on degree mode
[tex]\frac{46}{tan(26)}[/tex]≈94.31
Remember that [tex]\frac{46}{tan(26)}[/tex] is equal to y, which means that y is about 94.31
Hope this helps!
9 ) Jason bought 9 new baseball trading cards to add to his collection. The next day his dog ate half of his collection. There are now only 31 cards left. How many cards did Jason start with ?
Answer:
He started with 53 cards
Step-by-step explanation:
He has 31 now
If 31 is half of what he had, then we need to double it
31 x 2 = 62
If he had bought 9, then we need to do the opposite
62 - 9 = 53
Help me pls brainlist
Answer:
The y-intercept is (0, 35)
The y-coordinate of the y-intercept represents the height at which the line intersects the y-axis.
The slope is 5/2.
Step-by-step explanation:
What's the answer to this question
Answer:
x = -7
Step-by-step explanation:
Write out the equation: 3x - 2 = -x - 30
Isolate the x
3x - 2 = -x - 30
+2 +x
4x = -28
Divide to simplify the x
x = -7
A cone with a radius 4 m and a
height of 12 m.
What is the volume
Answer:
201.06 cu in
Step-by-step explanation:
Answer:
64π
Step-by-step explanation:
πr^2*h/3 is the formula for volume of a cone.
So 16pi * 12/3
Then 16pi *4
so 64 pi is the volume
Please help! I cant get this wrong ahh. Brainliest to correct
Answer:
About 80,000
Step-by-step explanation:
take the % multiply by the years to get your answer
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag correct position in the answer box. Release your mouse button when the item is place. If you change your m the item to the trashcan. Click the trashcan to clear all your answers. Indicate the equation of the line through (2, -4) and having slope of 3/5. IG V + + | C 123456 718190x y2 NEXT QUESTION O ASK FOR HELP
Answer:
Y=3/5 X -4 just trust me on this one. eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
[tex]y^2dy=(x+2)dx[/tex]
Integrate both sides:
y² dy = (x + 2) dx
∫ y² dy = ∫ (x + 2) dx
1/3 y³ = 1/2 x² + 2x + C
How do I solve this?
Answer:
X = 10
Step-by-step explanation:
<1 = 2x + 10
<2 = x + 20
<3 = 180 - 6x (linear angles = 180 degrees)
<1 + <2 + <3 = 180 degrees
2x + 10 + x + 20 + 180 - 6x = 180
-3x + 210 = 180
-3x = 180 - 210
x = -30/-3
x = 10
Answer:
Step-by-step explanation:
what you do id try to find the math book on quizelit or some websire and find the answer
please help me asapppp! excel computer
Answer:
dddddddddddddddddddddddddd
Step-by-step explanation:
Which is an arithmetic sequence?A)9, 12, 16, 20...B)9, 11, 13, 16...C)1, 5, 9, 13, 17...D)12, 14, 16, 18...
Answer: https://www.khanacademy.org/commoncore/grade-HSF-F-IF#HSF-IF.A.3
Step-by-step explanation:
copy and paste the link on to your search bar
Find the value of 6a + 4(3), if a = 2
Help
Credits: Hello! I'm from the Philippines! Mabuhay!!
Hey there!
6a + 4(3)
= 6(2) + 4(3)
= 12 + 12
= 12
Therefore, your answer is: 12
Good luck on your assignment and enjoy your day’
~Amphitrite1040:)
IN A CLASS OF 60 STUDENTS, 25 PLAYS BASKETBALL, 2O PLAY VOLLEYBALL, AND 10 STUDENTS PLAY BOTH OF THEM. HOW MANY STUDENTS PLAY NEITHER BASKETBALL NOR VOLLEYBALL ?
Answer:
5
Step-by-step explanation:
60-25=35
35-20=15
15-10=5
5 people dont play either of them
Answer:
25
Step-by-step explanation:
To solve this, we can add the number of basketball players and the number of volleyball players:
25 + 20 = 45
But we know that there are ten players who are counted twice because they play both. So we subtract 10:
45 - 10 = 35
And that is the total number of students who play either basketball or volleyball. Now to figure out those that play neither sport we subtract the number of students by the number of players:
60 - 35 = 25
That’s the number of students who don’t play one of those sports.
The sum of 8n²- 3n + 10 and 3n² - 6n-7 is ?
Step-by-step explanation:
= (8n² - 3n + 10) + (-3n² - 6n - 7)
= (8 - 3)n² + (-3 - 6)n + (10 - 7)
= 5n² - 9n + 3
Option → #1
17 = -13 - 8x
can i get it step by step
Answer:
x = 30/-8 = -15/4 = -3.75 = -3 3/4
Step-by-step explanation:
17 = -13 - 8x
add 13 to each side
30 = -8x
divide each side by -8
30/-8 = x
30/-8 = -15/4 = -3.75 = -3 3/4
___________________________________________________________
Answer:
A
Step-by-step explanation:
I think it is A because if you do the math when your double her time she has way more distance.
50 POINTS PLEASE HELP FAST!!!!!
The youth group is going on a trip to the state fair. The trip costs $62. Included in that price is $14 for a concert ticket and the cost of 2 passes, one for the rides and one for the game booths. Each of the passes costs the same price. Write an equation representing the cost of the trip, and determine the price of one pass. Solve your equation by showing your work and steps.
Answer:
11+2x= 52 , $20.50 equal one pass
Step-by-step explanation:52 is the total and $11 is included in that total. So you have part of your equation : 11 + something = 52. In order to find that " something " you have to set up a variable : 2x , 2 because that is the amount of passes bought and X because you don't know the cost of the passes yet. You now have your equation : 11+2x=52. Next you isolate the "2x" by subtracting eleven from itself and what you do to one side of the equation you have to do to the other, so you subtract 11 from 52 and are left with 41 . You then have the simplified equation : 2x=41 . Now you're going to isolate the variable by dividing 2x by 2 and doing the same to 41. You're then left with X= 20.50 , the cost of one ticket
