Answers
We need to find the derivative first. Think of x/(x+2) as x(x+2)^(-1). That will allow us to use the product rule. You could also use the quotient rule if you want. I'll go with the product rule route.
[tex]f(x) = \frac{x}{x+2}\\\\f(x) = x(x+2)^{-1}\\\\f'(x) = (x+2)^{-1}-x(x+2)^{-2}\\\\f'(x) = \frac{1}{x+2}-\frac{x}{(x+2)^2}\\\\f'(x) = \frac{x+2}{(x+2)^2}-\frac{x}{(x+2)^2}\\\\f'(x) = \frac{x+2-x}{(x+2)^2}\\\\f'(x) = \frac{2}{(x+2)^2}\\\\f'(x) = \frac{2}{x^2+4x+4}\\\\[/tex]
Since we want the tangent slope to be 1/2, we'll set f ' (x) equal to 1/2 and solve for x.
[tex]f'(x) = \frac{2}{x^2+4x+4}\\\\\frac{1}{2} = \frac{2}{x^2+4x+4}\\\\1*(x^2+4x+4) = 2*2\\\\x^2+4x+4 = 4\\\\x^2+4x = 0\\\\x(x+4) = 0\\\\x = 0 \ \text{ or } \ x+4 = 0\\\\x = 0 \ \text{ or } \ x = -4\\\\[/tex]
The two x values, x = 0 and x = -4, make f ' (x) equal to 1/2.
---------
If x = 0, then y is...
[tex]y = f(x)\\\\f(x) = \frac{x}{x+2}\\\\f(0) = \frac{0}{0+2}\\\\f(0) = 0\\\\[/tex]
Showing that (0,0) is one point we're after.
If x = -4, then,
[tex]y = f(x)\\\\f(x) = \frac{x}{x+2}\\\\f(-4) = \frac{-4}{-4+2}\\\\f(-4) = 2\\\\[/tex]
Making (-4, 2) the other point where the tangent slope is 1/2.
We use the original f(x) function, and not the derivative, when determining the y coordinates of the two points. If you plugged x = 0 or x = -4 into f ' (x), you'd get 1/2. So its good practice, but not what we're after ultimately.
Related Questions
1. What is the opposite of -17
Answers
Answer:
Step-by-step explanation:
17
Find the area of this trapezoid. Be sure to include the correct unit in your answer.
Answers
Answer:
60 m²
Step-by-step explanation:
Area of trapezium = 1/2 (a + b) h
= 1/2 (3 + 17) 6
= 1/2 * 20 * 6
= 60 m²
Step by step solution: see photo
what is the absolute value of the complex number −4−i 2√?
Answers
Answer:
-4-i2
The absolute value is the Square root of the real and Imaginary Parts of the Complex No
= √(-4)²+(-2)²
=√16+4
=√20
=2√5
Which of the following are point-slope equations of the line going through (-3,-5) and (2,4)
Answers
Answer:
y+5 = 9/5(x+3)
y - 4 = 9/5(x-2)
Step-by-step explanation:
First find the slope
m = ( y2-y1)/(x2-x1)
= ( 4- -5)/(2 - -3)
= ( 4+5)/(2+3)
= 9/5
Then using the point slope form
y -y1 = m(x-x1) where x1 and y1 are a point on the line
y - -5 = 9/5(x- -3)
y+5 = 9/5(x+3)
or using the other point
y - 4 = 9/5(x-2)
A box contains 5 red balls, 7 green balls, and 6 yellow balls. In how many ways can 6 balls be chosen if there should be 2 balls of each color
Answers
Answer:
12 balls
Step-by-step explanation:
take 3 red balls ,5 green balls and 4 yellow balls that 12 balls = 6 balls in bag
If bag contains 4 white balls, 6 yellow balls, and 5 red balls then 6 balls can be chosen if there must be 2 balls of each color in 900 ways
What are permutation and combination?Permutation is way of selecting and arranging things while combination is way of selecting things .
here, we have,
Given that bag contains 4 white balls, 6 yellow balls, and 5 red balls
we have to select 6 balls
it's given that there must be 2 balls of each color
So here's how we can select them
2 white balls ,2 yellow balls and 2 red balls
So we have to select 2 white balls out of 4 white balls ,2 yellow balls out of 6 yellow balls and 2 red balls out of 5 red balls
so number of ways of selecting
4C2 * 2C2 * 5C2
=6*15*10
=900
If bag contains 4 white balls, 6 yellow balls, and 5 red balls then 6 balls can be chosen if there must be 2 balls of each color in 900 ways
To learn more about combination visit :
brainly.com/question/25821700
#SPJ3
Find the measure of 2.
62 = [?]
121
42
Answers
Answer:
59°Step-by-step explanation:
∠2 and 121° are supplementary as consecutive interior angles:
m∠2 + 121° = 180°m∠2 = 180° - 121°m∠2 = 59°Evaluate 4 ÷ 3/5 Give your answer as a mixed number in its simplest form.
Answers
9514 1404 393
Answer:
6 2/3
Step-by-step explanation:
4/(3/5) = (4/1)×(5/3) = 20/3 = 6 2/3
Please help with this Ive been stressing out lately and I want a break I'll give hearts and 5 stars.
Answers
Answer:
8.8584073464
Step-by-step explanation:
area of the rectangle is 12
area of the circle is just pie
subtract the two and you get 8.8584073464
Answer:
Step-by-step explanation:
The Brazos River is the longest river in Texas with a length of 1, 352 km. The elevation of the source is 453 m above sea level, and the mouth is the Gulf of Mexico, with an elevation of m above sea levelAt what angle does the Brazos River flow, on average , in degrees ? (Round to the nearest hundredth .)
Answers
Answer:
0.02degrees
Step-by-step explanation:
Given the following
Length of the river (adjacent) = 1352km = 1352000m
Height of the source (opposite) = 453m
Required
angle of elevation theta
Using the SOH CAH TOA identity
tan theta = opposite/adjacent
tan theta = 453/1352000
tan theta = 0.0003351
theta = arctan(0.0003351)
theta = 0.02 degrees
Hence the Brazos river flows at an angle of 0.02degrees to the nearest hundredth
A biscuit recipe calls for 3 1/2 cups of flour to make 24 biscuits. Aaron wants to make only 8 biscuits, so he needs to use 1/3 of the amount of flour. How many cups of flour should Aaron use? Pls someone tell me the answer in fractions
Answers
Answer:
104 cups.
Step-by-step explanation:
Let's use a ratio:
biscuits : cups
24 : 312
8 : 104
He should use 104 cups of flour. (That's a lotta flour)
What closed figure do the coordinates 3,3), (-5,3), (-1, -3), (3, -3) make?
Answers
Answer:
(8,-4) Correct me if there's wrong QwQ
Pleas help? No links pleas. I will give you points...
Answers
Answer:
what are the answers?
Step-by-step explanation:
I can't give it to you without answer choices
Fine the length of segment x.
Answers
Answer:
10
Step-by-step explanation:
12+4=16
16-6=10
easy
HELPPPPPP PLEASe!!!!!!!!
Answers
Answer:
Cos x
Step-by-step explanation:
Help plzzzzz fast and no links
Answers
Answer:
x=60
Step-by-step explanation:
I am going to try to explain this to the best of my abilities, but if you dont understand please let me know and I'll clarify. There is a straight ine tha that equals 180, so you do 180-120=60
BRAINLIEST if correct NO LINKs
Answers
Answer:
just divide its simple
Step-by-step explanation:
from the left triangle (70) to the right triangle (23) it is a reduction of .329
please help I have no idea how to solve this. Please tell me what the volume of the prism is!
Answers
Answer:
Volume = area of base × height
Are of base(triangle)
A=b×h÷2
=12×4÷2
=12×2
24
V=area of base × height
=(24 inch)^2×15 inch
=(360 inch)^3
Step-by-step explanation:
to find the volume of a prism the formula is
area of base ×height.
In this question the area of base is a triangle so we first find the area of the triangle and multiply it with the height
Evaluate the expression and enter your answer in the box below.
8 + -9
Answer here
Answers
Answer:
Step-by-step explanation:
remember plus minus = minus
so 8+-=9
8-9=-1
The backboard of the basketball hoop forms a right triangle with the supporting rods, as shown. Use the
Pythagorean Theorem to approximate the distance between the rods where they meet the backboard. Round your answer to the nearest
hundredth.
Answers
Answer:
9.14 inches.
Step-by-step explanation:
From the question,
Assuming the diagram attached, is similar to diagram required to support the question,
From the diagram,
Applying pythagoras theorem
a² = b²+c²...................... Equation 1
Where a = 13.4 in, b = x in, c = 9.8 in.
Substitute these values into equation 1
13.4² = x²+9.8²
x² = 13.4²-9.8²
x² = 179.56-96.04
x² = 83.52
x = √(83.52)
x = 9.14 inches
Hence the distance between the rods is 9.14 inches
A rectangular tank measuring 35 cm by 28 cm by 16 cm is 2/5 filled with
water. The water is poured into an empty cubical tank of edge 18 cm until
it is full. How much water is left in the rectangular tank? Give your answer
in millilitres.
Answers
Answer:
Amount of water left in tank = 440 cm³
Step-by-step explanation:
Given:
Sides of tank respectively = 35 cm , 28 cm , 16 cm
Water level in tank = 2/5
Side of a cubic tank = 18 cm
Find:
Amount of water left in tank
Computation:
Volume level in rectangular tank = [2/5][35 x 28 x 16]
Volume level in rectangular tank = [2/5][15,680]
Volume level in rectangular tank = [31,360/5]
Volume level in rectangular tank = 6,272 cm³
Volume of cube = side³
Volume of cube = 18³
Volume of cube = 5,832 cm³
Amount of water left in tank = Volume level in rectangular tank - Volume of cube
Amount of water left in tank = 6,272 - 5,832
Amount of water left in tank = 440 cm³
The diameter of a circle is 1. What is the area??
Answers
Answer:
diameter=1
radius(r)=1/2 =0.5
area of circle=πr²
22/7×(0.5)²22/7×0.250.785cm²hope it helps.
plzzz help for a brainly
Answers
Answer:
b
Step-by-step explanation:
b
Here is my question it is worth 15 points!
Answers
Answer:
What is your question????
Answer:
you don't have a question here tho
Step-by-step explanation:
Simplify. -5x-3(-2y+ 3x) - 32
Answers
Answer:
-14x + 6y - 32
Step-by-step explanation:
After distributing you have:
-5x + 6y - 9x - 32
-14x + 6y - 32
Help pls I’ll give extra points and brainlist
Answers
Answer:
C.
Step-by-step explanation:
Sorry if wrong :> Please mark brainliest! Have a awesome day ^_^ You're a great hooman!!!!
Clearly mark on the coordinate plane the location of the ordered pairs and
identify what quadrant they are in.
J (4,0) quadrant ________ and M(-2,-3) quadrant ___________
Answers
Answer:
Point [tex]J(4,0)[/tex] lies on [tex]x-[/tex]axis and point [tex]M(-2,-3)[/tex] lies quadrant III.
Step-by-step explanation:
A coordinate plane is a plane that is divided into four quadrants by the coordinate axes.
Here, coordinate axes are [tex]x-[/tex]axis and [tex]y-[/tex]axis.
Let's first mark the points in the coordinate plane.
See the attached figure.
From the figure, it can be observed that point [tex]J(4,0)[/tex] lies on [tex]x-[/tex]axis and point [tex]M(-2,-3)[/tex] lies quadrant III.
what is the area and circumference please help just tell only the answer
Answers
the circumference is 84.19
hope this helped :)
Circumference = 82.896 inches
Area = 547.1136 inches squared
What answer do you get when you solve 0.4(2a-0.3b)
Answers
Answer:
0.8a-0.12b
Step-by-step explanation:
Use the distributive property:
0.8a-0.12b
solve x(x-2)=4 using the quadratic formula
Answers
Answer:
=1±(check mark thing)=5
Step-by-step explanation:
Sarah rode her bike 54km in 4hours what’s her average speed?
Answers
Answer:5.4 km
Step-by-step explanation: