Answer:
-60...make me brainlistt
Step-by-step explanation:
The graph of f(x)= 3/1+x^2 is shown in the figure to the right. Use the second derivative of f to find the intervals on which f is concave upward or concave downward and to find the inflection points of f.
Answer:
Concave Up Interval: [tex](- \infty,\frac{-\sqrt{3} }{3} )U(\frac{\sqrt{3} }{3} , \infty)[/tex]
Concave Down Interval: [tex](\frac{-\sqrt{3} }{3}, \frac{\sqrt{3} }{3} )[/tex]
General Formulas and Concepts:
Calculus
Derivative of a Constant is 0.
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Quotient Rule: [tex]\frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}[/tex]
Chain Rule: [tex]\frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Second Derivative Test:
Possible Points of Inflection (P.P.I) - Tells us the possible x-values where the graph f(x) may change concavity. Occurs when f"(x) = 0 or undefinedPoints of Inflection (P.I) - Actual x-values when the graph f(x) changes concavityNumber Line Test - Helps us determine whether a P.P.I is a P.IStep-by-step explanation:
Step 1: Define
[tex]f(x)=\frac{3}{1+x^2}[/tex]
Step 2: Find 2nd Derivative
1st Derivative [Quotient/Chain/Basic]: [tex]f'(x)=\frac{0(1+x^2)-2x \cdot 3}{(1+x^2)^2}[/tex]Simplify 1st Derivative: [tex]f'(x)=\frac{-6x}{(1+x^2)^2}[/tex]2nd Derivative [Quotient/Chain/Basic]: [tex]f"(x)=\frac{-6(1+x^2)^2-2(1+x^2) \cdot 2x \cdot -6x}{((1+x^2)^2)^2}[/tex]Simplify 2nd Derivative: [tex]f"(x)=\frac{6(3x^2-1)}{(1+x^2)^3}[/tex]Step 3: Find P.P.I
Set f"(x) equal to zero: [tex]0=\frac{6(3x^2-1)}{(1+x^2)^3}[/tex]Case 1: f" is 0
Solve Numerator: [tex]0=6(3x^2-1)[/tex]Divide 6: [tex]0=3x^2-1[/tex]Add 1: [tex]1=3x^2[/tex]Divide 3: [tex]\frac{1}{3} =x^2[/tex]Square root: [tex]\pm \sqrt{\frac{1}{3}} =x[/tex]Simplify: [tex]\pm \frac{\sqrt{3}}{3} =x[/tex]Rewrite: [tex]x= \pm \frac{\sqrt{3}}{3}[/tex]Case 2: f" is undefined
Solve Denominator: [tex]0=(1+x^2)^3[/tex]Cube root: [tex]0=1+x^2[/tex]Subtract 1: [tex]-1=x^2[/tex]We don't go into imaginary numbers when dealing with the 2nd Derivative Test, so our P.P.I is [tex]x= \pm \frac{\sqrt{3}}{3}[/tex] (x ≈ ±0.57735).
Step 4: Number Line Test
See Attachment.
We plug in the test points into the 2nd Derivative and see if the P.P.I is a P.I.
x = -1
Substitute: [tex]f"(x)=\frac{6(3(-1)^2-1)}{(1+(-1)^2)^3}[/tex]Exponents: [tex]f"(x)=\frac{6(3(1)-1)}{(1+1)^3}[/tex]Multiply: [tex]f"(x)=\frac{6(3-1)}{(1+1)^3}[/tex]Subtract/Add: [tex]f"(x)=\frac{6(2)}{(2)^3}[/tex]Exponents: [tex]f"(x)=\frac{6(2)}{8}[/tex]Multiply: [tex]f"(x)=\frac{12}{8}[/tex]Simplify: [tex]f"(x)=\frac{3}{2}[/tex]This means that the graph f(x) is concave up before [tex]x=\frac{-\sqrt{3}}{3}[/tex].
x = 0
Substitute: [tex]f"(x)=\frac{6(3(0)^2-1)}{(1+(0)^2)^3}[/tex]Exponents: [tex]f"(x)=\frac{6(3(0)-1)}{(1+0)^3}[/tex]Multiply: [tex]f"(x)=\frac{6(0-1)}{(1+0)^3}[/tex]Subtract/Add: [tex]f"(x)=\frac{6(-1)}{(1)^3}[/tex]Exponents: [tex]f"(x)=\frac{6(-1)}{1}[/tex]Multiply: [tex]f"(x)=\frac{-6}{1}[/tex]Divide: [tex]f"(x)=-6[/tex]This means that the graph f(x) is concave down between and .
x = 1
Substitute: [tex]f"(x)=\frac{6(3(1)^2-1)}{(1+(1)^2)^3}[/tex]Exponents: [tex]f"(x)=\frac{6(3(1)-1)}{(1+1)^3}[/tex]Multiply: [tex]f"(x)=\frac{6(3-1)}{(1+1)^3}[/tex]Subtract/Add: [tex]f"(x)=\frac{6(2)}{(2)^3}[/tex]Exponents: [tex]f"(x)=\frac{6(2)}{8}[/tex]Multiply: [tex]f"(x)=\frac{12}{8}[/tex]Simplify: [tex]f"(x)=\frac{3}{2}[/tex]This means that the graph f(x) is concave up after [tex]x=\frac{\sqrt{3}}{3}[/tex].
Step 5: Identify
Since f"(x) changes concavity from positive to negative at [tex]x=\frac{-\sqrt{3}}{3}[/tex] and changes from negative to positive at [tex]x=\frac{\sqrt{3}}{3}[/tex], then we know that the P.P.I's [tex]x= \pm \frac{\sqrt{3}}{3}[/tex] are actually P.I's.
Let's find what actual point on f(x) when the concavity changes.
[tex]x=\frac{-\sqrt{3}}{3}[/tex]
Substitute in P.I into f(x): [tex]f(\frac{-\sqrt{3}}{3} )=\frac{3}{1+(\frac{-\sqrt{3} }{3} )^2}[/tex]Evaluate Exponents: [tex]f(\frac{-\sqrt{3}}{3} )=\frac{3}{1+\frac{1}{3} }[/tex]Add: [tex]f(\frac{-\sqrt{3}}{3} )=\frac{3}{\frac{4}{3} }[/tex]Divide: [tex]f(\frac{-\sqrt{3}}{3} )=\frac{9}{4}[/tex][tex]x=\frac{\sqrt{3}}{3}[/tex]
Substitute in P.I into f(x): [tex]f(\frac{\sqrt{3}}{3} )=\frac{3}{1+(\frac{\sqrt{3} }{3} )^2}[/tex]Evaluate Exponents: [tex]f(\frac{\sqrt{3}}{3} )=\frac{3}{1+\frac{1}{3} }[/tex]Add: [tex]f(\frac{\sqrt{3}}{3} )=\frac{3}{\frac{4}{3} }[/tex]Divide: [tex]f(\frac{\sqrt{3}}{3} )=\frac{9}{4}[/tex]Step 6: Define Intervals
We know that before f(x) reaches [tex]x=\frac{-\sqrt{3}}{3}[/tex], the graph is concave up. We used the 2nd Derivative Test to confirm this.
We know that after f(x) passes [tex]x=\frac{\sqrt{3}}{3}[/tex], the graph is concave up. We used the 2nd Derivative Test to confirm this.
Concave Up Interval: [tex](- \infty,\frac{-\sqrt{3} }{3} )U(\frac{\sqrt{3} }{3} , \infty)[/tex]
We know that after f(x) passes [tex]x=\frac{-\sqrt{3}}{3}[/tex] , the graph is concave up until [tex]x=\frac{\sqrt{3}}{3}[/tex]. We used the 2nd Derivative Test to confirm this.
Concave Down Interval: [tex](\frac{-\sqrt{3} }{3}, \frac{\sqrt{3} }{3} )[/tex]
Bryce had a $25 gift card to use on songs and games at an online media store. Songs cost $2 each and games cost $5 each. Bryce spent all the money on the gift card to download 8 items. Solve the system to determine how many games he purchased. Let s represent the number of songs and g represent the number of games. s + g = 8 2s + 5g = 25 Bryce purchased games.
Answer:
Bryce purchased 3 games.
Step-by-step explanation:
To find the number of songs and games that Bryce downloaded, we need to solve the following system of equations:
s + g = 8
2s + 5g = 25
We know that:
s + g = 8 → 2s + 2g = 16 → 2s = 16 -2g
2s + 5g = 25 → 16 - 2g + 5g = 25
→3g = 25 - 16
→3g = 9
→ g = 3
Therefore, bryce downloaded 3 games and 5 songs!
Answer:
.
3x + 2y = 16,
Step-by-step explanation:
Juan is 1 1/4 feet shorter than maria.maria is 1/3 foot taller than Luis. if Luis is 62 inches tall, how tall are maria and Juan.
Answer:
Maria is 58 inches tall and Juan is 42 inches
Step-by-step explanation:
Write an ordered pair that is a solution to the equation of the line y=x+5
Answer:
(1,6)
(2,7)
(4,9)
(8,13)
Step-by-step explanation:
3. A $5,000 principal is invested in two accounts, one earning 1% interest and another earning 6%
interest. If the total interest for the year is $170, then how much is invested in each account?
Let, amount invested in first account is x.
So, amount invested in second account is ( 5000 - x ).
Now,
Total interest = Interest from 1 + Interest from 2
170 = x × 0.01 × 1 + ( 5000 - x ) × 0.06 × 1
17000 = x + 6( 5000 - x )
17000 = x + 30000 - 6x
5x = 30000 - 17000
x = $2600
Therefore, money invested in first and second account is $2600 and $2400.
Hence, this is the required solution.
Just for you :) happy thanksgiving
Answer:
thksss and happy thanksgiving to you 2
Step-by-step explanation:
Select the choice that translates the following verbal phrase correctly to algebra: (2 points)
the difference of m and 7 increased by 15
a.) m − (7 + 15)
b.) 7m + 15
c.) (m − 7) + 15
d.) m − 7 ÷ 15
What fraction is equivalent to .9?
Answer:
9/100
Step-by-step explanation:
00.9=9/100
9%
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000
Stealth Bank has deposits of $700 million. It holds reserves of $70 million and has purchased government bonds worth $215 million. The bank's loans have a market value of $490 million. What does Stealth Bank's net worth, or equity capital, equal?
Answer:
$75 million
Step-by-step explanation:
Given that:
Reserve value = $70 million
Purchased government bond = 215 million
Market value of loan = $490 million
Net worth :
Assets - liability
Assets = (Market value of loan + purchased government bond + reserve value)
(490 million + 215 million + 70 million)
275 million + 70 million
= $775 million
Liability = Deposits = $700 million
Net worth = ($775 - $700) million
Net worth = $75 million
what is one thousandth less than 0.061
Answer:
0.06
Step-by-step explanation:
0.061 - 0.001 = 0.060 = 0.06
8) Eugene borrows $250 at a 4% annual interest rate. If he does not
make any payments, how much simple interest will he owe in 18 months?
A) $10
B) $15
C) $18
D) $20
Answer:
The simplest interest will be $15 ⇒ B
Step-by-step explanation:
The rule of the simple interest is I = Prt, where
P is the initial amountr is the rate in decimalt is the time∵ Eugene borrows $250 at a 4% annual interest rate
∴ P = 250
∴ r = 4% = 4 ÷ 100 = 0.04
∵ The time is 18 months
→ Change the time to year because the rate is annual
∵ 1 year = 12 months
∴ t = 18 ÷ 12 = 1.5 years
→ Substitute the values of P, r, and t in the rule above to find the interest
∵ I = 250 × 0.04 × 1.5
∴ I = 15
∴ The simplest interest will be $15
A certain fraction has the value 3/4. If its numerator is decreased by 7 and its denominator is increase by 4, the resulting fraction has the value 1/2. Find the original fraction
Answer:
n = 16 - 7
n = 9
Step-by-step explanation:
If the numerator of a fraction is increased by 3, the fraction becomes 3/4."
Cross multiply
4(n+3) = 3d
4n + 12 = 3d
"If the denominator is decreased by 7, the fraction becomes 1."
Cross multiply
1n = d - 7
n = (d-7)
In the 1st equation replace n with d-7
4(d-7) + 12 = 3d
4d - 28 + 12 = 3d
4d - 3d - 16 = 0
d = 16 is the denominator
then n = 16 - 7
n = 9
9/16 = the original equation
Every quadrilateral is a rhombus true or false
Answer:
false
Step-by-step explanation:
Answer:
false
Step-by-step explanation:
. 。 • ﾟ 。 .
. . 。 。 .
. 。 ඞ 。 . • •
ﾟ Josie was not An Impostor. 。 .
' 1 Impostor remains 。
ﾟ . . , . .
there are 3 arms for every 2 eyes. If there are 6 eyes, how many arms are there?
Answer:
There are 9 arms.
Step-by-step explanation:
a small airplane flies 1 015miles with an average speed of 290 mph. 1.75 hours after the plane leaves, a Boeing 747 leaves from the same point. Both planes arrive at the same time; what was the average speed of Boeing 747?
Answer:
The Boeing 747 had an average speed of 580 mph.
Step-by-step explanation:
Constant speed motion
An object is said to travel at constant speed if the ratio of the distance traveled by the time taken is constant.
Expressed in a simple equation, we have:
[tex]\displaystyle v=\frac{d}{t}[/tex]
Where
v = Speed of the object
d = Distance traveled
t = Time taken to travel d.
From the equation above, we can solve for d:
d = v . t
And we can also solve it for t:
[tex]\displaystyle t=\frac{d}{v}[/tex]
The small airplane travels 1015 miles at a constant speed of v=290 miles/hour. The time it took to arrive its destiny was:
[tex]\displaystyle t=\frac{1015}{290}[/tex]
t = 3.5 hours
The Boeing 747 left from the same point 1.75 hours after the small plane and traveled the same distance. It needed a time t' = 3.5 - 1.75 = 1.75 hours, thus its speed must have been:
[tex]\displaystyle v=\frac{1015}{1.75}=580[/tex]
The Boeing 747 had an average speed of 580 mph.
The process for rationalizing a denominator in a variable expression is the same as in a numeric expression. Here’s a real-world example. The kinetic energy of the car of a rollercoaster is given by the formula k = one-half m v squared where k is kinetic energy, m is the mass of the car, and v is the velocity of the car. Solving this formula for v, we get v = StartRoot StartFraction 2 k Over m EndFraction EndRoot Which formula gives the velocity of the car in simplest form?
Answer:
It's B
Step-by-step explanation:
Got it right on EDGE2020
The value of velocity of the car will be v = √(2km) / m. Then the correct option is B.
What is kinetic energy?If the object of mass m is moving with speed v. Then the kinetic energy of the object will be
KE = (1/2) mv²
The process for rationalizing a denominator in a variable expression is the same as in a numeric expression.
Here’s a real-world example.
The kinetic energy of the car of a rollercoaster is given by the formula
k = 1/2 m v²
Where k is kinetic energy, m is the mass of the car, and v is the velocity of the car.
Solving this formula for v, we get
[tex]\rm v = \sqrt{\dfrac{2k}{m}}[/tex]
Simplify the equation, we have
[tex]\rm v = \sqrt{\dfrac{2km}{m^2}}\\\rm v = \dfrac{\sqrt{2km}}{m}[/tex]
Then the correct option is B.
The complete question is attached below.
More about the kinetic energy link is given below.
https://brainly.com/question/12669551
#SPJ2
What is 19,998 divided by 1,000,000,000,000,000,000,000,000,000,000,000
Answer:
1.9998e-29
Step-by-step explanation:
On a number line, between which two consecutive whole numbers would the square root of 277 be located
9514 1404 393
Answer:
16 and 17
Step-by-step explanation:
16² = 256
(√277)² = 277
17² = 289
The root of 277 is between 16 and 17.
Suppose a,b,c represent three positive whole numbers. if a+b=13 and b+c=22 and a+c=19 what is the value of c
Answer: C = 14
Step-by-step explanation: You can assume the A is less than B, and if you just go down in numbers such as A=6 and B=7 (To solve A + B = 13), you will eventually get to A=5 and B=8. If you do B = 8 + C = 14 ( That you get after subtracting 8 by 22 ) You should get 22, and to proof check it, you do A + C which is going to be 5 + 14 and you get 19 thus proving that C = 14.
Write the following in Scientific Notation. -18,500,000,000,000
Answer:
Its 1.85 x 10 to the 13th power
Step-by-step explanation:
plz i have no clue and this is due in 15 mins
Answer:
y = [tex]\frac{1}{2}[/tex] x
Step-by-step explanation:
Slope of perpendicular to y = - 2x - 5 line is [tex]\frac{1}{2}[/tex]
y - 2 = [tex]\frac{1}{2}[/tex] ( x - 4)
y = [tex]\frac{1}{2}[/tex] x
Answer:
[tex]y=\frac{1}{2} x[/tex]
Step-by-step explanation:
10 1/8 - 3 5/6=.......?
Answer:
6 7/24
Step-by-step explanation:
On Sunday, 69% of the tickets sold at a theme park were children tickets, the rest were adult tickets. If the theme park sold 260 tickets in all, about how many children tickets were sold on this particular day?
Answer:
182
Oh and btw, its funny because I'm in your 6th period class. And i was looking up the answer and couldn't find it so when i found your i decided to help you answer it too
-Mikey
Answer:182
Step-by-step explanation:
Find the value of the variable, x
Group of answer choices
6
3
15
5
Answer:
I think you might have a mistake for the numbers you put there.
But the answer is about 15
Step-by-step explanation:
I did the calculation and got 14, but 15 is the closeest answer
help pls :)))))))))))))))))
Answer:
I think all measure can be used.
I need help on this...
Answer:
The answer would be C.
Step-by-step explanation:
X is greater than and equal to -2. So it would be a closed circle and it would be going to the right.
Answer:
C
Step-by-step explanation:
when x is greater than AND equal to -2
the numberline will show a closed circle on -2 and a line to the right (because greater than means positive and all numbers to the right increase)
The tree in Lisa’s backyard is 7.4 m high. How high is it in centimeters?
Answer:
740 cm
Step-by-step explanation:
Answer: 740 centimeters
Step-by-step explanation:
All you have to do is multiply the length value by 100 giving you 740.
Pls help me in these questions i will mark u brainliest.
Answer:
each angle is 83
Step-by-step explanation:
166÷ 2 = 83
check
83+83=166
hope it helps!!
Answer:
sum of two vertically angle =166°
X=166°/2 = 83°.
hence, each angle is equal to 83°.
X=
Nicole is making a cake that uses 3/4 cup of flour and 1 and 1/8 teaspoons if nicole uses 1 cup of flour how much salt would she need
Answer:
1.5 teaspoons
Step-by-step explanation:
1/(3/4)
=4/3
9/8*4/3
=1.5 teaspoons
PLS GIVE BRAINLIEST
7% of $582 is how much?
Answer:
$541.26
Step-by-step explanation:
Please let me know if this helps
Plz mark B R A I N L I E S T