Answers
Consider the function F(x)= x³ +½x² −2x +3. Use calc and algebra to find any and all stationary points on the graph of the function.Precalc need help ASAP
Solution:
the above function has more than one root or more than one solution. The derivative of the function represents the slope of the tangent line to the curve
F(x)= x³ +½x² −2x +3, F'(x) = 3(x3-1)+(1/2)(2)(x2-1)-2(x1-1)+0
F'(x)=3x2+x-2 is the slope of the tangent line
setting the slope =0 and solving the quadratic equations, you find all the
critical points of interest
3x2+x-2=0, solve by factoring (3x-2)(x+1)=0, then 3x-2=0, x= 2/3
and x+1=0, x=-1 substituting these values of x in the original equation
you get the corresponding values of F(x) such that;
F(x)= x³ +½x² −2x +3, F(x)=(2/3)3+1/2(2/3)2-2(2/3)+3
= 8/27+4/18-4/3+3 = 8/27+2/9-4/3+3/1 = 59/27 and the first point is
(2/3, 59/27)
F(x)= x³ +½x² −2x +3, F(x)=(-1)3+1/2(-1)2-2(-1)+3
= -1+1/2+2+3 = 9/2 and the 2nd point is ( -1, 9/2)
these two points represents points where the slope of the tangent line to the curve is 0 and could be either maximum or minimum points
You can also find the y intercepts where x = 0 F(x)= x³ +½x² −2x +3, setting x = 0, y= F(x)=3 and the point ( 0,3) is a y intercept setting y = 0, then x intercepts can be found upon solving the equation x³ +½x² −2x +3 =0
Related Questions
The screen on a computer monitor has a length of 3 inches and a width of 4 inches. What is the length of the diagonal to the nearest tenth of an inch?
Answers
Answer:
0.12? i think its wrong
Step-by-step explanation:
Check the picture below.
[tex]\textit{using the pythagorean theorem} \\\\ d^2=a^2+b^2\implies c = \sqrt{a^2+b^2} \qquad \begin{cases} d=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ d = \sqrt{3^2+4^2}\implies d = \sqrt{9+16}\implies d = \sqrt{25}\implies d = 5\implies \stackrel{\textit{rounded up}}{d = 5.0}[/tex]
Lila evaluates the expression using the following steps:(−7.13+63.97)+(−54.8−3.4)−71.1+(−58.2)−129.3Describe the error that Lila made.
Answers
Lila's error was that she added -7.13 to 63.97 to get -71.1
Lila steps are as folows
(−7.13 + 63.97) + (−54.8 − 3.4) = −71.1 + (−58.2) = −129.3
In the first bracket, Lila was suppose to subtract 7.31 from 63.97 since there is a negative in front of 7.31.
So, the correct expression should be
(−7.13 + 63.97) + (−54.8 − 3.4) = 56.84 + (−58.2) = 56.84 - 58.2 = −1.36
So, Lila's error was that she added -7.13 to 63.97 to get -71.1
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Using the quadratic formula to solve 5x = 6x-
3, what are the values of x?
Answers
Answer:
x = -1
Step-by-step explanation:
Main goal move every variable towards the higher side which Makes it easier
5x-4 = 6x-3
Minus 5x on both sided
-4 = x -3
Add 3 on both sides
-1 = x
If I am ordering a custom wood frame costing $1.27 per inch and the entire area needing framing is 17" on all4 sides, how is price tabulated?
Answers
How to use is 5/8 of a gallon of paint to cover 4/5 of a walk what is the unit rate at which Martha paints in walls per gallon
Answers
Answer:
32/25
Step-by-step explanation:
Part A
As the company has increased in popularity, it has continued to add employees in all departments. The production facility manager has provided data that shows the relationship between the number of units produced in an hour and the number of workers on the production line during that hour. The data is shown in the table.
Question 1: What type of function would be model the data?
Question 3: Use the graphing tool and best fit function of the tool to write a function that models the data. Round coefficients and constants to the nearest hundredth.
Question 4: Produce about 2300 fidget spinners every hour. How many workers should Marco recommend. Show your work.
Answers
9514 1404 393
Answer:
1. a linear model
3. y = 24.97x +417.59
4. 75 workers
Step-by-step explanation:
1. A graph of the data seems to show it nearly follows a straight line. We have used a linear function to model the data.
3. The linear regression model is ...
y = 24.97x +417.59
4. The graphing calculator shows the point (x, y) ≈ (75.4, 2300) is on the line of best fit. Marco should recommend 75 workers for production of 2300 units per hour.
If you want to solve the linear equation ...
2300 = 24.97x +417.59
you get ...
x = (2300 -417.59)/24.97 ≈ 75.4
About 75 workers are needed.
What is the probability of getting an odd number total when two dice are rolled?
18/36
12/36
1/4
36/36
Answers
LCM =36
18/36×36 = 18
12/36×36 = 12
1/4×36 = 9
36/36 ×36 = 36
so it will be 1/4 since 9 is an odd number
Please hurry, question in the image.
Only real answers will get positive feedback.
Answers
Answer:
The answer is D
Step-by-step explanation:
rate my answer and I hope this helps
which of the following pairs of sets given below are equal?
Answers
Answer:
hi there is that OK for.
Step-by-step explanation:
ok bye por and thanks again and.
Write the equation of the line that passes through the given points.
(1,2.5) and (0,6.5)
Answers
Answer:
no c
Step-by-step explanation:
14. Explain why a rotation of positive 180 degrees is the same as a rotation of -180 degrees.
Answers
Answer:
t is the same because...
Step-by-step explanation:
turning -180 is like turning right turning left no matter how you turn you will still be in the opposite from which you started
In a particular class of 23 students, 14 are men. What fraction of the students in the class are
women?
Answers
Answer:
9/23
Step-by-step explanation:
w=23-m
m=14
w=23-14=9
There are 9 women
9/23
Janelle wrote the matrix addition below.
Which statement is true?
(n+4)-7=18
((m-1) +12)+0=12
((s +1)-18)+11=-28
n+(m-1) + (s+1) =-28
TIMED TEST PLEASE HELP!
Answers
Answer:
I think the second option is the right answer
So it will be ((m-1)+12)+0=12.
BRAINLIEST What is the probability of getting an odd number total when two dice are rolled?
18/36
12/36
1/4
36/36
Answers
Answer:
18/36
Step-by-step explanation:
There are 36 possible outcomes (6x6). Half of them (18) are odd.
A gym is selling monthly memberships for $40 each and reusable water bottles for $6 each. The gym needs to make $1248 by the end of the month.
Enter a linear equation that describes the problem.
An equation for the amount of money made by the gym is = $1248, where m is the number of monthly memberships sold, an
Answers
1248 = 40m + 6w
Or, in general form
20m + 3w - 624 = 0
84 divided 5,376 ? (Show work)
Answers
Answer:
64
Step-by-step explanation:
6 4
8 4 5 3 7 6
- 5 0 4
3 3 6
- 3 3 6
0
Which are equivalent to 2 3/4 x 8/9? Check all that apply.
Answers
Answer:
The second, fourth one
Step-by-step explanation:
2nd: First thing you need to do is make 2 3/4 into a fraction so you would multiple 4x2 and add 3 which gives you 11. So you get 11/4 x 8/9
4th: Using the number from the 2nd you gte 11/4 x 8/9. WHen you multiple fractions you multiply straight accross so 11x8 and 4x9 which gives you 88/36
I have to get this done by today pls help me
Answers
Answer:
16
Step-by-step explanation:
d = 800
t = ( 1 / 500 ) d
t = ( 1 / 500 ) 800
= 800 / 500
t = 1.6 hours
divide 60 crayons between 2 pupils so that get twice as many as the other
Answers
Answer:
First pupil will have 40 crayons
Second pupil will have 20 crayons
Step-by-step explanation:
Ratio will be 2:1, total ratio = 2+1 = 3
First pupil
[tex] = { \tt{ \frac{2}{3} \times 60 }} \\ \\ = { \tt{40 \: crayons}}[/tex]
Second pupil
[tex] = { \tt{ \frac{1}{3} \times 60}} \\ \\ = { \tt{20 \: crayons}}[/tex]
Monday evening, the jar of M & M's© is full. Tuesday, 1 8 of the M & M's are eaten. Wednesday, 1 3 of the M & M's that remained disappeared. Thursday morning, first thing, the jar had 42 M & M's remaining. How many M & M's were in the jar on Monday evening? M & M's
Answers
9514 1404 393
Answer:
72 M&Ms
Step-by-step explanation:
We understand the problem to say ...
Monday the jar was fullTuesday the jar was 7/8 full (1/8 gone)Wednesday, the jar was (7/8)(2/3) = 7/12 fullThat 7/12 full condition corresponds to 42 M&Ms being present.
42 = 7/12·full
full = 42(12/7) = 72
There were 72 M&Ms in the jar on Monday evening.
_____
Check
1/8 of 72 = 9 were eaten Tuesday
1/3 of the remaining 63 disappeared on Wednesday. That number is 21, so 63-21 = 42 remained after Wednesday. That is the number seen early Thursday.
There were 72 M & M's in the jar on Monday evening
How to determine the number of M & M's?Let the initial number be x.
When 1/8 of the M & M were eaten on Tuesday, the remaining proportion is:
Remaining = (1 - 1/8) * x
This gives
Remaining = 7x/8
When 1/3 of the M & M disappeared on Wednesday, the remaining proportion is:
Remaining = (1 - 1/3) * 7x/8
This gives
Remaining = 7x/12
On Thursday, the remaining number of M & M is 42.
This means that:
7x/12 = 42
Divide both sides by 7
x/12 = 6
Multiply both sides by 6
x = 72
Hence, there were 72 M & M's in the jar on Monday evening
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Suppose that your saving account earns interest at an APR of 1.8%, compounded daily. Determine the annual percentage yield (APY) of your saving account.
Answers
The annual percentage yield of your saving account will be 1.82%
One method of slowing the growth of an insect population without using pesticides is to introduce into the population a number of sterile males that mate with fertile females but produce no offspring. If P represents the number of female insects in a population, S the number of sterile males introduced each generation, and r the population's natural growth rate, then the female population is related to time t by
t =
P+S
P[(r−1)P − S]
dP
Suppose an insect population with 10,000 females grows at a rate of r = 0.10 and 900 sterile males are added in each generation. Evaluate the integral to give an equation relating the female population to time. (Note that the resulting equation cannot be solved explicitly for P.)
Answers
now, to do partial fraction decomposition, consider
(P+S)/P((r-1)P-S) = A/P + B/((r-1)P-S)
P + S = A((r-1)P -S) + PB
if P = 0, then:
A = -1
If (r-1)P - S = 0
=> p = S/(r-1)
B = 1 + r - 1
B = r
Therefore
t = integral(-1/P + (r-1+1)/((r-1)P - S))dP
t = -ln|P| + ln|(r-1)P-S| + 1/r-1 * integral((r-1)/[(r-1)P-S])
t = -ln|P| + ln|(r-1)P-S| + ln|(r-1)P-S|/(r-1)
t = -ln|P| + (r/r-1)ln|(r-1)P-S|
substituting known constants, we get:
t = -ln|P|-1/9(ln|-0.9P - 900|)
t = -ln|P| - 1/9(ln|-0.9P -900|)
t = -ln|P| - 1/9(ln(|(-9/10)(P + 1000)|))
t = -ln(P) - 1/9ln(P + 1000)- 1/9ln(9/10)
as P >= 0, ln(P) and ln(P + 1000) doesn’t need abs value
Note that our expression for t doesn’t account for P=0 as ln(P) is undefined at P = 0.
The expression for t is also undefined at P = -1000, but that falls outside our domain P >= 0, so we don’t really need to worry about that.
The equation relating female population with time requested by t = -ln(P) - 1/9ln(P + 1000)- 1/9ln(9/10)
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given that the female population is related to time t by;
[tex]t = \int\limits {\frac{(P+S)}{P((r-1)P-S)} } \, dP[/tex]
Now, to do partial fraction;
(P+S)/P((r-1)P-S) = A/P + B/((r-1)P-S)
P + S = A((r-1)P -S) + PB
if P = 0, then:
A = -1
If (r-1)P - S = 0
p = S/(r-1)
B = 1 + r - 1
B = r
Therefore,
[tex]t = \int\limits {\frac{(P+S)}{P((r-1)P-S)} } \, dP[/tex]
t = -ln|P| + ln|(r-1)P-S| + 1/r-1 x integral((r-1)/[(r-1)P-S])
t = -ln|P| + ln|(r-1)P-S| + ln|(r-1)P-S|/(r-1)
t = -ln|P| + (r/r-1)ln|(r-1)P-S|
Now substituting known constants then;
t = -ln|P|-1/9(ln|-0.9P - 900|)
t = -ln|P| - 1/9(ln|-0.9P -900|)
t = -ln|P| - 1/9(ln(|(-9/10)(P + 1000)|))
t = -ln(P) - 1/9ln(P + 1000)- 1/9ln(9/10)
as P >= 0, ln(P) and ln(P + 1000) doesn’t need abs value
Therefore, the equation relating female population with time requested by t = -ln(P) - 1/9ln(P + 1000)- 1/9ln(9/10)
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in an auditorium,there are 104 rows with 24 seats in each row.how many seats are available?
Answers
Answer:
2,496 seats
Step-by-step explanation:
If there are 104 rows with 24 seats in EACH row, we must multiply to find the answer. Which is gives you the equation: 104 x 24 = 2,496
hope this helps!
mark me brainliest :D
use the given conditions to write an equation!!!!
Twice the sum of five and a number is 36
Answers
Answer:
2(5+x)=36
Step-by-step explanation:
Answer:
N+5=36
Step-by-step explanation:
hope this helps good luck!
Any MATHEMATICIANS IN THE HOUSE PLS
Find the equation of the circle centre (-3,4) with radius 7 units
options
(a) x2+y2+6x+8y−24=0
(b) x2+y2-6x-8y+24=0
(c) x2+y2+6x-8y-24=0
(d) x2+y2+6x-8y+24=0
Answers
Answer:
A po
Step-by-step explanation:
pa like po and pa point ty po
(x-(-3))² + (y-4)² = 7²
x2+6x+9+y²-8y+16= 49
x2+y²+6x-8y+25-49=0
x2+y2+6x-8y-24=0
answer:
B. x2+y2+6x-8y-24=0
Nicole is playing a video game where each round lasts 7/12 of an hour. She has scheduled 3 3/4 hours to play the game.
How many rounds can Nicole play?
Answers
Answer:
6 3/7
Step-by-step explanation:
solve pls brainliest
Answers
Answer:
.166 repeating
Step-by-step explanation:
you must divide the numerator by the denominator to get your final answer
Answer: 0.1666666 (6 has the bar on top of it)
Describe a situation and write an equation that you could use in your everyday life.
Answers
Answer:
Variable Costs
Step-by-step explanation:
Imagine that you are taking a taxi while on vacation. You know that the taxi service charges $9 to pick your family up from your hotel and another $0.15 per mile for the trip. So you simply make an equation as y = 0.15x+9. Math is also used in stocks we use math daily in our life, calculating prices for something we use basic multiplication and addition almost everyday.
what is the slope of the line?
Answers
What value of x would result in the numerical value of zero in the expression 7+x+(−10) ?
Answers
Answer:
x = 3
Step-by-step explanation:
So if we plug in 3 to 7+x+(-10), it simplifys to
7+3+(-10)
10+(-10)
10-10 = 0
x=3
