Answer: 90,000
Step-by-step explanation:
Consider the function below. (If an answer does not exist, enter DNE.) f(x) = 1 2 x4 − 4x2 + 5 (a) Find the interval of increase. (Enter your answer using interval notation.) Find the interval of decrease. (Enter your answer using interval notation.) (b) Find the local minimum value(s). (Enter your answers as a comma-separated list.) Find the local maximum value(s). (Enter your answers as a comma-separated list.) (c) Find the inflection points.
Answer:
Please, read the answer below.
Step-by-step explanation:
You have the following function:
[tex]f(x)=12x^4-4x^2+5[/tex]
(a) To find the intervals of increase or decrease of f(x) you first calculate the derivative of f(x):
[tex]\frac{df}{dx}=\frac{d}{dx}[12x^4-4x^2+5]\\\\\frac{df}{dx}=12(4)x^3-4(2)x=48x^3-8x[/tex] (2)
Next, you equal the derivative to zero and obtain the roots of the obtained polynomial:
[tex]48x^3-8x=0\\\\6x^3-x=0\\\\x(6x^2-1)=0[/tex]
Then, you have the following roots for x:
[tex]x_1=0\\\\x_{2,3}=\pm \sqrt{\frac{1}{6}}[/tex] = ±0.40
Hence, there are three special points.
Next, you evaluate the derivative (expression (2)) for the x values close to the x1, x2 and x3. The values of the derivative give to us the value of the slope of a tangent line in that point, and so, if the function increases or decreases:
First interval, for a number lower than -0.40
[tex]48(-0.41)^3-8(-0.41)=-0.02<0[/tex]
The function decreases in the interval:
[tex](-\inft,-\frac{1}{\sqrt{6}})[/tex]
It is necessary that after x=-0.40 the function increases until the next special point, that is x=0. Then, the interval in which the function increases is:
[tex](-\frac{1}{\sqrt{6}},0)[/tex]
By symmetry, from the point x=0 until x=0.40 the function decreases.
[tex](0,\frac{1}{\sqrt{6}})[/tex]
Next, you evaluate the expression (2) for a number higher than 0.40:
[tex]48(0.41)^3-8(0.41)=0.02>0[/tex]
Then, the function increases for the following interval:
[tex](\frac{1}{\sqrt{6}},+\infty)[/tex]
(b) Due to the results obtained in the previous step you can conclude that the local minimum are:
[tex]x_{min}=-\frac{1}{\sqrt{6}}\\\\x_{min}=\frac{1}{\sqrt{6}}[/tex]
[tex]P_1(-\frac{1}{\sqrt{6}},f(-\frac{1}{\sqrt{6}}))=P_1(-\frac{1}{\sqrt{6}},4.66)\\\\P_2(\frac{1}{\sqrt{6}},f(\frac{1}{\sqrt{6}}))=P_2(\frac{1}{\sqrt{6}},4.66)[/tex]
[tex]P_1(-\frac{1}{\sqrt{6}},0)\\\\P_2(\frac{1}{\sqrt{6}},0)[/tex]
(these are the point in which the function change of a decrease to an increase)
The same reason as before. There in one local maximum:
[tex]x_{max}=0[/tex]
[tex]P(0,f(0))=P(0,5)[/tex]
(c) The inflection points are calculated by using the second derivative:
[tex]\frac{d^2f}{dx^2}=144x^2-8=0\\\\x^2=\frac{8}{144}=\frac{1}{18}\\\\x=\pm \frac{1}{\sqrt{18}}[/tex]
Then , there are two inflection points , given by:
[tex]P_1(-\frac{1}{\sqrt{18}},f(-\frac{1}{\sqrt{18}}))=P_1(-\frac{1}{\sqrt{18}},4.82)\\\\P_2(\frac{1}{\sqrt{18}},f(\frac{1}{\sqrt{18}}))=P_2(\frac{1}{\sqrt{18}},4.82)[/tex]
Anyone know the answer?
She used 25 equally sized stones to make a path that is 12 feet long. How long is each stone
Answer:
The length of each stone is
L = 12/25 = 0.48 ft
Hope this helps!
:)
Each stone measures 0.48 feet.
What is the unitary method?The unitary method is a method in which you find the value of a unit and then the value of a required number of units.
Given here, the number of stones is 25 and it is used to construct 12 feet long then measure of each stone =12/25
=0.48 feet
Hence, Each stone measures 0.48 feet.
Learn more about the unitary method here:
https://brainly.com/question/22056199
#SPJ2
a man received a salary of 4920 in two years what is his monthly salary?
Answer:
$205 per month
Step-by-step explanation:
Answer:
$205
Step-by-step explanation:
there are 24 months in 2 years
4920/24= 205
Mrs. Morton has a special reward system for her class. When all her students behave well, she rewards them by putting 3 marbles into a marble jar. When the jar has 100
or more marbles, the students have a party. Right now, the jar has 24 marbles.
Write an inequality to determine the number of additional times, r, Mrs. Morton could reward the class in order for the students to have a party.
Will the students have a party if Mrs. Morton rewards them 31 additional times?
Choose 1 answer:
Yes
No
Inequality:
3r + 24 ≥ 100
Will the students have a party if Mrs. Morton rewards them 31 additional times?
Yes
Victor has saved $89.25 for the bicycle that he wants. The bicycle costs $129.85. Victor
writes the equation below to help him determine the additional amount that he needs to
sove to have enough to buy the bicycle.
89.25 + 129.85=2
Does Victor's equation correctly model the problem? Click the arrows to choose an answer from
each menu
An equation that correctly represents this problem can show that the sum of the
Choose
- and the Choose.
to the Choose
-
is equal
-
models this situation correctly. Victor's equation is
The equation Choose...
Choose
Answer:
Victor's equation did not correctly model the problem.
The equation that correctly modeled the problem:
$129.85-$89.25=$40.60
Step-by-step explanation:
The amount required for bicycle purchase by Victor is $129.85 out of which $89.25 has been saved,in other words,the balance required for Victor to reach his target purchase price is the difference between the total cost of $129.85 and the $89.25 already saved.
The balance required=$129.85-$89.25=$40.6
This shows that the equation put forward by Victor is wrong.
An equation that correctly represents the problem is the difference between the target savings and the amount already saved as stated above
Answer:
Victors model is incorrect,
Step-by-step explanation:
the correct model would be $89.25 + x = $129.85 or in other words the amount of money he has already + the amount of money he still needs = the total price of the bike.
An equation that correctly represents this problem can show the sum of the amount of money he already has and the amount of money he needs equals the total cost of the bicycle
I hope this helped!!
It is currently 0 degrees outside, and the temperature is dropping 4 degrees every hour. The temperature after h hours is -4h. It can be described with the equation -4h=-14. What value of h makes the equation true?
The equation is -4h = -14
To find h, divide both sides of the equation by -4:
H = -14 / -4
H = 3.5 hours.
148, 139, 109, 146, 141, 179, 187, 131, 149, 141 What is the mean absolute deviation of the data set
Answer:
The mean absolute deviation is 15
Step-by-step explanation:
First you have to find the mean, which in this case is 147.
Then you need to find the difference between each individual number and the mean. Once you have all the diffences written down, you need to add all the differences together. If you take the sum of the differences and divide them by the mean, you'll get your answer!
Let me know if that makes sense! :)
whats the product of 6 and
q
Answer:
6q or 6 * q
Step-by-step explanation:
As you do not know what the value of the variable q is, you are essentially changing it from word form to expression form.
"product" in math means multiply, so you are multiplying 6 with q.
6q is your answer.
~
Answer:
6+9=15
6×9=54
Step-by-step explanation:
didnt know which one you wanted but hope this helps
Given f(x)=2x^2-8x+6 and g(x)=3x-1, what is f(x)+g(x) ?
Answer:
2x^2 -5x +5
Step-by-step explanation:
f(x)=2x^2-8x+6 and g(x)=3x-1
f(x)+g(x) = 2x^2-8x+6 +3x-1
Combine like terms
= 2x^2 -5x +5
Answer:
2x^2 -5x +5
Step-by-step explanation:
Which of these expressions is equivalent to log (9^2)?
A. log (2) - log (9)
B. 2 * log (9)
C. log (2) + log (9)
D. log (2) * log (9)
Answer:
B. 2 * log (9)
Step-by-step explanation:
I put them both into my calculator and got the same answer both times.
The expression that is equivalent to log(9^2) is 2log89. Option B is correct.
According to the law of logarithm,
log (a^b) = blog a
Note that the power of the function is taken to the back of the logarithmic function.
Given the log function log(9^2), to get the equivalent expression, we will simply take the power which is 2 to the back of the log function to have 2log9
Learn more here: https://brainly.com/question/23882267
(X-2)2+(y-3)2=16
X+y-1=0
Answer:
1. x=13
2.x=1
Step-by-step explanation:
What is the quotient
x24 - x18 + x12 ÷ x6
Answer:
Simplified expression: x^18 - x^12 + x^6
Step-by-step explanation:
1. Let us write down the question at hand, firstly: x^24 - x^18 + x^12/ x^6
2. Let us factor equation x^24 - x^18 + x^12/ x^6 ⇒ x^12(x^12 - x^6 + 1)/ x^6
3. Now apply exponential rules to get x^6 to the numerator:
x^12 - 6(x^12 - x^6 + 1)
4. Simplify this expression to be ⇒ x^6(x^12 - x^6 + 1)
5. And further simplify this expression by distributing the x^6:
Answer: x^18 - x^12 + x^6
An assembly line is operating satisfactorily if fewer than 2 % of the phones produced per day are defective. To check the quality of a day's production, the company randomly samples 5 0 phones from a day's production to test for defects. Define the population of interest to the manufacturer. all the phones produced during the day in question the 50 phones sampled and tested the 2% of the phones that are defective the 50 responses: defective or not defective
Answer:
all the phones produced during the day in question.
Step-by-step explanation:
Okay, we are given the following data or information or parameters in the question above and they are; 2 % of the phones produced per day are defective, the quality of a day's production was checked by sampling 50 samples randomly.
Therefore, the best option or Explanation that best Define the population of interest to the manufacturer is; ''all the phones produced during the day in question''.
Also, the 50 phones that are sampled randomly and 2% which are defective is a condition that the manufacturer should be interested in.
some help?I don't know how to solve it
What is the slope of the line that contains these points?x 15,17,19,21 y -10,2,14,26
Answer:
6
Step-by-step explanation:
The slope (m) can be found using the formula ...
m = (y2 -y1)/(x2 -x1)
Any pair of points will do. We can use the first two.
m = (2 -(-10))/(17 -15) = 12/2
m = 6
The slope of the line is 6.
Answer: 6
Step-by-step explanation:
A roulette wheel has 38 slots, of which 18 are black, 18 are red,and 2 are green. When the wheel is spun, the ball is equally likelyto come to rest in any of the slots. One of the simplest wagerschooses red or black. A bet of $1 on red returns $2 if the balllands in a red slot. Otherwise, the player loses his dollar. Whengamblers bet on red or black, the two green slots belong to thehouse. Because the probability of winning $2 is18/38, the meanpayoff from a $1 bet is twice 18/38, or 94.7 cents. Explain what the law of large numberstells us about what will happen if a gambler makes very many betson red.
Answer:
Step-by-step explanation:
The question says,
A roulette wheel has 38 slots, of which 18 are black, 18 are red,and 2 are green. When the wheel is spun, the ball is equally likely to come to rest in any of the slots. One of the simplest wagers chooses red or black. A bet of $1 on red returns $2 if the ball lands in a red slot. Otherwise, the player loses his dollar. When gamblers bet on red or black, the two green slots belong to the house. Because the probability of winning $2 is 18/38, the mean payoff from a $1 bet is twice 18/38, or 94.7 cents. Explain what the law of large numbers tells us about what will happen if a gambler makes very many betson red.
The law of large numbers tells us that as the gambler makes many bets, they will have an average payoff of which is equivalent to 0.947.
Therefore, if the gambler makes n bets of $1, and as the n grows/increase large, they will have only $0.947*n out of the original $n.
That is as n increases the gamblers will get $0.947 in n places
More generally, as the gambler makes a large number of bets on red, they will lose money.
A tire manufacturer has 1000 units of raw rubber to use in producing radial tires for passenger cars and tractor tires. Each radial tire requires 5 units of rubber; each tractor tire requires 20 units. Labor costs are $80 for a radial tire and $120 for a tractor tire. Suppose the manufacturer does not wish to pay more than $15,000 in labor costs and wishes to make a profit of $100 per radial tire and $250 per tractor tire. How many of each kind of tire should be made in order to maximize profit
Answer:
180 Passenger Car Tires and 5 Tractor Tires should be produced in order to maximize profit.
Step-by-step explanation:
Here, we can form two equations from the given situation.
First, we are given that the total raw tube units are 1000. And 5 units are required for passenger car tire, while 20 units are required for tractor tire. So, the equation becomes:
5 x + 20 y = 1000 -------- eqn (1)
where,
x = no. of passenger car tires produced
y = no. of tractor tires produced
Another condition is given that, maximum labor cost should be $ 15,000. Since, the labor cost is $80 for a passenger tire and $120 for a tractor tie. Thus, the equation becomes:
80 x + 120 y = 15000 -------- eqn (2)
Solving eqn (1) and eqn (2), simultaneously, we get:
x = 180
y = 5
Therefore,
No. of Passenger Car Tires Produced = x = 180
No. of Tractor Tires Produced = y = 5
Help meeeeeeeeeeeeeeeeeee
>_
Answer:
good news, the second one is relatively easy because it can be factored to (2x+1)(2x-3) which means that number two has solutions of -1/2 and 3/2
but for number one you have to either use the quadratic equation cause I've tried using synthetic division or just use the second equation to derive the first solutions so I tried move the graph up by two units and found that the intercepts are approximately (1+-√2)/2 or 1/2+-1/√2 for 4x^2-4x-1
19/20 into a percentage
Answer:
it will be 95%
hope that helps
Answer:
95 percent
Step-by-step explanation:
Since 20 is 1/5 of 100, one number is equivalent to 5 percent.
Multiply 5 by 19.
You will get your percentage.
3 and 1/4 minus 5/8 please help!
How much food can this container hold 3in 9in
Answer:
27
Step-by-step explanation:
Answer:
18Πin3
Step-by-step explanation:
The vertices of a quadrilateral are M(-4,2), N(6,2), P(6, -4), and Q(-4,-4). graph the quadrilateral. Then find the perimeter and area.
im timed and need help please THIS IS MY LAST EXAM
Answer:
P=32
A=60
Step-by-step explanation:
If you ever need to graph something quickly I recommend using Desmos (it's an online graphing calculator).
The sides end up looking like this: [tex]l=10, w=6[/tex]
Perimeter is [tex]2l+2w=2(10)+2(6)=20+12=32[/tex]
Area is [tex](10)(6)=60[/tex]
good luck!
Needs help with this
Answer:
m<1 = 50°
m<2 = 130°
m<3 = 50°
m<4 = 130°
m<5 = 50°
m<6 = 130°
m<7 = 50°
m<8 = 130°
Step-by-step explanation:
Angle 4 & Angle 2 are congruent angles because they are diagonal from each other, this lets us set m<4 = m<2.
Then solve for x.
2x-10 = x+60
x-10 = 60
x = 70
Use x to find m<4 or m<2 (doesn't matter which b/c they are equal).
m<2 = (70)+60
m<2 = 130°
Angles 2, 4, 6 & 8 are congruent, so they will all have be 130°.
Angles 1 & 2 create a straight line (180°).
Find m<1 by subtracting 130° from 180°.
180-130 = 50
Angles 1, 3, 5 & 7 are also congruent, so they will all have be 50°.
Lorelei tosses a coin 4 times. What is the probability of tossing four heads? Express as a percent. Round to the nearest tenth if necessary.
Answer:
6.2%
Step-by-step explanation:
For each time the coin is tossed, there are only two possible outcomes. Either it is heads, or it is not. The probability of a toss resulting in heads is independent of other tosses. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
Fair coin:
Equally as likely to be heads or tails, so [tex]p = 0.5[/tex]
Lorelei tosses a coin 4 times.
This means that [tex]n = 4[/tex].
What is the probability of tossing four heads?
This is P(X = 4).
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 4) = C_{4,4}.(0.5)^{4}.(0.5)^{0} = 0.062[/tex]
0.062 = 6.2% probability of tossing four heads
Farmer Smith Jr is putting together fruit baskets. He has 240 oranges and 150 grapefruits. What is the largest number of baskets he can put together so that he can have the same number of oranges in each basket and the same number of grapefruits in each basket?
Answer:
why does it say college even tho this is a question on my homework
Step-by-step explanation:
and i'm in 7th grade.
A flagpole casts a shadow that is 36 feet long, while a yardstick casts a shadow of 48 inches long. About how tall is the flagpole?
Answer:
27 ft
Step-by-step explanation:
The object is 3/4 times as tall as the shadow it makes. (1 yd/48" = 3'/4') So, the flagpole will be 3/4 times 36 ft, or 27 ft high.
The flagpole is 27 ft tall.
one third of a number is 12
what is half of that same number?
Answer:
18
Step-by-step explanation:
12 x 3 = 36
36 / 2 = 18
18 x 2 = 36
The answer is 18
Please help ASAP! Will give BRAINLIEST! Please read the question THEN answer correctly! No guessing.
Answer:
f is the correct option pls mark me as the brainliset
Answer:
D, E, F
Step-by-step explanation:
because you need to do this when you are gathering resources
PLEASE HELP WITH THIS EASY QUESTION!! EXPLANATION NEEDED!!
Answer:
100
Step-by-step explanation:
(b/2)^2
b= -20
(-20/2)^2
(-10)^2
100
