Determine the absolute maximum and minimum of f(x)= 2 cosx+ sin 2x
Answer:
2.598 and -2.598.
Step-by-step explanation:
f(x) = 2 cos x + sin 2x
f'(x) = -2 sin x + 2 cos 2x = 0 for turning points.
cos 2x = 1 - 2 sin^2 x so we have
-2 sin x + 2 - 4 sin^2 x = 0
4sin^2 x + 2 sin x - 2 = 0
2(2 sin^2 x + sin x - 1) = 0
2(2sinx - 1)(sinx + 1) = 0
sin x = 0.5, -1 when f(x) is at a turning point.
x = π/6, -π/2, 5pi/6
The second derivative is 2 cos x + 2 * -2 sin 2x
= 2 cos x - 4 sin 2x
When x = π/6, this is negative , when x = -π/2 it is positive
so x = π/6 gives a maximum f(x) and x = -π/2 gives 0 so this is a point of inflection
When x = π/6 , f(x) = 2.598
When x = 5pi/6, f(x) = -2.598.
slope of line passes through (7/20, 8/3) and (3/8, 7/9)
Answer:
[tex]slope = \dfrac{-680}{9}[/tex]
Step-by-step explanation:
We are given coordinates of two points:
Let the points be A and B respectively:
[tex]A(\dfrac{7}{20}, \dfrac{8}{3})\\B(\dfrac{3}{8}, \dfrac{7}{9})[/tex]
To find the slope of line AB.
Formula for slope of a line passing through two points with coordinates [tex](x_1, y_1)[/tex] and [tex](x_2,y_2)[/tex] is given as:
[tex]m = \dfrac{y_2- y_1}{x_2- x_1}[/tex]
Here, we have:
[tex]x_2 = \dfrac{3}{8}\\x_1 = \dfrac{7}{20}\\y_2 = \dfrac{7}{9}\\y_1 = \dfrac{8}{3}\\[/tex]
Putting the values in formula:
[tex]m = \dfrac{\dfrac{7}{9}- \dfrac{8}{3}}{\dfrac{3}{8}- \dfrac{7}{20}}\\\Rightarrow m = \dfrac{\dfrac{7-24}{9}}{\dfrac{15-14}{40}}\\\Rightarrow m = \dfrac{\dfrac{-17}{9}}{\dfrac{1}{40}}\\\Rightarrow m = \dfrac{-17\times 40}{9}\\\Rightarrow m = \dfrac{-680}{9}[/tex]
So, the slope of line AB passing through the given coordinates is:
[tex]m = \dfrac{-680}{9}[/tex]
It is estimated that 52% of drivers text while driving. How many people should a police officer expect to pull over until she finds a driver NOT texting while driving?
Answer:
2
Step-by-step explanation:
Let
P = percentage of those that text and drive
S = percentage of those that do not text and drive
P + S = 1
S = 1 - P
S = 1 - 0.52
S = 0.48
The expected number would be:
1/0.48 = 2.08
Which is approximately 2.
Therefore the expected number of people the police officer would expect to pull over until she finds a driver not texting is 2.
The number of people should a police officer expect to pull over until she finds a driver NOT texting while driving is; 2 people
Geometric Random ValueA geometric random value is one that gives a discrete time as to the the first success of an event.
Now, we are told that it is estimated that 52% of drivers text while driving. Thus, the success is a driver that is not texting, and the probability (p) is 0.52.
This means that the expected value of a geometric random variable is expressed as 1/p.
Therefore, In this question;
geometric random variable = 1/0.52
⇒ 1.923 ≈ 2
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different video games showing drug usewere observed. The duration times of drug use(in seconds) were recorded. When using this sample for a t test of the claim that the population mean is greater than 85sec, what does df denote, and what is its value
Your question is not complete, however, I have provided answers to it by suggesting that the question goes like this;
Twelve different video games showing drug use were observed. The duration times of drug use (in seconds) were recorded. When using this sample for a t test of the claim that the population mean is greater than 85sec, what does df denote, and what is its value
Answer:
df denote degree of freedom.
degree of freedom df is 11.
Step-by-step explanation:
what does df denote?
df denote degree of freedom
To find it value,
we have twelve different video games showing drug use, then, it means that the sample size "n" is 12
the degree of freedom is 1 < n ( i.e, one less than sample size)
df = n -1 = 12 -1 = 11
So, degree of freedom df is 11.
Note; use your sample size to solve the question as I don't know the exact value you were given. Thanks.
Two planes travel toward each other from cities that are about 1725 km apart at rates of 360 km/hr and 330 kr/hr. They started at the same time. In how many hours
will they meet?
hours.
The two planes will meet after
(Simplify your answer.)
Answer: 2 1/2 or 2.5 hours
Step-by-step explanation:
Add 360 and 330
360 + 330 = 690
Divide 1,725 by 690
1,725 / 690 = 2.5
The two planes will meet in 2.5 hours
The speed is the distance covered by an object at a particular time. The time it will take for the two planes to meet is 2.5 hours.
What is speed?The speed is the distance covered by an object at a particular time. Therefore, it is the ratio of distance and time.
[tex]\rm{Speed = \dfrac{Distance}{Time}[/tex]
Given that the speed of the two planes is 360 km/hr and 330 km/hr. Therefore, the relative speed of the two planes with respect to each other is,
Relative speed = 360 km/hr + 330 km/hr
= 690 km/hr
Now, since the total distance between the two cities is 1725 km. Therefore, the time it will take for two planes to meet is,
Time = Distance /Speed
= 1725 km / 690 km/hr
= 2.5 hour
Hence, the time it will take for the two planes to meet is 2.5 hours.
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A trapezoid has two bases that measure 11 cm and 8 cm. The height of the figure is 5 cm. What is the area of the
trapezoid?
O 95 cm
O 64 cm
O 47.5 cm
O 24 cm
Answer:
47.5cm
Step-by-step explanation:
A=1/2*h(b1+b2)
A=1/2*5(11+8)
A=1/2*95
A=47.5
Answer:
[tex]\boxed{Area = 47.5 cm^2}[/tex]
Step-by-step explanation:
Area of trapezoid = [tex]\frac{a+b}{2} h[/tex]
Where a = 11 cm, b = 8 cm and h = 5 cm
=> Area = [tex]\frac{11+8}{2} (5)[/tex]
=> Area = [tex]\frac{19}{2} (5)[/tex]
=> Area = [tex]\frac{95}{2}[/tex]
=> Area = 47.5 cm²
g python Suppose the instructor of the course is convinced that the mean engagement of students who become knowledgeable in the material (i.e., the eng1 population) is 0.75. Formulate null and alternative hypotheses for a statistical test that seeks to challenge this belief. What are the null and alternative hypotheses, and what type of test can be used
Answer:
Step-by-step explanation:
The null and alternative hypothesis that would seek to challenge this belief would be
Null hypothesis: u = 0.75
Alternative hypothesis: u =/ 0.75
The type of test to be used would be a one sample z test where one sample is drawn from the population and the mean engagement of students who become knowledgeable in the material is measured and tested in an experiment against the null hypothesis.
finding angle measures between intersecting lines
Answer:
[tex]\boxed{<x = 17 degrees}[/tex]
Step-by-step explanation:
<EGB = 73 degrees (Vertically Opposite angles are congruent)
=> <x = 90-<EGB (Complementary angles)
=> <x = 90-73
=> <x = 17 degrees
The population of a town is 9,000, and it grows at a rate of 7% per year. What will the population be in 6 years?
Answer:
12,780
Step-by-step explanation:
Initial population = 9000
grows 7% of 9000= 630 people in a year
after 6 yrs, number of added people = 630× 6=3780 ...... totally, population = 9000+ 3780
= 12,780
The population of the town after 6 years will be 13506.
Concept:As the population grows at r% per year and if the Current population is P, then After 'x' years, the population will be [tex]P_x = P(1 + \frac{r}{100} )^x[/tex]How to solve the given question?Initial Population, P = 9000Rate of increase in population, r = 7% per yearPeriod , x = 6 years∴ The population after 6 years,[tex]P_x = P(1 + \frac{r}{100} )^x[/tex]Thus, the population of the town after 6 years will be 13506.
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Let x be a variable, and let n be an arbitrary constant. What is the derivative of x^n?
Answer:
nx^(n-1)
Step-by-step explanation:
In interpreting a boxplot of a data set we note that the median is to the left of the center of the and the right line is longer than the left line. We can conclude that:___________.
A) The data is skewed right.
B) The data is symmetric.
C) Skewness or symmetry cannot be determined by a box plot.
D) The data is skewed left.
Answer:
Option A
Step-by-step explanation:
When the median is to the left of the center of the distribution with the right line longer than the left, we can conclude that the data is skewed to the right. Here the mean is larger than the median thus skewing the distribution to the right.
Representing this on an histogram including data will show a better description and also indica the longer right line.
6th term in the sequence -1,4,-16,64
6th term in the sequence is 1024
Answer:
1024
Step-by-step explanation:
I hope this helps!
A composition of reflections over parallel lines is the same as a __________. A. translation B. rotation C. glide reflection D. double rotation
Answer: A
Step-by-step explanation:
Answer: A.
Step-by-step explanation:
A composition of reflections over two parallel lines is equivalent to a translation.
choose the best selection for the following figure
In a certain city, 80% of the residents like coffee or tea . 30% of them like coffee. 60%
percent of them like tea. What is the probability of residents like (a) both? (b) tea but not
coffee? (c) only coffee (d) neither tea nor coffee ?
Answer:
a =10% b=50% c=20% d=20%
Step-by-step explanation:
n(CuT)=n(C)+n(T)-n(CnT)
so n(CnT)=10%
for b
tea but not coffee =nonly(T)
=n(T)-n(TnC)
=50%
for c
only coffee=nonly(C)
=n(C)-n(CnT)
=20%
A sequence starts 1, 4, 9, 16 ... The nth term is n^2. Use this fact to find the nth term of the following sequences: a) 2, 5, 10, 17 b) 2, 8, 28, 32
Answer:
n²+1
2n²
Step-by-step explanation:
We can see that 2, 5, 10, and 17 becomes 1, 4, 9, and 16 when we subtract 1.
So it adds 1. The nth will be n² + 1.
2, 8, 18, and 32 is the double of n². 1, 4, 9, and 16 are their half.
So the nth term becomes 2n².
The value of the equation is
a) The nth term of the equation is Aₙ = n² + 1
b) The nth term of the equation is Bₙ = 2n²
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
a)
Let the nth term of the equation be represented as Aₙ
Now , the sequence is
P = { 2 , 5 , 10 , 17 , .. }
when n = 1 , P₁ = 2
when n = 2 , P₂ = 5
So , the equation for the nth term is Aₙ = n² + 1
b)
Let the nth term of the equation be represented as Bₙ
Now , the sequence is
Q = { 2 , 8 , 18 , 32 , .. }
when n = 1 , P₁ = 2
when n = 2 , P₂ = 8
So , the equation for the nth term is Bₙ = 2n²
Hence , the equations are solved
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Solve the system of linear equations x - 3y = -3 x + 3y = 9
x-3y= -3x +3y=9
collect like terms
-3x will go to x and it will turn to
x+3x And -3y will go to +3y and it will turn to
×+3x=+3y+3y=9
solving time.
x+3x is 4x
3y +3y =6y
4x+6y =9
remove the 4x for now.
6y divided by 9.
3 in 6 is 2 and 3 in 9 is 3.
therefore 4x =2=9
4/2=2
2x=9.
4and half is the answer
Answer:
x = 3
y = 2
Step-by-step explanation:
x - 3y = -3
x + 3y = 9
Solve for x in the second equation.
x = 9 - 3y
Pu x as 9 - 3y in the first equation and solve for y.
9 - 3y - 3y = -3
9 - 6y = -3
-6y = -12
y = 2
Put y as 2 in the second equation and solve for x.
x = 9 - 3(2)
x = 9 - 6
x = 3
According to a report from the Center for Studying Health System Change, 20% of Americans delay or go without medical care because of concerns about cost (The wall street journal, June 26, 2008). Suppose eight individuals are randomly selected.
The probability no one delays or goes without medical care is ____________ ;
The probability only one person delays or goes without medical care is ____________.
Please keep three decimals.
Answer:
The probability no one delays or goes without medical care is 0.168;
The probability only one person delays or goes without medical care is 0.336.
Step-by-step explanation:
This problem can be modeled with a binomial random variable, with sample size n=8 and probability of success p=0.2.
The probability that exactly k Americans delay or go without medical care because of concerns about cost within the sample of eight individuals can be calculated as:
[tex]P(x=k) = \dbinom{n}{k} p^{k}(1-p)^{n-k}\\\\\\P(x=k) = \dbinom{8}{k} 0.2^{k} 0.8^{8-k}\\\\\\[/tex]
The probability no one delays or goes without medical care (x=0) is:
[tex]P(x=0) = \dbinom{8}{0} p^{0}(1-p)^{8}=1*1*0.168=0.168\\\\\\[/tex]
The probability only one person delays or goes without medical care (x=1) is
[tex]P(x=1) = \dbinom{8}{1} p^{1}(1-p)^{7}=8*0.2*0.21=0.336\\\\\\[/tex]
5x + 7y = -29 y = x + 1
Answer:
(x, y) = (-3, -2)
Step-by-step explanation:
Perhaps this is a system of equations you want the solution for.
Since you have an expression for y, substitution is a viable approach.
5x +7(x+1) = -29 . . . . . . substitute for y
12x = -36 . . . . . . subtract 7 and simplify
x = -3 . . . . . . . . . divide by 12
y = (-3) +1 = -2 . . . use the expression for y
The solution is (x, y) = (-3, -2).
What is the solution to the system of equations?
y = 3x - 10
h
2x + y = 4
04-8. 6)
O (-6, 16)
O (6.-8)
O (16.-6)
Answer:
The answer is option C
y = 1/3x - 10 ........ 1
2x + y = 4 .......... 2
Substitute the first equation into the second one
That's
2x + 1/3x - 10 = 4
7/3x = 14
Multiply through by 3
That's
7x = 42
Divide both sides by 7
x = 6
Substitute x = 6 into any of the Equations
y = 1/3x - 10
y = 1/3(6) - 10
y = 2 - 10
y = - 8
Therefore
x = 6 y = - 8
Hope this helps
A large mixing tank initially contains 1000 gallons of water in which 30 pounds of salt have been dissolved. Another brine solution is pumped into the tank at the rate of 4 gallons per minute, and the resulting mixture is pumped out at the same rate. The concentration of the incoming brine solution is 2 pounds of salt per gallon. If represents the amount of salt in the tank at time t, the correct differential equation for A is:__________.A.) dA/dt = 4 - .08AB.) dA/dt = 8 -.04AC.) dA/dt = 4-.04AD.) dA/dt = 2-.04AE.) dA/dt = 8-.02A
Answer:
(B)[tex]\dfrac{dA}{dt}=8-0.004A[/tex]
Step-by-step explanation:
Volume of fluid in the tank =1000 gallons
Initial Amount of Salt in the tank, A(0)= 30 pounds
Incoming brine solution of concentration 2 pounds of salt per gallon is pumped in at a rate of 4 gallons per minute.
Rate In=(concentration of salt in inflow)(input rate of brine)
[tex]=(2\frac{lbs}{gal})( 4\frac{gal}{min})=8\frac{lbs}{min}[/tex]
The resulting mixture is pumped out at the same rate, therefore:
Rate Out =(concentration of salt in outflow)(output rate of brine)
[tex]=(\frac{A(t)}{1000})( 4\frac{gal}{min})=\frac{A}{250}[/tex]
Therefore:
The rate of change of amount of salt in the tank,
[tex]\dfrac{dA}{dt}=$Rate In-Rate out\\\dfrac{dA}{dt}=8-\dfrac{A}{250}\\\dfrac{dA}{dt}=8-0.004A[/tex]
The manager of a computer retail store is concerned that his suppliers have been giving him laptop computers with lower than average quality. His research shows that replacement times for the model laptop of concern are normally distributed with a mean of 4.5 years and a standard deviation of 0.4 years. He then randomly selects records on 45 laptops sold in the past and finds that the mean replacement time is 4.4 years. Assuming that the laptop replacment times have a mean of 4.5 years and a standard deviation of 0.4 years, find the probability that 45 randomly selected laptops will have a mean replacment time of 4.4 years or less.
Answer:
The probability that 45 randomly selected laptops will have a mean replacment time of 4.4 years or less is P(M<4.4)=0.0468.
Step-by-step explanation:
We have a population normally distributed with mean 4.5 years and standard deviation of 0.4 years.
Samples of size n=45 are selected from this population.
We have to calculate the probability that a sample mean is 4.4 years or less.
Then, we calculate the z-score for the sample mean M=4.4 and then calculate the probability using the standard normal distribution:
[tex]z=\dfrac{M-\mu}{\sigma/\sqrt{n}}=\dfrac{4.4-4.5}{0.4/\sqrt{45}}=\dfrac{-0.1}{0.06}=-1.677\\\\\\P(M<4.4)=P(z<-1.677)=0.0468[/tex]
The probability that 45 randomly selected laptops will have a mean replacment time of 4.4 years or less is P(M<4.4)=0.0468.
Select the correct answer from the drop-down menu. The graphed linear equation is . (a) 3x-2y=-12 (b)2x-3y=-12(c) 3x+2y=12(d)3x+3y=-12
Answer:
Option (C) will be the answer.
Step-by-step explanation:
Let the equation of the given line is,
y = mx + b
Where 'm' is the slope of the line and 'b' is the y-intercept
Slope of a line passing through two points (x₁, y₁) and (x₂, y₂) is represented by,
Slope of the line (m) = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
For a line passing through (0, 6) and (4, 0)
Slope 'm' = [tex]\frac{6-0}{0-4}[/tex]
m = [tex]-\frac{3}{2}[/tex]
y-intercept of the line 'b' = 6
Therefore, equation of the line will be,
y = [tex]-\frac{3}{2}x+6[/tex]
2y = -3x + 12
3x + 2y = 12
Option (C) will be the answer.
Answer:
c is the answer
Step-by-step explanation:
3x+2y=12
NEED UGANT HELP really stuck xx
Answer:
0.6
Step-by-step explanation:
3+2=5
P (white) = 3/5 = 0.6
(Hopefully this works, if not, on hearty maths you can go back to your assigned tasks page and go back onto the task to get a new question if that makes sense)
What is the value of x?
O 40
O 70
O 140
O 160
what is the question? if u give the question , I might help and edit this :)
Answer:
i think it's 70
Step-by-step explanation:
sorry if its wrong let me know plz
Does anyone know the slope of this line?
Answer:
3/4
Step-by-step explanation:
Use [tex]\frac{rise}{run}[/tex]. From the bottom red point, you have to go up 3 and left 4 to get to the top point. That's your answer.
Solve for x: -4 - 4(2x + 1) = -4(2 + 2x)
Answer:
x = Infinite amount of solutions
Step-by-step explanation:
Step 1: Distribute
-4 - 8x - 4 = -8 - 8x
Step 2: Combine like terms
-8x - 8 = -8 - 8x
From here, we should see that both are equal to each other and if we graph them, they would be the same line. Therefore, any value of x works so our answer is infinite amount of solutions.
Answer: Infinite amount of solutions (-infinity, infinity)
Step-by-step explanation:
Hope this helped
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if 4x/2=4, then................
Answer:
x=2
Step-by-step explanation:
4x /2 = 4
Simplify the left side
2x = 4
Divide each side by 2
2x/2 = 4/2
x = 2
Define f(0,0) in a way that extends f(x,y)=x^2 - y^2/x^2 + y^2 to be continuous at the origin.
Answer:
It cannot be extended.
Step-by-step explanation:
Consider the function [tex]f(x,y) = \frac{x^2-y^2}{x^2+y^2}[/tex]. To extend this functions so it is continous at (0,0) we must define [tex] f(0,0) = \lim_{(x,y)\to(0,0)\frac{x^2-y^2}{x^2+y^2}[/tex]. However, this implies that the limit exists. So, we should find if the limit exists or not.
In this case, consider the case in which y =0. When y=0 then
[tex]\lim_{(x,y)\to(0,0) \frac{x^2-0^2}{x^2+0^2} = \lim_{x\to 0}\frac{x^2}{x^2}= 1[/tex]
But, when x=0, we get
[tex]\lim_{(x,y)\to(0,0) \frac{0^2-y^2}{0^2+y^2} = \lim_{y\to 0}\frac{-y^2}{y^2}=-1[/tex].
So, since the limit depends on how we approach to the point (0,0) the limit does not exist. So we can't extend f(x,y) so it is continous.
M is the centroid of the triangle.
CM=7, PM=10, & BQ=18
RM=[?]
Answer:
14
Step-by-step explanation:
As you can see the median containing RM is RC. Which means that RM=CM x 2
CM = 7
RM = 2*7 = 14
The length of RM from the given triangle PQR is 14 units.
What is centroid of a triangle?The point in which the three medians of the triangle intersect is known as the centroid of a triangle. It is also defined as the point of intersection of all the three medians.
Given that, M is the centroid of the triangle.
CM=7, PM=10 and BQ=18.
The centroid divides each median into two parts, which are always in the ratio 2:1.
So, RM:CM
RM:7
= 14:7
Therefore, the length of RM is 14 units.
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