What is the amplitude, period, and phase shift of f(x) = -3 cos (4x + pi) +6?
Answers
(x) = -3 cos(4x + π) + 6
The amplitude is |-3| = 3
If T is the period, then
(2π)/T = 4
4T = 2π
T = π/2
The period is π/2.
The phase shift is -π/4.
The vertical shift is 6.
A graph of the function is shown below.
Answer:
Amplitude = 3.
Period = π/2.
Phase shift = -π/4
The amplitude, period, and phase shift are 9, [tex]\dfrac{\pi }{2} [/tex] and [tex]\dfrac{\pi }{4} [/tex] respectively.
Periodic functionA periodic function is a function that repeats itself after a definite time interval.
Given[tex]f(x) = -3cos(4x+\pi ) +6[/tex]
The cosine function is a periodic function that repeats itself in the interval of [tex]2\pi [/tex].
Step by step explanationFor maximun amplitude
[tex]cos(4x+\pi )=-1\\ [/tex]
Then
[tex]f(x)=3+6\\ f(x)= 9[/tex]
For time period
The cosine function repeats itself in the interval of [tex]2\pi [/tex].
[tex]\begin{aligned} \frac{2\pi }{T} &= 4 \\\\ T &=\dfrac{\pi }{2}\\ \end{aligned}[/tex]
For phase shift
Phase is [tex]\dfrac{\pi }{4} [/tex]
Thus, the amplitude, period, and phase shift are 9, [tex]\dfrac{\pi }{2} [/tex] and [tex]\dfrac{\pi }{4} [/tex] respectively.
To more about the Period function link is given below.
https://brainly.com/question/8636691
Related Questions
Factor the expression.
Answers
The values should add to the b value and multiply to the c value.
Check:
2+1=3
2*1=2
Solve 4a+3=11 plz step by step
Answers
Again, we want to work on isolating the variable a. Let's start doing this by first getting rid of the 3.
We must do the inverse of the operation, which in this case will be subtraction since the 3 is positive. Also, always remember that when we do something on one side of the equation, we must do it on the other.
4a + 3 - 3 = 11 - 3
4a = 8
Since the 4 is multiplying our variable a, this means the inverse of the operation will be division. To fully isolate a by getting rid of the 4, we will divide by 4 on both sides.
4a / 4 = 8 / 4
a = 2
Hopefully, this helps.
The value of solution of expression is, a = 2
We have to give that,
An expression to simplify,
4a + 3 = 11
Now, Simplify the expression by combining like terms as,
4a + 3 = 11
Subtract 3 on both sides,
4a + 3 - 3 = 11 - 3
4a = 8
Divide 4 into both sides,
a = 8/4
a = 2
Therefore, the solution is, a = 2
To learn more about the mathematical expression visit:
brainly.com/question/1859113
#SPJ6
Find the ratio of 12:7
Answers
12:7 can equal 24:14 (multiply both by 2) 36:21 (multiply both by 3) etc etc
hope this helps
12 (2) = 24
7(2) = 14
So, your answer would mostly likely be; 24:14
Good luck on your assignment
And enjoy your day! :)
~MeIsKaitlyn :)
One pound of feathers would be easier weighing than one pound of iron
Answers
One pound of feathers = One pound of iron
In a test of a gender-selection technique, results consisted of 248 baby girls and 13 baby boys. based on this result, what is the probability of a girl born to a couple using this technique? does it appear that the technique is effective in increasing the likelihood that a baby will be a girl?
Answers
If sin 42° =2/3, then cos 48°=
Answers
Then:
sin 42° = cos(90° - 42°) = cos 48°
IF sin 42° = 2/3, the cos 48° = 2/3
if sin42=2/3 then cos(90-42)=2/3 as well (90-42=48)
The linear function y = 1.2x represents Alberto’s speed, y, in meters per minute, when his stride rate is x steps per minute. Alberto’s average stride rate during a 10-kilometer race is 180 steps per minute.
What is Alberto’s average speed during the race?
Answers
y = meters per minute
x = steps per minute = 180
y = 1.2 (180)
y = 216 meters per minute
Answer:
What is Alberto’s average speed during the race?
216 meters per minute
Based on the linear model, which is the best prediction of how long it will take Alberto to finish the 10-kilometer race?
B. 46 minutes
Which sequence can be defined by the recursive formula f (1) = 4, f (n + 1) = f (n) – 1.25 for n ≥ 1? 1, –0.25, –1.5, –2.75, –4, . . . 1, 2.25, 3.5, 4.75, 6, . . . 4, 2.75, 1.5, 0.25, –1, . . . 4, 5.25, 6.5, 7.75, 8, . . .
Answers
Answer:
[tex]4,2.75,1.5,0.25......[/tex]
Step-by-step explanation:
f (1) = 4, [tex]f (n + 1) = f (n) - 1.25[/tex]
To get the sequence we start with n=1
Plug in n=1 in the formula
[tex]f (n + 1) = f (n) - 1.25[/tex]
[tex]f (1 + 1) = f (1) - 1.25[/tex]
[tex]f (2) = f (1) - 1.25[/tex], replace f(1)=4
[tex]f (2) = 4 - 1.25=2.75[/tex]
n=2
[tex]f (2 + 1) = f (2) - 1.25[/tex]
[tex]f (3) = f (2) - 1.25[/tex], replace f(2)=2.75
[tex]f (3) = 2.75 - 1.25=1.5[/tex]
n=3
[tex]f (3 + 1) = f (3) - 1.25[/tex]
[tex]f (4) = f (3) - 1.25[/tex], replace f(3)=1.5
[tex]f (4) = 1.5 - 1.25=0.25[/tex]
Sequence is [tex]4,2.75,1.5,0.25......[/tex]
Answer:
C.
4, 2.75, 1.5, 0.25, –1
Step-by-step explanation:
Krystal left the hardware store and traveled toward the recycling plant at an average speed of 61 mph. Scott left at the same time and traveled in the opposite direction with an average speed of 65 mph. Find the number of hours Scott needs to travel before they are 252 mi. Apart
Answers
Since Krystal and Scott is heading on opposite directions, therefore the distance between the two would be the sum of their distances from where they left, so:
total distance (d) = distance covered by Krystal (dK) + distance covered by Scott (dS)
d = dK + dS
We know that the formula for distance is:
distance = velocity * time
So,
d = vK * t + vS * t
where
vK = velocity of Krystal = 61 mph
vS = velocity of Scott = 65 mph
d = 252 miles
Therefore:
252 = 61 t + 65 t
126 t = 252
t = 2 hours
Therefore Scott needs to travel for 2 hours.
What is the value of the 30th percentile for the data set 6283, 5700, 6381, 6274, 5700, 5896, 5972, 6075, 5993, 5581?
Answers
The 30th percentile for the given data set is 5758.8, calculated by arranging the data in ascending order and interpolating between the 3rd and 4th values.
To find the 30th percentile for the given data set, first arrange the data in ascending order and then calculate the rank of the 30th percentile. The formula to find the kth percentile for a data set with n observations is:
Rank = (k/100) * (n + 1)
For the given data set of 10 values, the 30th percentile rank would be:
Rank = (30/100) * (10 + 1) = 3.3
Since the rank is not a whole number, the 30th percentile lies between the 3rd and 4th values in the ordered set. After arranging the data:
5581
5700
5700
5896
5972
5993
6075
6274
6283
6381
The 3rd and 4th values are 5700 and 5896. We must interpolate to find the exact 30th percentile:
30th Percentile = 5700 + 0.3 * (5896 - 5700) = 5700 + 0.3 * 196 = 5700 + 58.8 = 5758.8
The 30th percentile is 5758.8.
The product of twice a number and three three is the same as the difference of five five times the number and three fourths 3 4. find the number.
Answers
Given,
[tex]2x*3 = 5x - \frac{3}{4} [/tex]
[tex]6x = 5x - \frac{3}{4} [/tex]
[tex]x = - \frac{3}{4} [/tex]
The ordered pairs below represent a relation between x and y. (-3,-3), (-2,0), (-1,3), (0,6), (1,9), (2,12).
Could this set of ordered pairs have been generated by a liner function?
A. No, because the y-values decrease then increase
B. Yes, because the relative difference between y-values and x-values is the same no matter which pairs of (x,y) values you use to calculate it
C. No, because the distance between consecutive y-values is different than the distance between consecutive x-values
D. Yes, because the distance between x-values is inconstant
Answers
are matched respectively to -3, 0, 3, 6, 9, 12.
Thus, as the x-coordinate changes by 1, the y-coordinate changes by 3:
We can represent this change by the following picture:
|
|
(2,12) _ |
|
|
(1,9) _ |
|
|
(0,6) _ |
So, the points are on a straight line, because:
B. Yes, because the relative difference between y-values and x-values is the same no matter which pairs of (x,y) values you use to calculate it
Choose the correct description of the graph of the compound inequality x - 3 less than or equal to 5
A- open circle on 8, shading to left
B- closed circle on 8, shading to left
C- open circle on 8, shading to right
D- closer circle on 8, shading to right
Answers
x < = 5 + 3
x < = 8
closed circle on 8 (it is closed because there is an equal sign in the problem)...and since it is less then, it will be shaded to the left.
Answer:
B- closed circle on 8, shading to left.
Step-by-step explanation:
We have been given an inequality [tex]x-3\leq 5[/tex]. We are asked to choose the correct description of the graph of the compound inequality.
Let us solve for x.
[tex]x-3+3\leq 5+3[/tex]
[tex]x\leq 8[/tex]
Since we have been given a less than or equal to sign, so we will have a solid dot at [tex]x=8[/tex].
Since the solutions for our given inequality are less than and equal to 8, so we will shade in all values of x that are to the left of 8.
Therefore, option B is the correct choice.
Follow the process of completing the square to solve 2x2 + 8x - 12 = 0. How will the left side of the equation factor in step 5?
A. (2x + 32)2
B. (4x + 8)2
C. (4x + 16)2
Answers
with form
ax^2+bx+c=0
move c to the other side
2x^2+8x=12
x^2 is multiplied -> divide equation by 2
x^2+4x=6
complete square:
divide b=4 by 2
4*1/2=2
square 2
2^2=4
add 4 to both sides
x^2+4x=6
x^2+4x+4=6+4
x^2+4x+4=10
transform to polynom
(x+2)^2=10
this left side is option B multiplied by a factor of 16 and therefore equal:
(4x + 8)^2
(4*4)x^2+(4*2*8)x+8*8
16x^2+64x+64
x^2+4+4
bonus: calculate root
x+2=+/-sqrt(10)
x=-2+/-sqrt(10)
so it is option B
Complete the square to solve [tex]2x^2 + 8x - 12 = 0[/tex].
Soooooooo, [tex](4x + 8)^2[/tex] is your answer. :)
Solve the inequality. Graph the solution set. 26 + 6b 2(3b + 4)
Answers
we have
[tex]26 + 6b\geq2(3b + 4)[/tex]
Applying the distributive property on the right side
[tex]26 + 6b\geq6b+8[/tex]
subtract [tex]6b[/tex] from both sides
[tex]26\geq 8[/tex] -------> is true
for all real numbers the inequality is true
therefore
the graph is a shaded area everywhere.
the answer is
the solution is all real numbers
The solution is all real numbers.
It is required to find the solution.
What is inequality?The relation between two expressions that are not equal, employing a sign such as ≠ ‘not equal to’, > ‘greater than’, or < ‘less than’.
Given:
Applying the distributive property on the right side
26+6b≥6b+8
Then subtract 6b from both sides we get,
26≥8
For all real numbers the inequality is true.
Therefore, the solution is all real numbers.
Learn more details about inequality here:
https://brainly.com/question/20383699
#SPJ2
Janelle is at the movie theater and has $20 to spend.
She spends $8 on a ticket and wants to buy some snacks. Each snack costs $4.99.
How many snacks, x, can Janelle buy?
Inequality: 20≥8 + 4.99x
Please answer, its urgent
Answers
After purchasing a movie ticket for $8, Janelle has $12 left to spend on snacks. Each snack costs $4.99, which means she can buy a maximum of 2 snacks.
Explanation:Janelle started with $20 and has already spent $8 on a ticket, leaving her with $20 - $8 = $12 for snacks. Each snack costs $4.99. To determine how many snacks, represented by x, Janelle can buy, we can set up the inequality 12 ≥ 4.99x. Dividing both sides of the inequality by the cost of one snack (4.99) gives us x ≤ ≈ 2.4. Since Janelle cannot buy a fraction of a snack, she can buy a maximum of 2 snacks with her remaining $12.
Learn more about the Inequality problem here:https://brainly.com/question/15086723
#SPJ12
Solution of this equation
Answers
5x - 2.5y = 5
Align the variables to make solving this easier.
2.5y + 3x = 27
-2.5y + 5x = 5
You can see that the 2.5y and -2.5y cancel each other out. Then add the 3x and 5x, and 27 + 5.
3x = 27
5x = 5
8x = 32
Divide both sides by 8.
x = 4
Now input that x into one of the equations to get y.
2.5y + 3(4) = 27
2.5y + 12 = 27
2.5y = 15
y = 6
The answer to this system of equations is x = 4, y = 6. (4, 6)
A man can run a mile in 4 minutes. calculate his average speed in kilometers per hour. show your work. (1 mile = 1.61 km)
Answers
1 mile =1.61km
60 minutes per hour
60/4 = 15 ( he can run 15 miles in one hour)
15 x 1.61 = 24.15 km per hour
round your answer if needed
The man's average speed in kilometers per hour is calculated by first converting the distance the man runs to kilometers, based on the 1 mile equals 1.61 kilometers conversion factor, and then converting time to hours, based on the 60 minutes in 1 hour conversion factor. The calculated speed is approximately 24.04 kilometers per hour.
Explanation:The man runs a mile in 4 minutes. Given that 1 mile equals 1.61 kilometers, we can first change the distance the man runs into kilometers: 1 mile * 1.61 km/mile = 1.61 km. Thus, the man's speed is 1.61 km per 4 minutes.
To convert this speed into kilometers per hour, we need to convert the time from minutes to hours. We know that 1 hour is equivalent to 60 minutes, so 4 minutes is equivalent to 4/60 = 0.067 hours. Therefore, the man's average speed in kilometers per hour is 1.61 km divided by 0.067 hours, which equals about 24.04 km/hr.
Learn more about Average Speed Calculation here:https://brainly.com/question/680492
#SPJ3
An and ac are opposite rays.all of the following are true except
A = A,B,C are collinear
B = A,B,C are coplanar
C = AB = AC
D = A is between B and C
Answers
B = A, B, C are coplanar.
(I believe this should be the answer, but I'm not so sure.)
→It is given that, AB and AC are Opposite rays.
Means point ,A , B and C are collinear that is lying in the same line.
→Points are said to be Coplanar , if they lie in the same Plane.
Line segment Joining Points A, B and C lies on the same surface , so we can say that ,these points are Coplanar.
→As, AB and AC are rays , so point A will be in between C and B.
But, it can be sometimes true that,
→AB=AC
So, Incorrect Statement is:
AB=AC
Samantha wants to use her savings of $1150 to buy shirts and watches for her family. the total price of the shirts she bought was $84. the watches cost $99 each. what is the maximum number of watches that samantha can buy with her savings? (1 point)
Answers
99w = 1150 - 84
99w = 1066
w = 1066/99
w = 10.76......so she can buy 10 watches maximum
Answer:
Maximum number of watches Samantha can buy equals:
10
Step-by-step explanation:
Samantha wants to use her savings of $1150 to buy shirts and watches for her family.
The total price of the shirts she bought was $84.
The watches cost $99 each.
Let she bought x watches
then, 84+99x≤1150
subtracting by 84 on both sides, we get
99x≤1066
dividing both sides by 99, we get
x≤ 10.7676
Hence, maximum number of watches Samantha can buy equals:
10
what is the reciprocal of 0.25
Answers
Suppose the graph of a cubic polynomial function has the same zeroes and passes through the coordinate (0, -5). Write the equation of this cubic polynomial function. Recall that the zeros are (2, 0), (3, 0), and (5, 0). What is the y-intercept of this graph?
Answers
So we will let specific cubic polynomial function of the form
[tex]f(x) = a(x - x_1)(x-x_2)(x-x_3)[/tex]
As we know zeros are that point where we will get value of function equal to zero. So it is basically in form [tex](x_n , 0)[/tex]
SO in given question zeros are (2 , 0) , (3, 0) and (5,0)
So we can say [tex]x_1 = 2 , x_2 = 3 , x_3 = 5[/tex]
So required equation is
[tex]f(x) = a (x-2)(x-3)(x-5)[/tex]
[tex]= a[(x^2 - 2x - 3x + 6)(x-5)][/tex]
[tex]= a[(x^2 - 5x+6)(x-5)][/tex]
[tex]= a(x^3 - 5x^2 + 6x- 5x^2 + 25x - 30)[/tex]
[tex]= a(x^3 - 10x^2+31x-30)[/tex]
Now we have one point (0 , -5) from which graph passes.
So we say at x = 0 , f(x) = -5
[tex]-5= a (0-0+0 - 30)[/tex]
[tex]-5 = -30a[/tex]
[tex]a = \frac{-5}{-30} = \frac{1}{6} [/tex]
So required equation of cubic polynomial is
[tex]f(x) = \frac{1}{6}(x^3 -10x^2+31x-30) [/tex]
For finding y - intercept we simply plugin x = 0 in given equation.
As we know at x = 0 , value of function is -5.
So y - intercept is -5.
The equation of the function is [tex]y = \frac 16(x -2)(x -3)(x -5)[/tex], and the y-intercept of the function is -5
A cubic function is represented as:
[tex]y = a(x -x_1)(x -x_2)(x -x_3)[/tex]
The zeros are (2, 0), (3, 0), and (5, 0).
This means that:
(x1, y) = (2, 0)
(x2, y) = (3, 0)
(x3,y) = (5, 0)
So, we have:
[tex]y = a(x -2)(x -3)(x -5)[/tex]
The graph passes through the point (0,-5).
So, we have:
[tex]-5 = a(0 -2)(0 -3)(0 -5)[/tex]
Evaluate the products
[tex]-5 = -30a[/tex]
Solve for a
[tex]a = \frac{5}{30}[/tex]
[tex]a = \frac{1}{6}[/tex]
Substitute 1/6 for a in [tex]y = a(x -2)(x -3)(x -5)[/tex]
[tex]y = \frac 16(x -2)(x -3)(x -5)[/tex]
The y-intercept of the function is when x = 0.
Hence, the y-intercept of the function is -5
Read more about cubic functions at:
https://brainly.com/question/20896994
Which of the following statements is true regarding the relationship between circles and triangles? A. There are many circles that can be circumscribed about a triangle. B. There are many triangles that can be inscribed in a given circle. C. There is only one unique triangle that can be inscribed in a given circle. D. There are many triangles that can be circumscribed about a given circle.
Answers
If you do you'll find that the answer is B.
The true statement regarding the relationship between circles and triangles is option B. There are many triangles that can be inscribed in a given circle.
A circle can be characterized by its center's location and its radius's length.
How to make an inscribed circle in a triangle?There can be many different ways, one can include arc way, one can include angle bisector and perpendicular, and we can even try to discover some.
But usually, (for the angle bisector and perpendiculars), we do the following:
Divide one of the angles in half. Divide another angle in half.
The incenter, or point where they cross, is the inscribed circle's centre.
Construct a perpendicular from the triangle's centre point to one of its sides.
Draw an inscribed circle by placing the compass on the centre point and adjusting the length to where the perpendicular crosses the triangle.
The true statement regarding the relationship between circles and triangles is option B. There are many triangles that can be inscribed in a given circle.
Learn more about inscribing circle here:
https://brainly.com/question/17043518
#SPJ2
The function f(x) = 5x is an exponential function true or false
Answers
Help with math!!!!!!
Answers
Look at the piecewise function to see where x = -1.5 would fit in. For this particular function, it fits in with the first piece where it says [tex]-2.5 \ \textless \ x \le -1.5 [/tex] The rule there is simply a "-2" meaning that whatever teh input is for that piece, the output is -2
Therefore, f(-1.5) = -2
----------------------------------------------------------------
The next answer is f(0.1) = 0
The reason why is because 0.1 fits in with the third piece. The value 0.1 is between -0.5 and 0.5
----------------------------------------------------------------
Finally, x = 0.5 makes the last inequality restriction true. So therefore, f(0.5) = 1
----------------------------------------------------------------
The three answers are
-2, 0, 1
in that exact order
The annual Gross Domestic Product (GDP) of a country is the value of all of the goods and services produced in the country during a year. During the period 1985-1999, the Gross Domestic Product of the United States grew about 3.2% per year, measured in 1996 dollars. In 1985, the GDP was $577 billion. I what year did/or will the GDP equal $1.6 trillion?
Answers
The multiplier is given by 100%+3.2% = 103.2% = 1.032
The initial amount of GDP is 577 billion
We are looking to find in how many years since 1985 that the GDP equals to 1.6 trillion, this is 1.6×10³ billion
The formula for a compound growth/decay is given as
[tex] A_{n}= A_{o} (Multiplier)^{n} [/tex], where [tex] A_{n} [/tex] is the final value and [tex] A_{o} [/tex] is the intial value.
We are looking to find 'n'
1.6×10³ = 577(1.032)ⁿ
(1.6×10³) ÷ 577 = 1.032ⁿ
1060/577 = 1.032ⁿ ⇒ take log both sides
log( 1060/577 ) = log (1.032)ⁿ
log (1060/577) ÷ log (1.032) = n
n = 19.31 ≈ 19 years
The year when GDP achieves 1.6 trillion is 19 years from 1985, which will be in 2004, providing the increase rates stays the same.
Where can the lines containing the altitudes of an obtuse triangle intersect.
Answers
Answer: The lines containing the altitudes of an obtuse triangle intersect at a point which lies outside the triangle called orthocenter.
Explanation:-
A line which passes through a vertex of the triangle and is perpendicular to the opposite side is called an altitude of the triangle.
The point where all three altitudes of the triangle intersect is called its orthocenter .
Orthocenter of acute triangle lies inside the triangle.Orthocenter of right triangle lies on the triangle.Orthocenter of obtuse triangle lies outside the triangle.Find the length of the missing side. The triangle is not drawn to scale.
A. 60
B. 34
C. 169
D. 13
Answers
By the Pythagorean theorem:
a² = 12² + 5² = 144 + 25 = 169
a = √169 = 13 units
A club has 12 members. In how many ways can we select four members to go on a trip?
Answers
12C4 = 12!
----------
4! 8!
= 12*11*10*9 11*5*9 = 495
-------------- =
4*3*2*1
The sum of 2 consecutive odd interferes is 92 find the numbers
Answers
92/2 = 46
46-1 =45
46+1 =47
45+47 = 92
numbers are 45 & 47