What are the amplitude, period, and midline of f(x) = 3 cos(4x − π) + 2?
Answer:
The amplitude of the function is 3, period of the function is [tex]\frac{\pi}{2}[/tex] and midline of the function is 2.
Step-by-step explanation:
The given function is
[tex]f(x)=3\cos(4x-\pi)+2[/tex] .... (1)
The standard form of a Cosine function is
[tex]g(x)=a\cos(bx+c)+d[/tex] ... (2)
where, a is amplitude, period is [tex]\frac{2\pi}{b}[/tex] and d is midline.
From (1) and (2), we get
[tex]a=3,b=4,d=2[/tex]
The amplitude of the function is
[tex]a=3[/tex]
The period of the function is
[tex]\frac{2\pi}{b}=\frac{2\pi}{4}=\frac{\pi}{2}[/tex]
The midline of the function is
[tex]d=2[/tex]
Therefore the amplitude of the function is 3, period of the function is [tex]\frac{\pi}{2}[/tex] and midline of the function is 2.
how much would an 185 astronaut weigh on the moon?
What is the length of the third side of the right triangle?
( Best explained and correct answer gets brainliest. )
6^2 + 3^2 = x^2
36 + 9 = x^2
45=X^2
X= sqrt(45) = 3squareroot5
answer is A
to the nearest whole degree, what angle measure has a sine of .9762
In the diagram, which two points are shown to be collinear?
In the given diagram, the points that are shown to be collinear are H and E.
Collinearity in geometry refers to the condition where three or more points lie on the same straight line. In this case, points H and E are collinear as they lie on the same straight line, which is represented by a vertical double-headed arrow passing through them.
The diagram consists of two parallelograms, labeled 'I M' and 'E P', with three points inside each. In the parallelogram 'I M', the points are labeled as I, H, and J from top to bottom. Similarly, in the parallelogram 'E P', the points are labeled as F, E, and G from top to bottom. Among these points, only H and E share the same straight line, making them collinear. The other points do not share this line and hence are not collinear with H and E. This concept is fundamental in understanding geometric relationships and properties.
If s is a sequence of consecutive multiples of 3, how many multiples of 9 are there in s? (1) there are 15 terms in s. (2) the greatest term of s is 126.
a lab researcher wants to find out whether mice will run through a maze quicker during the day or at night, after training. He has 100 mice available. He randomly assigns 50 of them into ech group. He trains the first group to run the maze ar 9:00am and trains the sevond group to run the maze ar 9:00 pm. Each mouse is trained the same way, and the last 3 years run times are recored. Describe what is being measured in this experiment and what variable is being manipulated?
In this case, since the run times are the one being compared and recorded, therefore the data being measured in the experiment is the run times.
The difference of the two groups of mice is the time of the day that the mice run, day or night. Therefore the variable being manipulated is the time of the day.
Determine if the solution set for the system of equations shown is the empty set, contains one point or is infinite. 3x + 2y = 6 x - y = 2
In triangle def, FE = 13 and angle f equals 34. Find DF to the nearest tenth.
When factored, the trinomials x^2-2x-15 and x^2-9x+20 have one binomial factor in common. What is this factor?
1. x-7
2. x+7
3. x-5
4. x+5
Express 257.36 multiplied by 10 in scientific notation
The height of the oversized container is 3 m it's diameter is 2 m what is its area?
Write 121 raised to the one-half power equals 11 as a logarithmic function
What is the lateral surface area of the prism below?
1200 in2
2400 in2
1392 in2
2592 in2
Which system of inequalities is represented by the graph?
y ≤ –1/2x
y > –1
y ≥ –1/2x
y < –1
y < –1/2x
y ≥ –1
y > –1/2x
y ≤ –1
the answer is D)y ≥ 2x
y > 1
on ed
just took the test
One week, Katie Hopper earned the following commissions: Monday, $124; Tuesday, $88; Wednesday, $62; Thursday, $137; Friday, $195. Find her total amount of commissions for the week
add them together:
124 + 88 + 62 +137 +195 = $606 total
What is the missing step in this proof?
Answer:
Option C is correct.
The missing steps in this proof is; [tex]\angle 1 \cong \angle 4[/tex] and [tex]\angle 3 \cong \angle 5[/tex].
Explanation:
Given ΔABC.
Prove that: The sum of the interior angle measures of ΔABC is [tex]180^{\circ}[/tex]
Let A ,B and C forms a triangle [Given]
Parallel lines are those two lines that are always the same distance apart and never touch.
then, by the definition of parallel lines and labeling angles
DE be the line passing through B, parallel to AC, with angles as labelled in the figure as shown below in the attachment.
Alternative Interior Angle theorem states that the angles that are formed on opposite sides of the transversal and inside the two lines are alternate interior angles also this theorem says that when the lines are parallel, then the alternate interior angles are equal.
Then,
[tex]\angle 1 \cong \angle 4[/tex] and
[tex]\angle 3 \cong \angle 5[/tex] [By Alternative Interior angle theorem]
Angles are always congruent if their measures in degrees are equal.
therefore,
[tex]m\angle 1 =m\angle 4[/tex] and
[tex]m\angle 3=m\angle 5[/tex] [By Congruent Angle have equal measure] ......[1]
Straight Angles states that angles on one side of a straight line always add to 180 degrees.
From the given figure;
By the addition angle and definition of straight angle we get;
[tex]m\angle 4 +m\angle 2 +m\angle 5 =180^{\circ}[/tex] ......[2]
Substituting equation [1] in [2] we get;
[tex]m\angle 1 +m\angle 2 +m\angle 3 =180^{\circ}[/tex]
Therefore, the sum of the interior angles measures of triangle ABC is [tex]180^{\circ}[/tex]
Jennifer is on a trip and travels a distance of 150 miles. she spends some of her time walking, and some of her time travelling by train. if she spends w hours walking and t hours travelling by train, what is the meaning of 3w in the equation below? 50t + 3w =150
In the equation 50t + 3w = 150, 3w represents the distance Jennifer travels by walking in 3 hours.
Explanation:In the equation 50t + 3w = 150, the term 3w represents the distance Jennifer travels by walking. Since w represents the number of hours she spends walking, 3w represents the distance she walks in 3 hours. This is because the rate of walking is constant, so if Jennifer walks for 1 hour and covers a certain distance, she would walk 3 times that distance in 3 hours.
If BC = 4.5, CD = 7.7, and AD = 16.7, find AB to the nearest tenth.
A. 2.1
B. 28.6
C. 9.8
D. 2.2
Jack is building a deck that is 8 ft by 27.63 ft. He has the base built; he just needs to cover the surface with wood. When he gets to the hardware store he finds sheets of wood that are four ft by eight ft. Use estimation to determine how many sheets of wood he should buy to cover the surface of the deck.
Write the equation of the line that passes through the points (-2,3) and (-2,5)
Convert 7.2 ⋅ 10–3 to standard form.
72,000
7,200
0.0072
0.00072
0.0072 hope that helped
Micah takes a job with a starting salary of $78,000 for the first year. He earns a 4% increase each year. How much does Micah make over seven years? $567,840 $616,067 $718,710 $718,499
Answer:
b
Step-by-step explanation:
Evaluate 9 y 1 − y 0 9y1−y0 if y=−8 y=−8 .
Answer:
Step-by-step explanation:
Solve the inequality -2x is less than or equal to 3x + 1 is less than or equal to 10
HELP PLEASE THANKS:(
The length of a rectangle is 2 yd longer than its width. if the perimeter of the rectangle is 24 yd , find its area.
When college students are asked to solve a puzzle problem independently, only about 10% solve it correctly. then, when students who did not solve the problem were allowed to discuss the problem together, 75% got it right. this illustrates the participants' _____?
The correct answer to fill in the blank is:
“Cognitive flexibility”
Cognitive flexibility refers to a person’s ability to adapt the mental processing strategies to face new and unexpected situations or problems. In this case, some of the students who initially did not solve the problem transformed their way of solving the puzzle after the discussion thus getting it right the next time.
can someone help me with this factoring problem? I forgot how to factor.
Factor completely −3x2 + 6x − 9.
−3(x2 − 2x + 3)
−1(x2 − 6x + 9)
−3x(x2 − 2x + 3)
−3(x2 + 2x − 3)
05.02)
Two right triangles are graphed on a coordinate plane. One triangle has a vertical side of 2 and a horizontal side of 6. The other triangle has a vertical side of 10 and a horizontal side of 30.
Could the hypotenuses of these two triangles lie along the same line?
No, because they are not similar triangles
No, because one is larger than the other
Yes, because they are both right triangles
Yes, because they are similar triangles
Answer:
Yes, because they are similar triangles
Step-by-step explanation:
I got the answer right on the test