Answers
Answer(s):
[tex]\displaystyle y = 4sin\:(2x + \frac{\pi}{2}) \\ y = 4cos\:2x[/tex]
Step-by-step explanation:
[tex]\displaystyle y = Asin(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{-\frac{\pi}{4}} \hookrightarrow \frac{-\frac{\pi}{2}}{2} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\pi} \hookrightarrow \frac{2}{2}\pi \\ Amplitude \hookrightarrow 4[/tex]
OR
[tex]\displaystyle y = Acos(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\pi} \hookrightarrow \frac{2}{2}\pi \\ Amplitude \hookrightarrow 4[/tex]
You will need the above information to help you interpret the graph. First off, keep in mind that although this looks EXACTLY like the cosine graph, if you plan on writing your equation as a function of sine, then there WILL be a horisontal shift, meaning that a C-term will be involved. As you can see, the photograph on the right displays the trigonometric graph of [tex]\displaystyle y = 4sin\:2x,[/tex]in which you need to replase "cosine" with "sine", then figure out the appropriate C-term that will make the graph horisontally shift and map onto the cosine graph [photograph on the left], accourding to the horisontal shift formula above. Also keep in mind that the −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must be careful with your calculations. So, between the two photographs, we can tell that the sine graph [photograph on the right] is shifted [tex]\displaystyle \frac{\pi}{4}\:unit[/tex]to the right, which means that in order to match the cosine graph [photograph on the left], we need to shift the graph BACKWARD [tex]\displaystyle \frac{\pi}{4}\:unit,[/tex]which means the C-term will be negative, and by perfourming your calculations, you will arrive at [tex]\displaystyle \boxed{-\frac{\pi}{4}} = \frac{-\frac{\pi}{2}}{2}.[/tex]So, the sine graph of the cosine graph, accourding to the horisontal shift, is [tex]\displaystyle y = 4sin\:(2x + \frac{\pi}{2}).[/tex]Now, with all that being said, in this case, sinse you ONLY have a graph to wourk with, you MUST figure the period out by using wavelengths. So, looking at where the graph WILL hit [tex]\displaystyle [-1\frac{1}{4}\pi, 0],[/tex]from there to [tex]\displaystyle [-\frac{\pi}{4}, 0],[/tex]they are obviously [tex]\displaystyle \pi\:units[/tex]apart, telling you that the period of the graph is [tex]\displaystyle \pi.[/tex]Now, the amplitude is obvious to figure out because it is the A-term, but of cource, if you want to be certain it is the amplitude, look at the graph to see how low and high each crest extends beyond the midline. The midline is the centre of your graph, also known as the vertical shift, which in this case the centre is at [tex]\displaystyle y = 0,[/tex]in which each crest is extended four units beyond the midline, hence, your amplitude. So, no matter how far the graph shifts vertically, the midline will ALWAYS follow.
I am delighted to assist you at any time.
Related Questions
Noah's Diner offers its clients a choice of regular and diet soda. Last night, the diner served
18 regular sodias and 57 diet sodas. What percentage of the sodas served were regular?
Answers
Answer: 24%
Step-by-step explanation:
for these problems you can use this equation: [tex]\frac{x}{n} *100=p[/tex]
where x=given quantity, n=total amount, and p is your answer.
for this problem x=18 (regular sodas)
we add the amount of regular and diet sodas to get n=75 (18+57)
when we plug it in we have [tex]\frac{18}{75} *100[/tex] which gives us our answer, p, 24%
hope this helped ♡
Tim will buy a pair of shoes that cost $120.He received a 35% discount coupon. Luckily his friend Mario gets an additional 15% discount being an employee of the store. If Mario buys the shoes for Tim, how much will Mario pay if the tax is 8%? Round your answer to the nearest centavo
Answers
Answer:
$69.60
Step-by-step explanation:
Which of the following equations has no solution?
1: 3x=5
2: 5x+7=3
3: 4x=9x
4: x=x−2
Answers
Answer:
4
Step-by-step explanation:
3x = 5:
x = 1 ⅔
5x + 7 = 3
5x = 3- 7
5x = -4
x = -⅘
4x = 9x
9x - 4x = 0
5x = 0
x = 0 / 5
x = 0
x = x - 2:
x -x = -2
0 = -2?
Answer:
4
Step-by-step explanation:
Its because x=x-2 =-2 subtract x from both sides and you get 0 so theres no solution and you get -2
Which number is an irrational number?
A) 3.5
B) √ 36
C) √ 148
D)
37
—
100
Answers
Answer:
C) √ 148
Step-by-step explanation:
The difference is
Part B 287
Find the product of the expressions.
Answers
Answer:
12
Step-by-step explanation:
Arkansas is __________ of Oklahoma?
Answers
Answer:
East
Step-by-step explanation:
Arkansas is East of Oklahoma.
Refer to the image below:
Answer: East
Step-by-step explanation:
70 points and brainliest if the answer is correct
5^4x5^7
A. 125^11
B. 15^11
C. 5^28
D. 5^11
Answers
Answer:
Option D
Step-by-step explanation:
If the bases are the same in a multiplication problem, then you can simply add the exponents. (i.e., a² × a⁶ = a²⁺⁶ = a⁸)
[tex]\bullet \rightarrow 5^4\times5^7[/tex]
[tex]\bullet\rightarrow 5^{4 + 7}[/tex]
[tex]\bullet \rightarrow \boxed{5^{11}}[/tex]
Answer: D
Step-by-step explanation:
5^4 x 5^7
You will add the exponent 4 + 7 = 11
You will keep your base 5^11
Match each equation to the situation it represents.
Answers
Answer:
First one is 10x + 5 = 35
Second one is 5x + 10 = 35
Third one is 35x + 5 = 10
Find the smallest side of APQR, given that mZP = 46°, mZR = 97°, and m2Q =37°,
Answers
Answer:
|PR|
Step-by-step explanation:
The smallest side is the side that sees the angle with the smallest measure:
If we were to draw a triangle with the given information we can see that the side length with the smallest value is the one that sees angle Q, |PR|
A manager drew this box-and-whisker plot to represent the ages of the company’s 240 employees. How many employees are younger than 42?
24
48
60
75
Answers
Answer:
its 60, need proof?
Step-by-step explanation:
Answer: 60
Step-by-step explanation: I took the test and got it right. Goodluck with the rest!
The equation is :
Answer x =
Answers
Answer:
4x-11=73,
x=21
Step-by-step explanation:
11 subtracted from means -11
four times a number means 4(x) because x is the number
is = equals
so
4x-11=73
+11 +11
4x=84
/4 /4
x=4
How to be good at math???
Answers
Answer:
Step-by-step explanation:
To get good at math is to pay attention to the formulas and quiz yourself with what ever your learning over and over until you get it.
I think the best place to start would be algebra, I’ve used it in every math class since passing, and it would actually be useful in the real world.
Khan academy is one of the best resources available, they have videos on pretty much any math topic.
You watch a video, then do a few practice problems, and if you need help with the problems there’s a button that shows you the entire problem solving process. You can review and practice as much as you need, and then at the end of each topic they have a practice quiz.
Besides that I think math homework is a great way to get better. If you make mistakes on the homework you will loose less points than if you make mistakes on the test/quiz. Also, going over your mistakes is key.
If you haven’t had any good math teachers it can be very hard to learn these topics, but take it at your own pace.
With math you have to understand before you move on, or else it’s like trying to read words without knowing the alphabet.
Keep practicing, you can do it!
A trough contains a certain amount of sand. After Jamie used it to fill 2.4-kilogram bag, a 650- gram bowl, and a 3-kilogram, 125- gram pail, she realized she had a kilogram of sand left in the trough. How much sand was in the trough at first?Give your answer in grams, using a comma.
Explain how you got your answer
Answers
Answer:
7kg 275g
Step-by-step explanation:
hope this helps
Answer:
7kg 275g
Step-by-step explanation:
Add all of them together and then add what's left. Hope this helps! :)
What percent of 1/4 is 1/5
5%
16%
24%
80%
Answers
[tex]\text{Let it be x percent}\\ \\\dfrac 14 \times x\% = \dfrac 15\\\\\\\implies\dfrac 14 \times \dfrac x{100} = \dfrac 15\\ \\\\\implies x = \dfrac{400}{5} = 80\\\\\\\text{Hence the answer is}~ 80\%[/tex]
Shannon has a paper cone filled with water. The cone has a diameter of 8 centimeters and a height of 9 centimeters. Select the containers that could hold all of the water in Shannon's paper cone
Answers
how many part time and full time employees does the company have?
Answers
Answer:
there are 36 part time employees and there are 144 full time employees
Step-by-step explanation: multiply 45 by 4
then multiply 180 by 0.2 to get 36 and 180 by 0.8 and get 144
Today Zack sold twice as many bags of popcorn at the ball game as he sold last Saturday. In the 2 days he sold a total of 96 bags. Write a system of equations to determine s, the number of bags Zack sold last Saturday, and t, the number of bags he sold today?
Answers
Answer:
[tex]s=32\\t=64[/tex]
Zack sold 32 bags of popcorn last Saturday, and 64 bags of popcorn today.
Step-by-step explanation:
Start by determining what information the question gives us, and what we need to find.
Given:
Zack sold twice as many bags of popcorn as he sold last Saturday
He sold 96 bags altogether in the 2 days
Find:
s, number of bags he sold last Saturday
t, number of bags he sold today
Equation/System of Equations:
[tex]t=2s[/tex] (OR "number of bags he sold today = number of bags he sold last Saturday multiplied by 2, or twice the amount he sold last Saturday)
[tex]t+s=96[/tex] (OR "number of bags he sold today + number of bags he sold last Saturday is equivalent to the amount of bag he sold altogether which is 96 bags as given by the question)
Solve:
We can solve this system of equations using substitution. In this case, we can substitute "2s" for "t" into the second equation giving us...
[tex]2s+s=96\\3s=96[/tex]
Divide both sides by 3. Notice that the Division Property of Equality states that if you divide on side of the equation by something, you must divide the other side by the same quantity.
[tex]s=\frac{96}{3}\\s=32[/tex]
Substitute 32 in for "s" to solve for "t"...
[tex]t=2s\\t=2(32)\\t=64[/tex]
Answer:
Zack sold 32 bags of popcorn last Saturday, and 64 bags of popcorn today.
90 is the product of five and Diego’s age use a variable D to represent Diego’s age
Answers
Answer:
Deigo is 18years of age
explaination
[tex]5 \times d = 90 \\ 5 d = 90 \\ 5d \div 5 = 90 \div 5 \\ d = 18[/tex]
this is how to solve it.
solve following problem
Answers
Answer:
p²=h²-b²
p² =10²-6²
p² =100-36
p²=64
p=( √8)²
p=8
Let [tex]x[/tex] and [tex]y[/tex] be the length and height, respectively, of the rectangle.
Let the bottom left vertex be the origin (0, 0), and position the triangle so that the bottom leg lies on the horizontal axis in the [tex]x,y[/tex]-plane. The hypotenuse of the triangle then lies on the line through (0, 0) and (6, 8), with slope 8/6 = 4/3. Then for some [tex]x[/tex] between 0 and 6, we have [tex]y = \frac43x[/tex].
This means for some fixed distance [tex]x[/tex] from the origin, the rectangle has length [tex]6-x[/tex] and height [tex]\frac43x[/tex]. Thus the area of the rectangle can be expressed completely in terms of [tex]x[/tex] as
[tex]A(x) = (6-x) \times \dfrac43x = 8x - \dfrac43 x^2[/tex]
Non-calculus method:
Complete the square to get
[tex]8x - \dfrac43 x^2 = -\dfrac43 (-6x + x^2) = 12 - \dfrac43 (9 - 6x + x^2) = 12 - \dfrac43 (x-3)^2[/tex]
which is maximized when the quadratic term vanishes at [tex]x=3[/tex], giving a maximum volume of [tex]\boxed{12\,\mathrm{in}^2}[/tex].
Calculus method:
Differentiate [tex]A(x)[/tex] and find the critical points.
[tex]A'(x) = 8 - \dfrac83 x = 0 \implies x = 3[/tex]
Differentiate again to check the sign of the second derivative at the critical point.
[tex]A''(x) = -\dfrac83 \implies A''(3) = -\dfrac83 < 0[/tex]
which indicates a local maximum at [tex]x=3[/tex]. Hence the maximum area is [tex]A(3) = 12[/tex], as before.
Help picture below problem 8
Answers
Solution :-
Here, we have been given that lines f and g are parallel. Thus, the angle measuring 135° and ∠2 are vertically opposite angles.
And we know that vertically opposite angles measure same. Thus,
∠2 = 135°
Hope that helps ~~~
How do I get the answer??
Answers
Answer:
4√10
Step-by-step explanation:
Hello!
Let's first simplify the radical.
We can do this by expanding the radical:
We need to pull out a perfect square factor to expand a radical and simplify it. In 45, we have 9 and 5 multiplied, and 9 is a perfect square.
Let's work with √45:
√45 can be written as √9 * √5 (using the rule √ab = √a * √b)√9 simplifies to 3, so it is 3√5Now we can simplify the operation in the parenthesis by combining like terms:
3√5 + √5√5 + √5 + √5 + √54√5Now using the same rule as above, we can multiply the values:
√2(4√5)4√10Your solution is 4√10
Q13
A man has a flight at 19:15 on Thursday. He must arrive at the airport 2 hours before this time to
check in.
He needs to know what time he should leave home.
He will park his car at the airport car park and it will take 15 minutes to get to the check in counter.
The distance from his house to the airport is 90 miles.
He will drive at an average of 60miles per hour.
Answers
Answer: around 6 or 5 o clock
Step-by-step explanation: hope this helps
Please solve with explanation
Answers
Try this option, all the details are in the attachment. Note the equation a) is performed with green, the equation b) with red line.
With break green line is the cureve y= -x²; with break red line is y=2x².
solve this problem pls don't spam
Answers
#3
Did solve that in one of your question
#4
Total spent
10-1/4+25-3/4+16-1/210.25+25.75+16.536+16.5₹52.54 2/3 divided by 1 1/9
Answers
Answer:
4.2 or 21/5
Step-by-step explanation:
i used demos
Answer:
4 1/5
[tex]\frac{14 * 9}{3 * 10} = \frac{126}{30}~which~is~also~4\frac{1}{5}[/tex]
help plsssssssssssssssssssssssssssssssssssssssssss
Answers
Answer:
g(40 or more)
Step-by-step explanation:
30 represents the median or the 50% mark so it cant be this
60 represents the highest amount of minutes. so this is unlikly
40 represents the hqr or the median between 30 and the max. this means that you now have 50% of 50% or 25%
The roof of a tower in a castle is shaped like a cone. The height of the roof is 30 ft, and the radius of the base is 15 ft. What is the area of the roof? What is the lateral area of the roof?
Answers
Answer:
The area of the roof: ≈2287.44 ft^2, the lateral area of the roof:≈1580.58 ft^2
Step-by-step explanation:
The area of the roof is computed by the equation of the area of a cone:
A = πr(r + [tex]\sqrt{h^{2}+r^(2) }[/tex])
(r: radius, h: height, πr^2 is the area of the base of the cone, πr[tex]\sqrt{h^{2}+r^(2) }[/tex] is the lateral area of the cone). So:
A = [tex]15\pi (15 + \sqrt{30^{2} +15^{2} } )[/tex] ≈ 2287.44 ft^2.
As I stated earlier, the lateral area of the roof can be computed:
A[tex]L[/tex]=[tex]15\pi \sqrt{30^{2} +15^{2} }[/tex] ≈ 1580.58 ft^2.
PLEASE EXPLAIN
Why is the unit in volume measured with units cubed instead of units squared?
Answers
Answer:
It's cubic because volume occupies a three dimensional space. Area is measured in a second unit of length
Step-by-step explanation:
Answer:
Volume is 3 dimensions
Step-by-step explanation:
Cubed is 3 dimensions: length, width, and height - like measuring how much water will fit in a cup. Squared is only 2 dimensions - like when you measure a piece of paper or a floor tile or a piece of fabric.
enter the correct value in each box to write the equation of the trend line in slope-intercept form
Answers
Answer:
y = -3x +15
Step-by-step explanation:
(2,9) (4,3)
slope is -6/2 or -3
use slope intercept form to solve for y-intercept
y = mx + b
9 = (-3)(2) + b
9 = -6 + b
15 = b
y = -3x + 15
Brainliest if correct
Answers
Answer:
correct answer here
Step-by-step explanation: