plot the graph of y=cos x
Answers
Step-by-step explanation:
[tex]\displaystyle \boxed {y = sin\:(x + \frac{\pi}{2})} \\ 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}{2}} \hookrightarrow \frac{-\frac{\pi}{2}}{1} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{2\pi} \hookrightarrow \frac{2}{1}\pi \\ Amplitude \hookrightarrow 1[/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{2\pi} \hookrightarrow \frac{2}{1}\pi \\ Amplitude \hookrightarrow 1[/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 = sin\:x,[/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}{2}\: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}{2}\:unit,[/tex]which means the C-term will be negative, and by perfourming your calculations, you will arrive at [tex]\displaystyle \boxed{-\frac{\pi}{2}} = \frac{-\frac{\pi}{2}}{1}.[/tex]So, the sine graph of the cosine graph, accourding to the horisontal shift, is [tex]\displaystyle y = sin\:(x + \frac{\pi}{2}).[/tex]Now, with all that being said, in this case, sinse you ONLY have a wourd problem to wourk with, you MUST use the above formula for calculating the period. Onse you do that, the rest should be easy. 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 one unit 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.
Answer:
Step-by-step explanation:
Cosine is a trigonometric function defined as the ratio of length of adjacent side and the hypothesis in a right-angle triangle.
It is a periodic function with a period of 2pi.
Graph of its plot is attached.
Related Questions
A boat is trying to determine its speed, in feet per second. The boat spots a 245 foot tall lighthouse at point A at an angle of elevation of 12°. Five minutes later it arrives at point B after traveling in a straight line towards the light house. The angle of elevation is now 28°. What is the boat’s speed to the nearest foot per minute.
Answers
Using the slope concept, it is found that the boat traveled at a speed of 138 feet per minute.
What is a slope?The slope is given by the vertical change divided by the horizontal change, and it's also the tangent of the angle of depression.
At point A, we have that the vertical change is of 245 ft with an angle of 12º, hence the position in feet is given by:
[tex]\tan{12^\circ} = \frac{245}{x_A}[/tex]
[tex]x_A = \frac{245}{\tan{12^\circ}}[/tex]
[tex]x_A = 1152.6[/tex]
At point B, we have an angle of 28º, hence:
[tex]\tan{28^\circ} = \frac{245}{x_B}[/tex]
[tex]x_B = \frac{245}{\tan{28^\circ}}[/tex]
[tex]x_B = 460.7[/tex]
The distance in feet the boat traveled in 5 minutes was of:
[tex]d = x_A - x_B = 1152.6 - 460.8 = 691.8[/tex]
Velocity is distance divided by time, hence:
v = 691.8/5 = 138.
The boat traveled at a speed of 138 feet per minute.
More can be learned about the slope concept at https://brainly.com/question/18090623
Which graph below represents a functional relationship? A. 10 10 8 8 6 6 4 2 2 X 10864 6 8 10 10 8 6 4 4 6 8 10 -21 4 -61 -8 -8 10. -10 B. OD. 107 101 8 8 6 6 108 4 2 6 8 10 2. -2) 108 -64 2
Answers
Answer:
Graph (C)
Step-by-step explanation:
To find whether the graph\table represents a relationship or a function we have to analyze the input-output values given.
Graph A.
In this graph for every input value (x-value) there are two output values (y-values).
For x = -2, y = -2, 2
So the graph doesn't represent a function.
Graph B.
For every x value there are two y-values
For x = -5, y = -3, 3
So the graph doesn't represent a function.
Graph C.
For every input value there is a different y-value.
Therefore, graph represents a function.
Graph D.
In this graph for x = 3, y = 1, 2, 3, 4
For one value of x, there are four values of y.
Therefore, graph doesn't show the relationship.
Graph C has exactly one output (y-value) corresponding to each input (x-value), therefore, the graph that represents a functional relationship is: Graph C.
What is a Functional Relationship?A functional relationship is a relationship whereby every input in the relation has exactly one possible output.
In other words, a functional relationship must have exactly one output that corresponds to each of the input values.
Thus, graph C has exactly one output (y-value) corresponding to each input (x-value), therefore, the graph that represents a functional relationship is: Graph C.
Learn more about functional relationship on:
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a map has a scale of 1/2 inches:12 miles if the actual distance between the cities is 480 miles how far apart are they on the map
Answers
Answer:
20 inches
Step-by-step explanation:
Since there are 480 miles in total, we have to divide it by 12 so we can see how many half inches that would be.
480÷12 = 40
That would mean you can fit forty 12's in 480. Since 12 miles equals 1/2, you would multiply it by 40.
1/2 × 40 =20
This means that the distance between the cities on the map would be 20 inches.
Find the total amount of an investment of $413.99 compounded at 4.25% for 8.5 years
Answers
Answer:
Present Value = $413.99
Interest rate = 4.25%
Years = 8.5 years
Future value = P(1+I)^n
Future value = $413.99*(1+0.425)^8.5
Future value = $413.99*(1.0425)^8.5
Future value = $413.99*1.4244478
Future value = $589.707144722
Future value = $589.71
The total amount to be earned as a result of the investment for 8.5 years is $589.71.
Write the midpoint of the segment as an ordered pair (-3,2),(4,-5)
Answers
Answer:
[tex] \huge{ \bold{ \boxed{ \tt{( \frac{1}{2} \: ,\: \: \frac{ - 3}{2} )}}}}[/tex]
Step-by-step explanation:
[tex] \text{Let \: the \: points \: be \: A \: and \: B}[/tex]
[tex] \text{A( - 3 \: 2) } \longrightarrow \text{(x1 \: , y1)}[/tex]
[tex] \text{B(4 \: - 5)} \longrightarrow \text{(x2 \:, y2)}[/tex]
[tex] \underline{ \text{Finding \: the \: midpoint}} : [/tex]
[tex] \boxed{ \sf{Midpoint = ( \frac{x1 + x2}{2} \:, \frac{y1 + y2}{2} )}}[/tex]
[tex] \sf{Midpoint = ( \frac{ - 3 + 4}{2} \: , \frac{2 + ( - 5)}{2} })[/tex]
[tex] \underline{ \text{Remember}} : [/tex]
[tex] \text{( + ) * ( - ) = ( - )}[/tex]
[tex] \text{( + ) \: * \: ( + ) = ( + )}[/tex]
[tex] \text{( - ) \: * \: ( + ) = ( - )}[/tex]
[tex] \text{( - ) \: * \: ( - ) = ( + )}[/tex]
[tex] \sf{Midpoint = ( \frac{ - 3 + 4}{2} \:, \frac{2 - 5}{2}) }[/tex]
[tex] \underline{ \text{Remember}}: [/tex]
The positive integers are always added but posses the positive ( + ) sign.The negative integers are always added but posses the negative ( - ) sign.The negative and positive integers are always subtracted but posses the sign of the bigger integer[tex] \sf{Midpoint = ( \frac{1}{2} \: , \frac{ - 3}{2} )}[/tex]
[tex] \text{Hope \: I \: helped}[/tex]!
[tex] \text{Best \: regards}[/tex]!
~[tex] \text{TheAnimeGirl}[/tex]
Linda pays $24.84 for 7.2 gallons of gas.
Find the unit price in dollars per gallon.
If necessary, round your answer to the nearest cent.
Answers
Answer:
3.45
Step-by-step explanation:
24.84/7.2 = 3.45
The unit rate is $3.45 per gallon
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: Linda pays $24.84 for 7.2 gallons of gas.
Thus unit rate ( dollars per gallon) = $24.84/7.2
=$3.45 per gallon
Hence, The unit rate is $3.45 per gallon
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Gabrielle is 11 years younger than Mikhail. The sum of their ages is 77 What is Mikhail's age?
Answers
Answer:
44
Step-by-step explanation:
The relations can be written using one variable to represent Mikhail's age: m. Gabrielle's age is (m-11), so the sum of their ages is ...
m +(m -11) = 77
2m = 88 . . . . . . add 11
m = 44 . . . . . . . divide by 2
Mikhail's age is 44.
__
Additional comment
Gabrielle is 33.
You could solve this using two variables:
m - g = 11m + g = 77Adding these two equations gives the one we have above:
2m = 88
m = 44
__
You may have noticed we are given the sum and the difference of the two ages. The older Mikhail's age is half the sum of those two numbers. The younger Gabrielle's age is half their difference: (77 -11)/2 = 33. This "half the sum, half the difference" solution is the generic solution to a "sum and difference" problem.
Gabrielle : 33
Mikhail : 44
Explanation:
Let Mikhail's age be x
And Gabrielle's age be y.
======================
Gabrielle is 11 years younger than Mikhail
y = x - 11 [ equation 1 ]
sum of their ages is 77
x + y = 77 [ equation 2 ]
Insert equation 1 into 2
x + x - 11 = 77
2x = 77 + 11
2x = 88
x = 44
Therefore, the age of Mikhail is 44
Find Gabrielle's age:
y = x - 11
y = 44 - 11
y = 33
Therefore, the age of Gabrielle is 33
Identify the cluster in the data
Answers
The one that has the most circles in a group :D
Connie has two credit cards, u and v. card u has a balance of $414.55, and card v has a balance of $751.81. the minimum monthly payment on card u is 2.82% of the balance, and the minimum monthly payment on card v is 3.09% of the total balance. how much greater is the minimum payment on card v than on card u? a. $8.70 b. $10.73 c. $9.51 d. $11.54 please select the best answer from the choices provided a b c d
Answers
The minimum payment of card u of Connie is $11.54 is greater than the minimum payment of credit cart v.
What is percentage ?Percentage of a number is the part of the number expressed in the in every hundred. Percentage of a number is expressed with the symbol '%'.
Connie has two credit cards, u and v. The card u has a balance of $414.55 and the minimum monthly payment on card u is 2.82% of the balance. Thus, the minimum payment for card u is,
[tex]P_u=\dfrac{2.82}{100}\times414.55\\P_u=11.69[/tex]
Card v has a balance of $751.81 and the minimum monthly payment on card v is 3.09% of the total balance. Thus, the minimum payment for card v is,
[tex]P_v=\dfrac{3.09}{100}\times751.81\\P_v=23.23[/tex]
The difference between the minimum payment of both the cards is,
[tex]d=23.23-11.69\\d=11.54[/tex]
Thus, the minimum payment of card u of Connie is $11.54 is greater than the minimum payment of credit cart v.
Learn more about the percentage here;
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The first few steps in solving the quadratic equation 8x2 80x = −5 by completing the square are shown. 8x2 80x = −5 8(x2 10x) = −5 8(x2 10x 25) = −5 ______ which number is missing in the last step? −200 −25 25 200
Answers
The number is missing in the last step in the quadratic equation is 200. Then the correct option is D.
What is a factorization?It is the method to separate the polynomial into parts and the parts will be in multiplication. And the value of the polynomial at this point will be zero.
The quadratic equation is 8x² + 80x = −5
On adding and subtracting 200 on both sides, we have
8x² + 80x + 200 = −5 + 200
8 (x² + 10x + 25) = −5 + 200
Thus, the number is missing in the last step in the quadratic equation is 200. Then the correct option is D.
More about the factorization link is given below.
https://brainly.com/question/6810544
Please someone help me out!!!!! Bill is bying a pair of jeans that costs $20. He has to pay 5% sales tax. How much will he pay in all?
Answers
Answer:
21
Step-by-step explanation:
First determine the amount of tax
20 * .05
1
Add this to the original amount
20+1
21
He will pay 21 dollars
The Swinger family recycles about 15 pounds of waste a week. This is 2/3 of the total waste for the week. How many pounds of waste does the family produce each week?
Answers
The answer 37.5 lbs
Can someone please help me? :(
Answers
Answer: 4 units, 3 units
Step-by-step explanation:
The side length of the square is measured to be 4 units on the graph
The height can be seen to be 3 units on the graph
4 units on each side
Height is 3 units
Step-by-step explanation:
Perpendicular height is 3 squares up, from the base of the square, to the top of the triangles.
The square measures 4 by 4 on each side.
Hope this helps!
Simplify 4.2^2 x 5.1^2 x 4.2^4 x 5.1^3
Answers
Answer:
=18938545.55220... x^3
Step-by-step explanation:
than paid $40 for 5 cardio dance workout classes. He’s trying to set up an equation to help him find the cost of each class. What should Nathan put in the blank of the following equation? c=$40÷___ ?
Answers
Answer:
$40/5
Step-by-step explanation:
If you're trying to figure out the cost of each class divide the amount of money you pay in all ($40 dollars) by 5. Once you do that you should get 8, so $8 per class.
PLZ HELP!!
Choose the best answer.
Solve the equation.
e – 8 = 22
Question 1 options:
e = 14
e = 30
e = -8
e = 22
Question 2 (1 point)
Choose the best answer.
Solve the equation.
n + 11 = –29
Question 2 options:
n = 18
n = 40
n = –17
n = –40
Question 3 (1 point)
Choose the best answer.
Solve the equation.
e – 14.4 = –20.8
Question 3 options:
e = –35.2
e = 6.4
e = –6.4
e = 35.2
Question 4 (1 point)
Choose the best answer.
Solve the equation.
t – (–16) = –13
Question 4 options:
t = –3
t = 29
t = –29
t = 3
Question 5 (1 point)
Choose the best answer.
On Wednesday, William wrote a check in the amount of $45.60. This brought his balance down to –$15.75. Suppose n represents William's balance before he wrote the check.
Which equation can be used to represent this situation?
Question 5 options:
n + 45.60 = –15.75
n – 45.60 = –15.75
n – 15.75 = –45.60
n – 15.75 = 45.60
Question 6 (1 point)
Choose the best answer.
Solve the word problem.
Luke mowed a lawn today to earn some extra money. He spent $2.10 on fuel and $4.45 on lunch. He charged $13.50 to mow the lawn.
What was his profit for mowing the lawn?
Question 6 options:
$20.05
$11.15
$15.85
$6.95
Question 7 (1 point)
What is the LCD of 12 and 35
?
Question 7 options:
2
7
10
20
Question 8 (1 point)
Choose the best answer.
Which statement correctly compares512 and 716
?
Question 8 options:
512>716
512=716
512<716
Question 9 (1 point)
Add.
23+58
Question 9 options:
724
711
3124
78
Question 10 (1 point)
Add.
−23+14
Question 10 options:
14
−512
17
37
Answers
Answer:
[tex]e = 30 \\ n = –40 \\ e = –6.4 \\ t = –29 \\ n – 45.60 = –15.75 \\ 6.95 \\ the \: LCD \: of \: 12 \: and \: 35 \: is \: 2 \\{ 512 < 716} \\ 81(not \: in \: the \: option) \\ - 9(not \: in \: the \: option)[/tex]
what is the are of triangle ABC with vertices A(-2,1),B(-2,3),C(2,1)?
Answers
Answer:
A. 4 square units
Step-by-step explanation:
The area of a triangle is given by the formula ...
A = 1/2bh
Your triangle has a base of 4 units and a height of 2 units. Its area is ...
A = 1/2(4)(2) = 4 . . . . square units
__
The triangle dimensions are easily found from your diagram by counting grid squares. If you like, you can subtract the x-coordinates of the points on the horizontal line y=1 to find the base length: 2 -(-2) = 4. And you can subtract the y-coordinates of the points on the vertical line x=-2 to find the height: 3 -1 = 2.
Pls help I will award brainiest
The ratio of the number of people who
threw tomatoes onto the stage to the
number of people who threw cabbage was
8 to 9. If 168 people threw tomatoes onto
the stage, how many threw cabbage?
Answers
Answer:
189
Step-by-step explanation:
ratio is 8:9
multiply ratio by 21 to get 168:189
The number of people who threw the cabbage should be considered as the 189 when the ratio is given.
Calculation of the number of people who threw the cabbage:Since
The ratio of the number of people who threw tomatoes onto the stage to the number of people who threw cabbage was 8 to 9.
And, 168 people threw tomatoes onto the stage
So
[tex]= 168 \times 9 \div 8[/tex]
= 189
hence, The number of people who threw the cabbage should be considered as the 189 when the ratio is given.
learn more about ratio here; https://brainly.com/question/4136664
CRIS 100 A hostel had rations for 60 days for 500 students. After 12 days, 300 more students join the hostel mess How long will the remaining ration last?
Answers
Answer:
30
Step-by-step explanation:
[tex]500\times\left(60-12\right)\div\left(300+500\right)[/tex]
Calculate
[tex]\frac{500\times\left(60-12\right)}{300+500}[/tex]
Calculate the sum or difference
[tex]\frac{500\times48}{300+500}[/tex]
Calculate the sum or difference
[tex]\frac{500\times48}{800}[/tex]
Cross out the common factor
[tex]\frac{5\times48}{8}[/tex]
Cross out the common factor
[tex]5\times6[/tex]
Calculate the product or quotient
[tex]30[/tex]
Eight out of 32 students in the class wear
glasses. What is the probability that the first
student who walks out of the class will be
wearing glasses?
Answers
Answer:
[tex]\dfrac14[/tex]
Step-by-step explanation:
[tex]\mathsf{Probability \ of \ an \ event \ occurring = \dfrac{Number \ of \ ways \ it \ can \ occur}{Total \ number \ of \ outcomes}}[/tex]
If 8 students in a class of 32 wear glasses, then the probability of the first student who walks out of class wearing glasses will be:
[tex]\dfrac{8}{32}[/tex]
Simplifying:
[tex]\dfrac14[/tex]
What is the pattern for this sequence? 2 , 0 , -2 , -4 , -6 , ... A. Each number in the sequence is 3 less than the previous number. B. The sequence decreases by multiples of 3: first by 3, then 6, then 9, then 12. C. The sequence decreases by multiples of 2: first by 2, then 4, then 6, then 8. D. Each number in the sequence is 2 less than the previous number.
Answers
Answer:
I believe the correct answer is D
what is 1+2+3+4+5+6+7+8+9..+100
Answers
Answer:
5050
Step-by-step explanation:
we can use the formula n(n+1)/2
Answer:
5050
Step-by-step explanation:
because n(n+1)/2 is compatible here, which is (100x101)/2, and that gives us 5050.
Could I get some help, please?
Answers
Answer: 110 degrees
Step-by-step explanation:
A machinery worth rupees 10,500 depreciated by 5% find its value after one year
Answers
Answer:
Step-by-step explanation:
10,500*5% =525
10,500-525
=9975
3.
(a)
Expand and simplify 3(x - 3y) + 6y - 8x
SOME1 PLSS HELPP
Answers
Answer:
3(x - 3y) + 6y - 8x
Perform the distributive property;
3x - 9y + 6y - 8x ← Expanded form
Group like terms:
(3x - 8x) (-9y + 6y)
-5x - 3y ← Simplified form
Answer:
I believe it is -5x - 3y
If y=2x+3 and 2x+5=9, then y =
(A) 4 (B) 5 (C) 6 (D) 7 (E) 8
Answers
© ? Jordan invests £2100 into his bank account. He receives 5.1% per year simple interest. How much will Jordan have after 2 years? Give your answer to the nearest penny where appropriate.
Answers
Answer:
£2314.20
Step-by-step explanation:
Simple interest formula: A = P(1 + rt)
where:
A = final amountP = principal amountr = annual interest rate (as a decimal)t = time (in years)Given:
P = £2100r = 5.1% = 0.051t = 2 years⇒ A = 2100(1 + 0.051 · 2)
⇒ A = 2100(1.102)
⇒ A = £2314.20
17 Mia wants to compare the 100-meter
dash times of 14.084 seconds and
14.102 seconds. Which is the correct
way to compare these two times?
A. 14.084 > 14.102
B. 14.084 < 14.102
C. 14.102 = 14.084
D. 14.102 < 14.084
Answers
B. 14.084 < 14.102
< means : less than - smaller than
Suppose that the relation I is defined as follov T= {(-3.3), (0.7). (7.-9).(-3.-4)} at Give the domain and range of T
Answers
Answer:
The domain is the set of all the values of x. The range is the set of all the values of y.
Domain:
{−3,0,7}
Range:
{3,7,−9,−4}
pee
What is the inverse of the equation y = 3x + 2?
Answers
Answer: y = (x-2)/3
This is equivalent to y = (1/3)x - 2/3
=================================================
To get this answer, we need to swap x and y in the original equation. Then solve for y to get the inverse.
y = 3x+2
x = 3y + 2 ... x and y swapped
x-2 = 3y
3y = x-2
y = (x-2)/3
y = x/3 - 2/3
y = (1/3)x - 2/3
This final equation has slope 1/3 and y intercept -2/3