Answers
Answer(s):
[tex]\displaystyle y = 4cos\:(4\theta \pm \pi) \\ y = -4cos\:4\theta[/tex]
Step-by-step explanation:
[tex]\displaystyle y = Acos(B\theta - 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{\pm\frac{\pi}{4}} \hookrightarrow \frac{\pm\pi}{4} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\frac{\pi}{2}} \hookrightarrow \frac{2}{4}\pi \\ Amplitude \hookrightarrow 4[/tex]
OR
[tex]\displaystyle y = -Acos(B\theta - 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{\frac{\pi}{2}} \hookrightarrow \frac{2}{4}\pi \\ Amplitude \hookrightarrow 4[/tex]
You will need the above information to help you interpret the graph. First off, keep in mind that this cosine graph will have TWO equations because the curvature begins upward from [tex]\displaystyle [0, -4][/tex] instead of downward from [tex]\displaystyle [0, 4],[/tex] telling you that one equation will have a “negative” symbol inserted in the beginning of the equation. Before we go any further though, we must figure the period of the graph out. So, 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 hits [tex]\displaystyle [0, -4],[/tex]from there to [tex]\displaystyle [-\frac{\pi}{2}, -4],[/tex] they are obviously [tex]\displaystyle \frac{\pi}{2}\:unit[/tex]apart, telling you that the period of the graph is [tex]\displaystyle \frac{\pi}{2}.[/tex] Now, as you can see, the photograph on the right displays the trigonometric graph of [tex]\displaystyle y = 4cos\:4\theta.[/tex] Now, if you look hard enough, you will see that both graphs are “mirror reflections” of one another, meaning you can figure the rest of the terms out one of two ways. The first way is to figure the appropriate C-term out that will make the graph horisontally shift and map onto the original cosine graph [photograph on the left], accourding to the horisontal shift formula above. Also, keep in mind that −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 rightward graph is shifted [tex]\displaystyle \frac{\pi}{4}\:unit[/tex] on both sides of the y-axis, which means that in order to match the original graph, we need to shift the graph back, which means the C-term will be both negative and positive; and by perfourming your calculations, you will arrive at [tex]\displaystyle \boxed{\pm\frac{\pi}{4}} = \frac{\pm\pi}{4}.[/tex]So, one equation of the cosine graph, accourding to the horisontal shift, is [tex]\displaystyle y = 4cos\:(4\theta \pm \pi).[/tex] Now that we got this out the way, we can focuss on finding the second equation. Another way is to write an equation with a “negative” symbol inserted in the beginning [like I mentioned earlier]. Now, sinse we are writing an equation with the negative, the graph will not have a horisontal shift; so, C will be zero. With this said, the second equation is [tex]\displaystyle y = -4cos\:4\theta.[/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
simplify completely 3x^2+21x-54 over x^2+3x-54
Answers
Answer: 3(x-2) / x-6
Step-by-step explanation: find gcf..
in the following equation solve for t, 2t-s=p
Answers
2t=p+s Divide
t=[tex] \frac{p+s}{2}[/tex]
+s +s
2t=p+s
—- —-
2 2
T= (p+s)/2
One 16-ounce bottle of an energy drink has an average of 400 mg of caffeine with a standard deviation of 20 mg. What is the probability that the average caffeine in a sample of 25 bottles is no more than 395 milligrams?
Answers
What is one possible solution for the triangle below?
Answers
Answer:
The correct answer is C, i can promise you that
Step-by-step explanation:
the only one with Angle Z as 94.6 degrees.
One possible solution for the triangle below is:
Option D:
YZ = 95.4
∠X = 26.7°
∠Z = 85.3°
How use law of sines and cosines?If only one of these is missing, the law of cosines can be used.
3 sides and 1 angle. So if the known properties of a triangle are SSS (side-side-side) or SAS (side-angle-side), then this law applies.
If you want the ratio of the sine of an angle and its inverse to be equal, you can use the law of sine. This can be used if the triangle's known properties are ASA (angle-side-angle) or SAS.
Using Law of sine:
40/sin 68 = 43/sin Z
sin Z = (43/40) * sin 68
sin Z = 0.9967
Z = sin⁻¹0.9967
Z = 85.3°
The only option with the correct value of angle Z is Option D with:
YZ = 95.4
∠X = 26.7°
∠Z = 85.3°
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What type of conic section is the following equation? 4x2 + y2 = 36
Answers
The signs of the terms are both positive, so it is a circle or an ellipse.
The coefficients of the terms are different, so it is not a circle, it is an ELLIPSE.
Answer:
Ellipse
Step-by-step explanation:
The signs of the terms are both positive, so it is either a circle or an ellipse.
The coefficients of the terms are different, so it can not be a circle.
Therefore it is an Ellipse.
which word best describe 8(2x+4)
Answers
~~~~~~~~~~~~~~~~~~
8*2 is 16
Then 8*4 is 32.
Answer is 16x+32
Distribution it should be used 8(2x+4).
-Charlie
A coefficient is a number that is in front of a variable. Examples of this are 6 in 6x, 100 in 100s, and 45 in 45h. Thus making 8 the coefficient of the problem.
There are also no like terms (like 4 and 6 or 5x and 9x), there is no inequality sign (greater than, less than, etc), and there are no constant variables (like 2 and 7 in the equation " 2x - 2 = 7).
I hope this helps!
In a woodworking you are planing boards to make shelves. The planer is set to remove 1/16 inch from a board on each pass the board makes through the planer. If a board starts out at 3/4 inch thick, how many times will you need to send it through the planer to get it down to 5/8 inch?
Answers
Initial thickness = 3/4 in
Final thickness = 5/8 in
If x is the number of passes,
The material removed = (1/16)x in.
Therefore,
3/4 - (1/16)x = 5/8
3/4 - x/16 = 5/8
x/16 = 3/4 - 5/8 = 1/8
x = 16*1/8 = 2
Therefore, the board will be passed through the plane twice.
graph each question y =2x + 0.5
Answers
What is the structural number of a pavement section with a1, a2 a3 = 0.44, 0.14, and 0.10 respectively if the depths are 5, 10 and 10 inches?
Answers
Evaluate the expression. 10p5
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The number of permutations of n objects taken r at a time is defined as [tex]_nP_r = \dfrac{n!}{(n-r)!}[/tex].
Here, you have 10 objects and 5 of them will be taken.
So that would be 10! / (10-5)! = 10! / 5! = 30240
Final answer: 30240
Hope this helps.
Answer:
The correct answer is
30,240
Caleb bought a car for $6,900. He agreed on a five-year loan at a 5.4% interest rate. Calculate what Caleb's monthly payments will be.
Answers
To calculate Caleb's monthly car payments, use the loan amortization formula that deals with compound interest, not simple interest. Input the loan amount of $6,900, the monthly interest rate (annual rate of 5.4% divided by 12), and the total number of payments (5 years times 12 payments per year) into the formula to find the monthly payment.
Explanation:Caleb's car loan scenario comes under financial mathematics, specifically, it deals with loan amortization using the concept of compound interest. Since the car loan spans multiple years, compound interest is the accurate model to use, not simple interest. As opposed to simple interest which only accrues on the original amount or principal, compound interest accrues on the principal and all interest previously added.
The formula to calculate the monthly payment, P, on a loan is given by, where PV represents t
[tex]P = [r*PV] / [1 - (1 + r)^-n][/tex]he present value or the amount of loan, which is $6,900 in this case; r is the monthly interest rate which can be calculated as annual interest rate divided by 12, translating to 0.054/12 in this case; and n is the total number of payments (i.e., 5 years of payments with 12 payments per year, hence, 5*12).
To calculate the monthly payment, plug these values into the formula which should give you the monthly payment amount that Caleb needs to pay for his car loan.
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what is the solution to the system y= 3/4 x - 12 and y = 4x - 31
Answers
A round table top has a diameter of 2.6 meters.What is its surface area
Answers
To find the area of a circle you use the equation
[tex] \pi r^{2} [/tex]
r is radius which is half the diameter
r = 2.6 / 2
r = 1.3
Put in the values you know
[tex] \pi 1.3^{2} [/tex]
Square the number
[tex]1.69 \pi = 5.31[/tex]
The answer is [tex]1.69 \pi [/tex] or ≈5.31
Hope this helps!
remmber that [tex]A=\pi r^2[/tex] where r=radius and A is area and pi is pi or about 3.14159265
so if diameter is 2.6, ah, tricky, they give you dameter
rmemeber that d/2=r so 2.6/2=d/2=r=1.3
so
[tex]A=\pi r^2[/tex]
[tex]A=\pi (1.3)^2[/tex]
using your calculator
[tex]A=5.309 m^2[/tex]
the surface area is [tex]5.309 m^2[/tex]
The graph of a proportional relationship passes through (3, 24) and (1, y). Find y.
Answers
[tex]\bf (\stackrel{x}{3},\stackrel{y}{24})\textit{ we also know that } \begin{cases} x=3\\ y=24 \end{cases}\implies 24=k3\implies \cfrac{24}{3}=k \\\\\\ 8=k\qquad therefore\qquad \boxed{y=8x} \\\\\\ (\stackrel{x}{1},\stackrel{y}{y})\textit{ when x = 1, what is \underline{y}?}\qquad y=8(1)[/tex]
PLEASE HELP WILL GIVE BRAINLIEST!!!The table below represents the closing prices of stock ABC for the last five days
Answers
Answer:
A. [tex]y=-8.583x+475.215[/tex]
Step-by-step explanation:
We are given,
The table representing the closing prices of stock for the last five days is,
Day Value
1 472.08
2 454.26
3 444.95
4 439.49
5 436.55
Using the linear regression calculator, we have that,
The linear equation that best fits the data is [tex]y=-8.583x+475.215[/tex]Thus, option A is correct.
hey can you please help me posted picture of question
Answers
If Disc> 0, the function has two distinct roots
If Disc = 0, the function has a repeated root
If Disc < 0, the function has no real root.
The discriminant can be calculated as:
Disc = b² - 4ac
For the given equation:
Disc = 9 - 4(2)(1) =1
Since the value of discriminant is positive, the function will have two distinct roots.
So, the answer to this question is option B
What is the annual rate of productivity advance implied by moore's law? (assume linear growth from the base.) instructions: enter your response rounded to the nearest whole number. %?
Answers
hey can you please help me posted picture of question
Answers
P (m) = m / 6 + 9
Clearing m we have:
m = 6 * (p-9)
m= 6*p - 6*9
Rewriting:
m (p) = 6p-54
Answer:
The inverse function for this case is given by:
m (p) = 6p-54
option A
The solution is shown below
[tex]P(m)= \frac{m}{6} -9 \\ \\ p=\frac{m}{6} -9 \\ \\ p+9=\frac{m}{6} \\ \\ 6(p+9)=m \\ \\ m=6p+54 \\ \\ M(p)=6p+54 \\ \\ M(p)=6m+54 \\ \\[/tex]
the width of a rectangular picture is 13 in less than the length the area of the picture is 30in 2 what is the length of the picture
Answers
A = length*width
30 = x(x -13)
This quadratic equation can be put into standard form and factored to find the solutions.
x² -13x -30 = 0
(x -15)(x +2) = 0
x ∈ {15, -2}
A negative length makes no sense, so we conclude ...
the length of the picture is 15 inches.
2 would be your length. The exact length would be 2.3
Explanation:
When we multiply using the formula your answer should always add up to 2.3
If P(A or B)equals=0.60.6, P(A)equals=0.40.4, and P(A and B)equals=0.350.35, find P(B).
Answers
Answer:
P(B) = 0.55 .
Step-by-step explanation:
We are given that P(A or B) = 0.6 , P(A) = 0.4 , and P(A and B) = 0.35 .
As we know that;
P(A or B) = P(A) + P(B) - P(A and B)
0.6 = 0.4 + P(B) - 0.35
P(B) = 0.35 + 0.6 - 0.4 = 0.55
Therefore, P(B) = 0.55 .
What is the length of the hypotenuse of the triangle?
sides 7cm and 3cm
A. sqrt 20cm
B. sqrt 23cm
C. sqrt 40cm
D. sqrt 58cm
Answers
7² + 3² = c²
49 + 9 = c²
49 + 9 = 58
58 = c²
Sqrt of 58 = 7.6 cm
So the answer is D) Sqrt 58 cm.
Hope this Helps!!
The length of the hypotenuse of the triangle is √58 cm (Option D).
To find the length of the hypotenuse of a right triangle, we can use the Pythagorean theorem, which states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Let's label the sides of the triangle:
Side a = 7 cm (one of the legs)
Side b = 3 cm (the other leg)
Side c = ? (the hypotenuse)
The Pythagorean theorem is:
[tex]c^2 = a^2 + b^2[/tex]
Substitute the given values:
[tex]c^2 = 7^2 + 3^2\\\\c^2 = 49 + 9\\\\c^2 = 58[/tex]
Now, we can find the square root of both sides to solve for c:
c = √58 cm
So, the length of the hypotenuse of the triangle is √58 cm.
The correct answer is: D. √58 cm
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A rectangular dartboard has an area of 648 square centimeters. The triangular part of the dartboard has an area of 162 square centimeters. A dart is randomly thrown at the dartboard. Assuming the dart lands in the rectangle, what is the probability that it lands inside the triangle?
To the nearest whole percent, the probability is
A) 18
B) 25
C) 35
D) 50
Answers
Hope this helps!!
Answer: B) 25
Step-by-step explanation:
Given: A rectangular dartboard has an area of 648 square centimeters.
The triangular part of the dartboard has an area of 162 square centimeters.
If a dart is randomly thrown at the dartboard. Assuming the dart lands in the rectangle, the probability (in percent) that it lands inside the triangle will be :
[tex]\dfrac{162}{648}\times100=25\%[/tex]
Hence, the probability that it lands inside the triangle = 25%.
A bag contains 8 yellow cubes,7 blue cubes,and 5 red cubes.If you select a cube at random,what is the probability the cube will not be blue or red
Answers
7/20 + 5/20 = 12/20 = probability that the cube WILL be blue or red. Can be reduced to 3/5
Therefore, the probability that the cube will NOT be blue or red is 8/20 or 2/5.
[tex] |\Omega|=20\\
|A|=8\\\\
P(A)=\dfrac{8}{20}=\dfrac{2}{5}=40\% [/tex]
PLEASE PLEASE HELP WITH THIS
Answers
[tex] \frac{AC}{BC} = \frac{BC}{CD} [/tex]
We can infer from our picture that [tex]BC=m[/tex]. Also we can find the length of AC by adding AD and CD:
[tex]AC=AD+CD[/tex]
[tex]AC=11+7[/tex]
[tex]AC=18[/tex]
Lets replace the values in our proportion:
[tex] \frac{AC}{BC} = \frac{BC}{CD} [/tex]
[tex] \frac{18}{m} = \frac{m}{7} [/tex]
Solving for [tex]m[/tex]:
[tex]m^2=(18)(7)[/tex]
[tex]m^2=126[/tex]
[tex]m= \sqrt{126} [/tex]
We can conclude that the correct answer is: D [tex] \sqrt{126} [/tex]
HI :) I NEED HELP PLEASE BEFORE 12 AM
Answers
The total cost of a prescription is $119.25. Mr. Jones's co-insurance plan requires him to contribute 15 percent of the cost. What's Mr. Jones's out-of-pocket cost for this prescription?
Answers
To find Mr. Jones's out-of-pocket cost for his prescription, calculate 15% of the total cost of $119.25, resulting in $17.89 after rounding.
Explanation:The question asks us to calculate Mr. Jones's out-of-pocket cost for his prescription if his co-insurance plan requires him to pay 15% of the total cost. The total cost of the prescription is $119.25.
To find out Mr. Jones's out-of-pocket expense, we calculate 15% of $119.25:
Out-of-pocket cost = 15% of total cost
= 0.15 × $119.25
= $17.8875
So, Mr. Jones's out-of-pocket cost will be $17.8875, which we can round to $17.89 for practical purposes.
determine the perimeter of a sector circular AOB whose radius has a length of 4m its central angle is 0.5 rad
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[tex] \sqrt[3]{ 3x + 1 - 4 = - 6} [/tex]
Answers
In case of [tex] \sqrt[3]{3x+1-4} =sqrt[3][-6][/tex] --> (by multiplying the power by 3)
[tex] 3x+1-4 = -6[/tex]
[tex] 3x -3 = -6 [/tex] ---> by adding 3 for the both sides
[tex] 3x = -3 [/tex] ---> by dividing both sides by 3
[tex] x = -1 [/tex]
in case of [tex] \sqrt[3]{3x+1-4} = -6[/tex] ----> we will repeat the first step again
therefore,
[tex] 3x + 1 -4 = (-6)^{3} = -216 [/tex]
[tex] 3x -3 = -216 [/tex] ----> by adding both sides by 3
[tex] 3x = -213 [/tex] ----> by dividing both sides by 3
[tex] x = \frac{-213}{3} = -71 [/tex]
then x = -71
I hope that helps ;)
3/a=9/b-10c solve for a.
Answers
3 / a = 9 / b-10c
Rewriting we have:
3 = a * (9 / b-10c)
Clearing to have:
a = 3 / (9 / b-10c)
Answer:
The value of a in terms of variables b and c is given by:
a = 3 / (9 / b-10c)
Factor completely the following quadratic expression 16x^2-25y^2
Answers
[tex](4x)^2-(5y)^2[/tex]
[tex](4x+5y)(4x-5y)[/tex]
Answer:
(4x+5y)(4x-5y)
Step-by-step explanation:
it is correct i got it right