Use trigonometric identities and algebraic methods, as necessary, to solve the following trigonometric equation. Please identify all possible solutions by including allanswers in [0, 2x) and indicating the remaining answers by using n to represent any integer. Round your answer to four decimal places, if necessary. If there is nosolution, indicate "No Solution."cos(x) + cos(x) = 4cos(x) + 4
Answers
The solutions to the quadratic trigonometric equation are given as follows:
x = kπ, k = ± 1, ± 3, ± 5, ± 7.
How to solve the quadratic trigonometric equation?The quadratic trigonometric equation is defined as follows:
cos²(x) + cos(x) = 4cos(x) + 4.
Then the following transformation is applied to solve the equation:
y = cos(x).
Hence:
y² + y = 4y + 4
y² - 3y - 4 = 0
(y - 4)(y + 1) = 0.
Applying the Factor Theorem, the solutions are given as follows:
y - 4 = 0 -> y = 4.y + 1 = 0 -> y = -1.However, we want the solutions for x, hence they are obtained as follows:
cos(x) = 4.
x = arccos(4), which has no solution, as there are no angles with a cosine of four.
cos(x) = -1.
x = arccos(-1)
x = kπ, k = ± 1, ± 3, ± 5, ± 7
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Related Questions
The equation of a line is: y = 4/7x - 12Which equation would have a line that is perpendicular to this line?1. y = - 4/7x - 12. y = - 7/4x - 53. y = 7/4x - 84. y = 4/7x - 2
Answers
Let's recall the framework of the equation of a line:
We say that two lines are perpendicular if the slope of one line is minus the multiplicative inverse of the slope of the other one; mathematically, this amounts to the following equation:
[tex]m_1=-\frac{1}{m_2}.\leftarrow\begin{cases}m_1=\text{Slope of one line} \\ m_2=\text{ Slope of the other line}\end{cases}[/tex]In this case, the slope of our line is 4/7. Then the slope (m) of any line perpendicular to it must satisfy
[tex]m=-\frac{1}{\frac{4}{7}}\text{.}[/tex]Solving this equation for m, we get
[tex]\begin{gathered} m=-\frac{1}{\frac{4}{7}}, \\ m=-\frac{\frac{1}{1}}{\frac{4}{7}}, \\ m=-\frac{1}{1}\cdot\frac{7}{4},\leftarrow\text{ Flipping rule when dividing fractions} \\ m=-\frac{7}{4}. \end{gathered}[/tex]AnswerThe answer is 2.
Select all value of c for which f(x) = g(x)Please look gráficos.
Answers
Statement Problem: Select all values of x for which;
[tex]f(x)=g(x)[/tex]Solution:
The value of x for which the two functions are equal is the x-coordinate of their insections;
The coordinates of the intersections are;
[tex](0,-3)\text{ and }(4,5)[/tex]Thus, the values of x that is correct are;
[tex]x=0,x=4[/tex]Hence, CORRECT OPTIONS are;
[tex]A\text{ and D}[/tex]Please help I don’t get what did teacher even wants bro
Answers
Base of the rectangle is 9 inches.
What is Area of Rectangle ?
You may determine the area of any form by counting how many unit squares fit inside of it.
In this context, a square with a side of 1 unit is referred to as a unit square.
In other words, the area of the rectangle is equal to the number of unit squares inside its perimeter.
Area = base * height
Given,
Area = 108 in²
height = 12 inches
put these values in given formula,
108 = 12 * base
base = 108 / 12
= 9 inches
Therefore, Base of the rectangle is 9 inches.
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26. If 25% of a number p is 19, what is 15% of p?
Answers
Given:
25% of p is 19.
[tex]\begin{gathered} \frac{25}{100}\times p=19 \\ p=19\times\frac{100}{25} \\ p=19\times4 \\ p=76 \end{gathered}[/tex]The expression to calculate the 15% of p is,
[tex]\frac{15}{100}\times p[/tex]Substitute value of p=76 in the above expression.
[tex]\begin{gathered} \frac{15}{100}\times76=\frac{3}{20}\times76 \\ =\frac{228}{20} \\ =11.4 \end{gathered}[/tex]Thus, 15% of p is 11.4.
Find the common ratio and write out the first four terms of the geometric sequence (1.06)n−1 Common ratio is a1= a2= a3= a4=
Answers
Solution
Step 1
Write the nth term ex[pression and the common ratio formula.
[tex]\begin{gathered} T_n\text{ = \lparen1.06\rparen}^{n-1} \\ Common\text{ ratio = }\frac{2^{nd}term}{1^{st}term} \end{gathered}[/tex]Step 2
[tex]\begin{gathered} T_1\text{ = \lparen1.06\rparen}^{1-1}\text{ = 1} \\ T_2\text{ = \lparen1.06\rparen}^{2-1}\text{ = 1.06} \\ T_3\text{ = \lparen1.06\rparen}^{3-1}\text{ = \lparen1.06\rparen}^2\text{ = 1.1236} \\ T_4\text{ = \lparen1.06\rparen}^{4-1}=\text{ \lparen1.06\rparen}^3\text{ = 1.191016} \end{gathered}[/tex]Step 3
[tex]Common\text{ ratio r = }\frac{1.06}{1}\text{ = 1.06}[/tex]Final answer
What is the end behavior of the polynomial function?
Drag the choices in to the boxes to correctly describe the end behavior of the function.
Answers
The end behaviours of the functions are
f(x) = 6x⁹ - 6x⁴ - 6: As x ⇒ +∝, f(x) ⇒ +∝ and as x ⇒ -∝, f(x) ⇒ -∝f(x) = -3x⁴ - 6x + 4x - 5: As x ⇒ +∝, f(x) ⇒ -∝ and as x ⇒ -∝, f(x) ⇒ -∝How to determine the end behaviours of the functions?Function 1
The equation of the function is given as
f(x) = 6x⁹ - 6x⁴ - 6
Calculate f(∝) and f(-∝)
So, we have
f(∝) = 6(∝)⁹ - 6(∝)⁴ - 6
Evaluate
f(∝) = ∝ - ∝ - 6
So, we have
f(∝) = ∝
Also, we have
f(-∝) = 6(-∝)⁹ - 6(-∝)⁴ - 6
Evaluate
f(-∝) = -∝ - ∝ - 6
So, we have
f(∝) = -∝
This means that
As x ⇒ +∝, f(x) ⇒ +∝ and as x ⇒ -∝, f(x) ⇒ -∝
Function 2
The equation of the function is given as
f(x) = -3x⁴ - 6x + 4x - 5
Evaluate the like terms
f(x) = -3x⁴ - 2x - 5
Calculate f(∝) and f(-∝)
So, we have
f(∝) = -3(∝)⁴ - 2(∝) - 5
Evaluate
f(∝) = -∝ - ∝ - 5
So, we have
f(∝) = -∝
Also, we have
f(-∝) = -3(-∝)⁴ - 2(-∝) - 5
Evaluate
f(∝) = -∝ + ∝ - 5
So, we have
f(∝) = -∝
This means that
As x ⇒ +∝, f(x) ⇒ -∝ and as x ⇒ -∝, f(x) ⇒ -∝
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Find the difference between 3 /5 of 125 and 5/8 of 144
Answers
The answer to this question will be 15.
3/5 of 125 = 3/5 x 125 = 75
5/8 of 144 = 5/8 x 144 = 90
So, 5/8 of 144 - 3/5 of 125 = 90 - 75 = 15
The difference between 3/5 of 125 and 5/8 of 144 is 15.
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ANSWERS ASAP PLEASEEEEE
Answers
Answer:
y= -3x+3
Step-by-step explanation:
atleast I think so
f(x)=7x-3 for f(x)= -38
Answers
Answer:
f(x)= -269
Step-by-step explanation:
f(x)=7x-3
Since we know f(x)= -38, we can substitute x for -38.
So:
f(-38)=7(-38)-3
f(-38)= -266-3
f(x)= -269
Answer:
-7x=38+3
-7x=41/-7=5.8
35.4 divided by 0.59
Answers
To do the operation, first the numerator and denominator by 100:
[tex]\frac{35.4\cdot100}{0.59\cdot100}=\frac{3540}{59}[/tex]Now simplify
[tex]\frac{3540}{59}=\frac{59\cdot60}{59\cdot1}=\frac{60}{1}=60[/tex]Therefore,
[tex]\frac{35.4}{0.59}=60[/tex]Answer:
60
Step-by-step explanation: 35.4 / 0.59 = 60
Graph the line 3x + 6y =12.
Use the line tool and select two points on the line.
Answers
Answer: First divide everything by 3 to make it simpler. Then subtract 12 on both sides to get the equation "x+2y-12 = 0. You can then graph this.
Step-by-step explanation:
Find the distance between the two points.(-6, -3) and (194,42)The distance is(Type an exact answer, using radicals as needed.)
Answers
distance=205
Explanation
Step 1
the distance between is given by:
[tex]\begin{gathered} \text{distance=}\sqrt[]{(x_1-x_2)^2+(y_1-y_2)^2} \\ \text{where} \\ P1(x_1,y_1) \\ P2(x_2,y_2) \end{gathered}[/tex]Let
P1(-6,-3)
P2(194,42)
Step 2
apply the formula.
[tex]\begin{gathered} \text{distance=}\sqrt[]{(x_1-x_2)^2+(y_1-y_2)^2} \\ \text{distance=}\sqrt[]{(-6-194)^2+(-3-42)^2} \\ \text{distance=}\sqrt[]{(-200)^2+-45^2} \\ \text{distance=}\sqrt[]{40000+2025} \\ \text{distance=}\sqrt[]{42025} \\ \text{distance}=205 \end{gathered}[/tex]I hope this helps you
A tree trunk may be considered a circular cylinder.
Suppose the diameter of the trunk increases 1 inch per
year and the height of the trunk increases 6 inches per
year. How fast is the volume of wood in the trunk
increasing when it is 100 inches high and 5 inches in
diameter?
Answers
The volume of the tree trunk increases 52.64% in one year.
Given,
The height of a tree trunk = 100 inches
The diameter of a tree trunk = 5 inches
Diameter increases 1 inch per year
Height increases 6 inches per year
We have to find the increase in its volume.
Consider the trunk as a circular cylinder.
Volume of circular cylinder = πr²h
Radius, r = 5/2
Height, h = 100
Initial Volume = πr²h
Volume = π × (5/2)² × 100 = π × 6.25 × 100 = 1963.50 cubic inches
After one year
Diameter = 6
Height = 106
Increased Volume = πr²h
Volume = π × (6/2)² × 100 = π × 9 × 106 = 2997.08 cubic inches
The rate of increase in volume = (Increased volume × 100) ÷ Initial volume
= (2997.08 × 100) ÷ 1963.50 = 152.64
That is,
The volume of the tree trunk increases 52.64% in one year.
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PLS HELP ASAP WILL GIVE BRAINLIST
Answers
X=2
Y=15
I need help with putting 64/128 fully simplified and to a decimal
Answers
Given:
[tex]\frac{64}{128}[/tex]To convert into decimal:
Explanation:
Let us write it as the factored form for each term.
[tex]undefined[/tex][tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{\dfrac{64}{128}}\\\\\mathsf{= \dfrac{64\div8}{128\div8}}\\\\\mathsf{= \dfrac{8}{16}}\\\\\mathsf{= \dfrac{8\div4}{16\div4}}\\\\\mathsf{= \dfrac{2}{4}}\\\\\mathsf{= \dfrac{2\div2}{4\div2}}\\\\\mathsf{= \dfrac{1}{2}}\\\\\\\huge\text{Therefore, the answer simplified is:}\\\huge\boxed{\mathsf{\dfrac{1}{2}}}\huge\checkmark[/tex]
[tex]\mathsf{\dfrac{1}{2}\rightarrow 1\div2 \rightarrow 0.5}\\\\\\\huge\text{Therefore your decimal form of }}\huge\boxed{\boxed{\rm{\dfrac{1}{2}}}}\huge\text{ is:}\\\\\huge\boxed{\mathsf{0.5}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Write Expression to represent the total area as the sum of the areas of each room
Answers
We are given the following areas:
The total area of the square is given by:
[tex]11(7+4)[/tex]If we apply the distributive property we get:
[tex]11(7+4)=11\times7+11\times4[/tex]Which is equivalent to determining the area of the interior rectangle and adding them together.
Answer:
11x7+11x4
Step-by-step explanation:
your welcome <3
HELPP PLEASE
Answers
Choose A
( A is the answer <3)
Two forces 30-lb and 50-lb are pulling an object at an angle of 30°between them. Find the magnitude of the resultant force. Round answer to 2 decimal places.
Answers
Answer: The magnitude of the resultant force is 77.45-lb
Explanation:
Resultant is represented as R
A rectangular picture measures 32 by 28. when the picture is framed, a margin 2cm wide is left all the way round .1: what is the area of the picture without the frame?2:what is the area of the frame3:what is the area of the margin
Answers
1) The area of the picture without the frame will be A.
[tex]A=32\times28=896cm^2[/tex]So the area without frame is 896 square centimeters.
2) If the frame is 2 cm all around then the length and width increase by 4.
So the length becomes 32+4=36cm and the width becomes 28+4=32.
The area of big rectangle which is the frame is A'.
[tex]A^{\prime}=36\times32=1152cm^2[/tex]So the area of the frame is 1152 square centimeters.
3) The area of the margin will be the difference of the area of the frame and area of the picture, so it will be A'-A
[tex]A^{\prime}-A=1152-896=256cm^2[/tex]So the area of the margin is 256 square centimeters.
Here are the recorded temperatures at the different times on a winter evening
Answers
ANSWER
Tyler was right
EXPLANATION
To answer the question, we have to find the rate at which the temperature dropped between 4pm - 6pm and 6pm - 10pm
By 4pm, the temperature was 25°F and by 6pm, the temperature was 17°F.
The temperature difference is:
T = 17 - 25 = -8°F
There are 2 hours between 4 and 6 pm.
Now, we divide by the number of hours that elapsed:
[tex]\text{Rate = }\frac{-8}{2\text{ hours}}\text{ =}-4\degree F\text{ / hr}[/tex]By 6 pm the temperature was 17°F and by 10pm, the temperature was 8°F.
The temperature difference is:
T = 8 - 17 = -9°F
There are 4 hours between 6 and 10 pm.
Now, divide by the number of hours that elapsed:
[tex]\text{Rate = }\frac{-9}{4}\text{ = }-2.25\degree F\text{ / hr}[/tex]As we can see, the rate at which the temperature dropped between 4pm and 6 pm is more (since it became colder at a faster rate during that period)
Therefore, Tyler was right.
A manufacturer of kitchen utensils and gadgets is considering changing the design of their salt and pepper shakers. Their current design is a standard cylinder, while the new design they are considering is an oblique cylinder. The figure shows both designs.Which set of additional details are the minimum required to ensure the new design will have the same volume as the original design?A. The heights of both designs must be the same, and at least one cross-section taken at the same height on both designs must have the same area.B. The heights of both designs must be the same, the base areas of both designs must be the same, and each cross-section taken at the same height on both designs must have the same area.C. The heights of both designs must be the same, and the base areas of both designs must be the same.D. The heights of both designs must be proportional, the base areas of both designs must be proportional, and each cross-section taken at the same height on both designs must have the same radius.
Answers
1) In this problem, we need to keep in mind the formula for the volume of one cylinder:
[tex]V=\pi r²h[/tex]Or in other words, the base area (area of a circle) times the height.
2) Since the point here is not to lose capacity (volume) the new design must keep its base areas as well as their height, so examining the answers we can tell that the answer is:
[tex]C[/tex]
These are the minimum requirements
Plant A is 2 inches tall and is growing
at 14 inches per week. Plant B is 12
inches tall but is only growing at
inch per week. How many weeks will it
take for Plant A to be the same height
as Plant B?
Answers
It will take Plant A 5 days to be the same height as Plant B and this can be calculated through unitary method of mathematical calculation.
Unitary Method: What is it?The unitary technique used in here involves at first determining the value of a particular single unit, that is thus followed by the value of the necessary number of units.
What is an example of a unitary method?A single or type of a distinct unit is referred to by the word of unitary.
Therefore, the goal of this strategy is to establish values in reference to a single unit.
The unitary technique, for instance, can be used to calculate how many kilometers a car will go on one liter of gas if it travels 44 km on two liters of fuel.
Plant A initial height = 2 inches
Growth rate = 14 inches/ week
= 2 inches/ day
Plant B initial height = 12 inches
Growth rate = 1 inch/ week
After 5 days we can see that plant A will be
2 + (5 x 2) = 12 inches
this is the same height as that of Plant B.
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During a physics lab, students added weights of different masses to aspring. After adding each weight to the spring, they measured how far theweight was from the lab tabletop, in centimeters. Then they graphed thedata and calculated the line of best fit to be y = -1 x + 10.25Weight Distance fromthe Tabletop (cm)108642Effect of Weightson a Spring0 50 100 150 200 250 300Mass (g)What does the x-intercept represent?-XAt 250 grams, the weight will touch thetabletop.With no weight, the spring is 10centimeters above the tabletop.The weight will be 250 centimetersabove the tabletop when the spring hasa mass of 10 grams on it.The spring stretches and the weight is 1centimeter closer to the tabletop forevery 25 grams added to it.
Answers
Solution:
Given the graph below:
where the equation of the line of best fit is expressed as
[tex]y=-\frac{1}{25}x+10[/tex]The x-intercept represents:
The correct option is
Use the number line to find the coordinate of the midpoint of
¯¯¯¯¯
J
P
.
Answers
Answer: -1
Step-by-step explanation:
The midpoint of a segment is the same as the average of the coordinates of the endpoints. So, the midpoint is [tex]\frac{-7+5}{2}=-1[/tex].
savings 50,000 in 30 years with a saving compounded monthly at an interest rate of 6%. How much would I need to deposit a month?
Answers
If the saving compounded monthly at an interest rate of 6%. The amount you need to deposit a month is $8,302.
How to find the compound interest?Using this formula to determine the principal amount
P = A / (1 + r/n) ^nt
Where:
P = principal = ?
A = amount = $50,000
r = interest rate = 6%
t = time = 30
Now let plug in the formula
P = $50,000 / (1 + 0.06/12) ^( 12 × 30 )
P = $50,000 / (1 + 0.005) ^ 360
P = $50,000 / (1.005)^360
P = $50,000 / 6.022575
P = $8,302
Therefore $8,302.10 is the amount deposited.
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The tree diagram represents an experiment consisting of two trials
P(A)=
Answers
Based on the parameters in the question, the value of probability P(A) is 0.60
How to determine the probability?The given parameters from the tree diagram are:
Probability of event A: P(A only) = 0.6Probability of event A: P(A and C) = 0.3Probability of event A: P(A and D) = 0.7The probability is calculated using the following probability formula
P(A) = P(A and D) + P(A and C)
Substitute the known values in the above equation
P(A) = 0.6 * 0.7 + 0.6 * 0.3
Evaluate the products
P(A) = 0.42 + 0.18
Evaluate the sum
P(A) = 0.60
Hence, the value of the probability of A is 0.60
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Female
Male
Total
10
113
Snellville Stone
Mountain
12
14
26
316
10
20
30
Suwanee
8
16
24
Consider the following table with information about a sample of students from Phoenix High School and where they
live. If a person is randomly selected determine the following probability provided the condition: P(Female | Suwanee).
Total
30
50
80
Answers
If a person is randomly selected, the probability provided the condition is P(Female | Suwanee) is 1/3.
What is the probability?Probability is used to determine the odds in favor or against a random event happening. The odds in favor or against an event happening has a probability value that lies between 0 and 1.
The higher the odds of an event happening, the closer the probability value would be to 1. If it is equally likely that the event might happen or not happen, the probability value will be 0.5.
P (Female | Suwanee) is the probability that a person is female given that the person is from Suwanee.
P (Female | Suwanee) = total number of females from Suwanee / total number of people from Suwanee
8 / 24 = 1/3
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What is 78,600 rounded to the nearest thousand
Answers
Answer:
79,000
Step-by-step explanation:
:]
Answer:
79000.
Step-by-step explanation:
Identify the types of sampling errors that exist in the following sampling designs:A radio show asks people to phone in their views on whether the United States should house the homeless.The student newspaper plans to make a prediction for the student council election based on a survey of its readers.A new gym chooses to survey the first 20 members who enter the facility one day to determine whether members favor the new elliptical machines. I, voluntary; II, nonresponse; III, convenience I, nonresponse; II, voluntary; III, convenience I, nonresponse; II, convenience; III, voluntary I, voluntary; II, convenience; III, nonresponse I, convenience; II, voluntary; III, nonresponse
Answers
We are goinf to analise each case properly
1) As the radio show is asking it could be that their listners do not attend this demand. Then the error would be nonresponse.
2) As the students do the survey based of its readers it depends only of this part of the poblation. Then the error would be voluntary.
3) As the gym ask only to the first 20 members it makes the error would be convenience
So, the correct answer is B.
whats 2+2 i cant figure it out
Answers
Answer: 4
Step by step solution:
[tex]2+2=4[/tex]