QuestionUse trigonometric identities, algebraic methods, and inverse trigonometric functions, as necessary, to solve the following trigonometric equation on the interval [0, 22).Round your answer to four decimal places, if necessary. If there is no solution, indicate "No Solution."12sin?(x) - 20sin(x) = -8
Answers
STEP - BY - STEP EXPLANATION
What to do?
Solve the given trigonometric equation.
Given:
\(12\sin ^2x-20\sin x=-8\)To solve the given problem, we will follow the steps below:
Step 1
Let y=sinx
Step 2
Replace sinx by y.
\(12y^2-20y=-8\)Step 2
Re-arrange the above into the form:
\(ax^2+bx+c=0_{}\)That is;
\(12y^2-20y+8=0\)a=12 b=-20 and c=8
Step 3
Use the quadratic formula below to solve.
\(y=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}\)\(y=\frac{20\pm\sqrt[]{(-20)^2-4(12)(8)}}{2(12)}\)\(=\frac{20\pm\sqrt[]{400-384}}{24}\)\(\begin{gathered} =\frac{20\pm\sqrt[]{16}}{24} \\ \\ =\frac{20\pm4}{24} \end{gathered}\)Either
\(\begin{gathered} y=\frac{20+4}{24}=\frac{24}{24}=1 \\ \\ or \\ \\ y=\frac{20-4}{20}=\frac{16}{24}=\frac{2}{3} \end{gathered}\)Step 4
Substitute the value of y in;
y=sinx
If y = 1
Then,
\(\sin x=1\)\(x=\sin ^{-1}(1)\)\(x=90\degree\)\(\begin{gathered} x=90\times\frac{\pi}{180} \\ \\ =\frac{\pi}{2}\text{rads} \end{gathered}\)Step 5
Substitute y=2/3 in y=sinx
\(\sin x=\frac{2}{3}\)\(x=\sin ^{-1}(\frac{2}{3})\)\(x=41.8103148958\degree\)Change to radians
\(x=41.8810348958\times\frac{\pi}{180}\)\(=0.2323\pi rads\)Therefore,
\(x=\frac{1}{2}\pi rads,0.2323\pi rads\)Related Questions
Multiply.
8×35
Enter your answer as a mixed number in simplest form by filling in the boxes
PLS HELP
Answers
Answer:
280
Step-by-step explanation:
Answer:
8×35=280.
This is the best I can give to you
How many lines of symmetry does this picture have?
Answers
Answer:
1 line of symmetry so answer should be C
a square has the side length (x+5) units whats is its area
Answers
Answer:
25 square units
Step-by-step explanation:
Hope this helps :)
Decimals to the tenths?
Answers
The first digit to the right of the decimal point indicates the number of tenths. For example, the decimal 0.3 is the same as the fraction 3/10.
Suppose that the matrix A has repeated eigenvalue with the following eigenvector and generalized eigenvector: A = 1 with eigenvector = [] and generalized eigenvector - [1-3]. Write the solution to the linear system' = Ar in the following forms. A. In eigenvalue/eigenvector form: [x(t)] = C1 [8] 248-89 + e B. In fundamental matrix form: [x(t)] [y(t)] [188 C. As two equations: (write "c1" and "c2" for c₁ and c₂) x(t) = y(t) = Note: if you are feeling adventurous you could use other eigenvectors like 47 and other generalized eigenvectors like - 37. Just remember that if you change , you must also change for its fundamental solution!
Answers
The solution for the linear system will be , x(t) = 4 c₁e^t + 4 c₂e^t and
y(t) = -c₂e^t + c₂(1 - t)e^t .
The solution is given by ,
matrix | x y | = c₁ .v . e^λt + c₂( w + v.t ) e^λt
Given that the matrix has repeated eigenvalue with eigenvector generalized vectors ,
λ = 1 with eigenvector v = [ 4 , -1 ] and generalized vectors w =[ 0,1 ].
then the solution will be,
c₁ [ 4 , 1 ] e^t + c₂[ 0 , 1] + [ 4 , -1 ] )e^t
therefore,
x(t) = 4 c₁e^t + 4 c₂e^t
y(t) = -c₂e^t + c₂(1 - t)e^t
Matrixes represent linear maps and allow for explicit linear algebra operations. As a result, matrices play an important role in linear algebra, and most characteristics and operations in abstract linear algebra may be represented in terms of matrices.
Matrix multiplication, for example, depicts the combination of linear maps.
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For an outdoor concert by the city orchestra, concert organizers estimate that 19,000 people will attend if it is not raining. If it is raining, concert organizers estimate that 4000 people will
attend. On the day of the concert, meteorologists predict a 60% chance of rain. Determine the expected number of people who will attend this concert.
It is expected that people will attend the concert.
Answers
Answer:
Hope it helps you stay safe<3
Kim has a new job. She decided to follow this savings plan: Month Dollars
1 - 65
2 - 72
3 -79
4 - 86
5 93
6 -100
7 - ?
Answers
Step-by-step explanation:
For every month increase by 1, the amount of dollars increase by 7. (from 65 to 72, 72 to 79, 79 to 86 etc.)
Hence at Month 7, there will be 100 + 7 = 107 dollars.
Answer:
107 dollors
Step-by-step explanation:
For every month, It increase 7 dollars, So it would be 107 bdollors
You have one type of chocolate that sells for $6.00/lb and another type of chocolate that sells for $9.70/lb. You would like to have 11.1 lbs of a chocolate mixture that sells for $7.50/lb. How much of each chocolate will you need to obtain the desired mixture? You will need ______ lbs of the cheaper chocolate and ______ lbs of the expensive chocolate.
Answers
Answer:
lbs of the cheaper chocolate => x = 6.6 pounds(Ibs)
lbs of the expensive chocolate => y = 4.5 pounds(Ibs)
Step-by-step explanation:
Let's the :
lbs of the cheaper chocolate => x
lbs of the expensive chocolate => y
You would like to have 11.1 lbs
Hence:
x + y => 11.1
x = 11.1 - y
You have one type of chocolate that sells for $6.00/lb and another type of chocolate that sells for $9.70/lb. of a chocolate mixture that sells for $7.50/lb.
Hence:
$6.00 × x + $9.70 × y = $7.50 × 11.1
6x + 9.7y = 83.25
Hence, we substitute 11.1 - y for x
6(11.1 - y) + 9.7y = 83.25
66.6 -6y + 9.7y = 83.25
-6y + 9.7y = 83.25 - 66.6
= 3.7y => 16.65
y = 16.65/3.7
y = 4.5 pounds
x = 11.1 - y
x = 11.1 - 4.5
x = 6.6 pounds
Hence:
You will need 4.5 lbs of the cheaper chocolate and 6.6 lbs of
(09.01 LC)
What is the relationship between the circumference C of the circle in which the degree measure A of a central angle of a circle intercepts an arc
length s of the arc?
A)C=360°(s)(A)
B)C=360 degrees s over A
C)C=360 degrees(s+A)
D)C = 360°A over s
Answers
The relationship between the circumference C of the circle in which the degree measure A of a central angle of a circle intercepts an arc length s of the arc is
B) C=360 degrees s over A
How to find the relationshipThe relationship between the circumference C of a circle and the degree measure A of a central angle that intercepts an arc length s of the arc can be described by the formula:
s = A / 360 * C
Make C the subject of the formula
s = AC / 360
360s = AC
rearranging
AC = 360s
C = 360 degrees s / A
C = (s / A) * 360°
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Answer:
\(\textsf{B)} \quad C=\dfrac{360^{\circ}\:s}{A}\)
Step-by-step explanation:
In a circle, the ratio of an arc length (s) to the circumference (C) is equal to the ratio of the measure of the arc's central angle (A) to 360°.
This is because:
The circumference (C) represents the distance around the entire circle, and so an arc (s) is a fraction of the whole circumference. In a circle, there are 360° in total, and so a central angle (A) is a fraction of 360°.Therefore, this can be expressed as:
\(\dfrac{s}{C}=\dfrac{A}{360^{\circ}}\)
Cross multiply:
\(360^{\circ} \cdot s=C \cdot A\)
Now, divide both sides by A to isolate C:
\(\dfrac{360^{\circ} \cdot s}{A}=C\)
Therefore, the relationship between the circumference (C) of the circle in which the degree measure (A) of a central angle of a circle intercepts an arc length (s) of the arc is:
\(\large\boxed{\boxed{C=\dfrac{360^{\circ}\:s}{A}}}\)
A man needed money for college. He borrowed $5,000 at 12% simple interest per year. It he paid $150 interest, what was the duration of the loan
Answers
Given:
Principal or the money borrowed - $5,000
Interest Rate = 12% or 0.12 in decimal form
Interest - $150
Find: duration of the loan (t in years)
Solution:
To be able to determine the duration of the loan, let's use the formula of Simple Interest and solve for t.
\(I=Prt\)To solve for t, divide both sides of the equation by Pr.
\(\frac{I}{Pr}=\frac{Prt}{Pr}\Rightarrow\frac{I}{Pr}=t\)Hence, to solve for the duration, we need to divide the interest by the product of the principal and the interest rate.
\(t=\frac{Interest}{Principal\times Rate}=\frac{150}{5,000\times0.12}=\frac{150}{600}=0.25\)Answer:
The duration of the loan is 0.25 years or 3 months.
A cylinder has a base radius of 9 feet and a
height of 4 feet. What is its volume in
cubic feet, to the nearest tenths place?
Answers
Answer:
1017.88
Step-by-step explanation:
Answer:
1017.876 cubic ft.
Step-by-step explanation:
To find the volume of a cylinder, use the formula: V = π * r^2 * H
In this case: V = π * (9^2) * (4)
V = π * 324
V = 1017.876 cubic ft. or ft^3
Hope this helps =)
Please if ur good at pre calc stop to help with the first question please
Answers
Answer:
Step-by-step explanation:
The first thing you ought to do is find out what you are trying to get. Desmos is an ideal program to do that if you don't have a graphing calculator. Just search for Desmos. It is pretty obvious once you get there. I've enclosed the graph to show you what it looks like.
Notice what happens around 5. The graph splits because effectively, you are dividing by 0 when you put 5 into the denominator. The question arises why doesn't the same thing happen at 0. It should: There is a discontinuity but it is very tiny. So the domain numbers that you should graph are
-1 0™ 1 2 3 4 4.5 4.8 5.3 5.4 6 7
™I wouldn't make 0 a part of this domain. But you can indicate with a dot where the graph goes.
I haven't filled in the range numbers. That's your job. All you have to do is fill in the table with points. Or you can put them on the graph that I have enclosed just to see where they points belong.
A graph is not to convey accuracy. It is to show the shape of function in question.
In the equation (x-3)²+(y-2)2=16, the radius of the circle is...
16
3
32
4
Answers
Step-by-step explanation:
This is of the form
(x-h)^2 + ( y-k)^2 = r^2 so r^2 = 16 means r = 4 units
n a basket of fruit, 5/6 of the pieces of fruit are apples. There are 20 apples in the display. The equation 5/6f= 20 can be used to find how many pieces of fruit f are the basket. Use words and numbers to explain how to solve the equation to find how many pieces of fruit are in the basket.
Answers
Step-by-step explanation:
5/6f=20apples. that means the total number of fruits is 6/6 which is whole thus
if 5/6=20
6/6=?
that is 6/6x20 divide by 5/6
=24fruits
Which line is perpendicular to the line y=-1/3x-2 and passes through the point (1, 4)?
Answers
Answer:
it's answer choice 3
y=3x+1
this is correct on edmentum
Finding the Equation of a Line
You have discovered another alien.
Move the sliders to change the slope and y-intercept.
Create an equation to produce the correct line of travel.
slope: 0
6
What is the equation of the line that provides the
correct path to rescue this alien?
A. Y=5
B. Y=x+5
C. Y=-x+5
D. Y=5x
Answers
Answer:
the answer is Y=-x+5
Step-by-step explanation:
Given a mean of 34 and a standard deviation of 5. Find the following z-scores.
Answers
The z-score for the raw score of 39 is 1.The z-score for the raw score of 30 is -0.8.Z-scores measure the number of standard deviations a raw score is from the mean. A positive z-score indicates a raw score above the mean, while a negative z-score indicates a raw score below the mean.
To find the z-scores, we need to use the formula:
z = (x - μ) / σ
where:
z is the z-score,x is the raw score,μ is the mean, andσ is the standard deviation.
Let's calculate the z-scores for the given mean of 34 and standard deviation of 5.For a raw score of 39:
z = (39 - 34) / 5
z = 5 / 5
z = 1
So, the z-score for the raw score of 39 is 1.For a raw score of 30:
z = (30 - 34) / 5
z = -4 / 5
z = -0.8
The z-score for the raw score of 30 is -0.8.
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Your taxable wages for Social Security purposes are $1100. How much is your Social Security tax if you have previous taxable wages of $102,000?
Answers
If you have previous taxable wages of $102,000 and your current taxable wages are $1,100, your Social Security tax would be $6,324 for the previous wages and $68.20 for the current wages.
To calculate the Social Security tax, we need to know the tax rate for Social Security and the taxable wages. Let's assume the Social Security tax rate is 6.2% for both the employee and the employer.
Given that your taxable wages for Social Security purposes are $1,100, and your previous taxable wages are $102,000, we can determine the Social Security tax amount.
First, we need to calculate the Social Security tax on the previous taxable wages of $102,000. Multiply $102,000 by 6.2% (0.062) to find the Social Security tax for that amount:
Social Security tax = $102,000 x 0.062 = $6,324
Next, we calculate the Social Security tax on the current taxable wages of $1,100. Multiply $1,100 by 6.2% to find the tax amount:
Social Security tax = $1,100 x 0.062 = $68.20
Therefore, if you have previous taxable wages of $102,000 and your current taxable wages are $1,100, your Social Security tax would be $6,324 for the previous wages and $68.20 for the current wages.
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y=-0.024x^2+0.0791x+4.873
Answers
The equation y = \(-0.024x^2\) + 0.0791x + 4.873 represents a quadratic function with a downward-opening parabol
The given expression is a quadratic equation in the form y = -0.024x^2 + 0.0791x + 4.873. Let's analyze its components and characteristics.
The equation represents a quadratic function, where x is the independent variable and y is the dependent variable. The coefficients in front of each term determine the shape, position, and direction of the graph.
The term with the highest power of x is -0.024x^2, which indicates a downward-opening parabola. The coefficient -0.024 determines the steepness of the curve. A negative coefficient means the parabola is concave down.
The term 0.0791x is the linear term and determines the slope of the line. A positive coefficient indicates an upward or positive slope. It affects the overall direction and position of the graph.
The constant term 4.873 is the y-intercept. It indicates the point at which the graph intersects the y-axis when x = 0.
To analyze the graph of the quadratic equation further, we can calculate the vertex. The x-coordinate of the vertex can be found using the formula x = -b/(2a), where a and b are the coefficients of x^2 and x, respectively. In this case, a = -0.024 and b = 0.0791. Substituting these values into the formula, we have x = -0.0791 / (2 * -0.024) ≈ 1.643. By substituting this x-coordinate into the equation, we can find the y-coordinate of the vertex.
Overall, the equation y =\(-0.024x^2 + 0.0791x\) + 4.873 represents a quadratic function with a downward-opening parabola. The specific properties, such as the vertex and other key points, can be determined by further calculations and analysis of the equation.
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1.Which of the following statements is true for the expression 2w3 + 7w2 - 4w?
A. The power of the expression is
B. A factor of the expression is -4w.
C. The coefficient of the expression is w.
D. The expression has 3 terms.
Answers
Answer: D
Step-by-step explanation:
The given expression is 2w3 + 7w2 - 4w.
The power of the expression is the highest exponent of the variable w, which is 3. However, this is not one of the options given.
A factor of the expression is a term or expression that divides the given expression completely. -4w is not a factor of the given expression.
The coefficient of a term is the numerical factor that is multiplied by the variable. The coefficient of the first term 2w3 is 2, and the coefficient of the second term 7w2 is 7. The coefficient of the last term -4w is -4. Therefore, the statement "The coefficient of the expression is w" is false.
The given expression has three terms: 2w3, 7w2, and -4w. Therefore, the statement "The expression has 3 terms" is true.
everyone have a great day & take care
What is the slope of the line shown? The graph of a line passes through the points (0, -2) and (6, 0). What is the equation of the line? please help fast 20 pt will mark the branliest
Answers
Answer:
slope = 1/3, equation is y = 1/3x - 2
Step-by-step explanation:
slope formula = change in y / change in x
= (0 - (-2)) / (6 - 0) = 2 / 6 = 1/3
Since we know the slope and the y-intercept we can write the equation in slope-intercept form which will be y = 1/3x - 2.
Answer:
y=1/3x -2
Step-by-step explanation:
points (0, -2) and (6, 0)
Slope- intercept form:
y=mx+b
m=(y2-y1)/(x2-x1)= (0+2)/(6-0)= 2/6= 1/3y=1/3x+b
0= 1/3*6+b b= -2y=1/3x -2
3(8+2) is the same as
Answers
Answer:
3(8 + 2) = 3(8) + 3(2) = 3(10) = 30
A homeowner
has a budget of $135 for
the installation of a light fixture. An
electrician charges $60 per hour plus a
one-time trip charge of $45. What is the
greatest amount of time, in hours, the
electrician can work on the installation
while staying within the homeowner's
budget? Write your answer as a decimal.
Answers
The greatest amount of time that the electrician can work is 1.5 hours.
What is the greatest amount of time that the electrician?The first step is to form a linear equation using the information provided in the question. A linear equation is an equation that increases at a constant term.
Total cost = cost of the one-time trip + (cost per hour x number of hours)
$135 = $45 + ($60 x h)
$135 = $45 + $60h
$135 - $45 = $60h
$90 = $60h
h = $90 / $60
h = 1.5 hours
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HELP PLEASE URGENT!!!
A Ferris wheel is 50 meters in diameter and boarded from a platform that is 4 meters above the ground. The six o'clock position on the Ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 2 minutes. How many minutes of the ride are spent higher than 38 meters above the ground?
answer in minutes.
Answers
The number of minutes spent higher than 38 meters above the ground on the Ferris wheel ride is approximately 1.0918 minutes.
To solve this problem, we need to determine the angular position of the Ferris wheel when it is 38 meters above the ground.
The Ferris wheel has a diameter of 50 meters, which means its radius is half of that, or 25 meters.
When the Ferris wheel is at its highest point, the radius and the height from the ground are aligned, forming a right triangle.
The height of this right triangle is the sum of the radius (25 meters) and the platform height (4 meters), which equals 29 meters.
To find the angle at which the Ferris wheel is 38 meters above the ground, we can use the inverse sine (arcsine) function.
The formula is:
θ = arcsin(h / r)
where θ is the angle in radians, h is the height above the ground (38 meters), and r is the radius of the Ferris wheel (25 meters).
θ = arcsin(38 / 29) ≈ 1.0918 radians
Now, we know the angle at which the Ferris wheel is 38 meters above the ground.
To calculate the time spent higher than 38 meters, we need to find the fraction of the total revolution that corresponds to this angle.
The Ferris wheel completes one full revolution in 2 minutes, which is equivalent to 2π radians.
Therefore, the fraction of the revolution corresponding to an angle of 1.0918 radians is:
Fraction = θ / (2π) ≈ 1.0918 / (2π)
Finally, we can calculate the time spent higher than 38 meters by multiplying the fraction of the revolution by the total time for one revolution:
Time = Fraction \(\times\) Total time per revolution = (1.0918 / (2π)) \(\times\) 2 minutes
Calculating this expression will give us the answer in minutes.
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O
Which of the following could be used to calculate the area of the sector in the circle sho
O
m(Sin)
O
WE OD
m(Sin)2
O n(30in)2
O
r-5 in 30
m(30in)
O
above? (5 points)
Answers
The Circle Sector Area correct answer is: O n(30in)2
To calculate the area of the sector in the circle, you would typically use the formula:
Area = (θ/360) * π *\(r^2\)
where θ is the angle of the sector in degrees, π is a mathematical constant approximately equal to 3.14159, and r is the radius of the circle.
From the options you provided, the correct choice would be:
O n(30in)2
This option represents the square of the radius (30in) squared, which gives you the value of \(r^2.\)
Therefore, the Circle Sector Area correct answer is: O n(30in)2
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The translation of triangle STO (72, 72), (9, 108), and (-108, -27) after a dialation is (-8, -8), (-1,-12), and (12, 3). What is the dialation?
Answers
Answer:
The dialation is of -(1/9)
Step-by-step explanation:
I will write a matrix for the triangle before dialation. It is:
\(B=\begin{bmatrix}{72} & {9} & {-108} \\ {72} & {108} & {-27}\end{bmatrix}\)The matrix after the dailation is:
\(A=\begin{bmatrix}{-8} & {-1} & {12} \\ {-8} & {-12} & {3}{}\end{bmatrix}\)The relationship between the matrix is:
\(A=Bx\)In which x is the dilation.
So
\(\begin{bmatrix}{-8} & {-1} & {12} \\ {-8} & {-12} & {3}\end{bmatrix}=\begin{bmatrix}{72} & {9} & {-108} \\ {72} & {108} & {-27}\end{bmatrix}x\)Taking two elements at the same position, i will take the first ones:
\(-8=72x\)Now we find the dilation x.
\(x=-\frac{8}{72}=-\frac{1}{9}\)The dialation is of -(1/9)
Find the quotient of z₁ by z2. Express your answer in
trigonometric
form.
² - 3 (0 (4) + (*))
Z₁ cos
+/sin
Z₂
²2 = 7 (cos(377)+
COS
8
O A. 7 (cos (577) + i sin (5/77))
8
B.
21(cos(577)+isin (577))
8
OC. 21 cos
21(cos(-7)+ i sin(-77))
O D. 7 (cos(-7) + + sin(-7))
i
+/sin
37T
8
Answers
The quotient of z₁ by z₂ in trigonometric form is:
7/21 * (cos(584°) + i sin(584°))
To find the quotient of z₁ by z₂ in trigonometric form, we'll express both complex numbers in trigonometric form and then divide them.
Let's represent z₁ in trigonometric form as z₁ = r₁(cosθ₁ + isinθ₁), where r₁ is the magnitude of z₁ and θ₁ is the argument of z₁.
We have:
z₁ = 7(cos(577°) + i sin(577°))
Now, let's represent z₂ in trigonometric form as z₂ = r₂(cosθ₂ + isinθ₂), where r₂ is the magnitude of z₂ and θ₂ is the argument of z₂.
From the given information, we have:
z₂ = 21(cos(-7°) + i sin(-77°))
To find the quotient, we divide z₁ by z₂:
z₁ / z₂ = (r₁/r₂) * [cos(θ₁ - θ₂) + i sin(θ₁ - θ₂)]
Substituting the given values, we have:
z₁ / z₂ = (7/21) * [cos(577° - (-7°)) + i sin(577° - (-7°))]
= (7/21) * [cos(584°) + i sin(584°)]
The quotient of z₁ by z₂ in trigonometric form is:
7/21 * (cos(584°) + i sin(584°))
Option C, 21(cos(-7°) + i sin(-77°)), is not the correct answer as it does not represent the quotient of z₁ by z₂.
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For Mean = 73.19, Mode = 79.56 and Variance = 16, the Karl Pearson's Coefficient of Skewness will be -0.0256 -1.64 0.0256 0
Answers
Answer:
To calculate Karl Pearson's coefficient of skewness, we need to use the formula:
Skewness = 3 * (Mean - Mode) / Standard Deviation
Given the Mean = 73.19, Mode = 79.56, and Variance = 16, we need to find the Standard Deviation first.
Standard Deviation = √Variance = √16 = 4
Now we can substitute the values into the formula:
Skewness = 3 * (73.19 - 79.56) / 4
Skewness = -6.37 / 4
Skewness = -1.5925
Rounded to four decimal places, the Karl Pearson's coefficient of skewness for the given values is approximately -1.5925.
Wich measurement is closest to the cone in cubic feet?
Answers
We have that the diameter of the base of the cone measures 8 ft, then the radius is r=4. Now we can find the volume using the general formula:
\(\begin{gathered} V=\pi\cdot r^2\cdot\frac{h}{3} \\ \pi=3.1416 \\ r=4 \\ h=9 \\ \Rightarrow V=(3.1416)(4)^2(\frac{9}{3})=(3.1416)(16)(3)=48\cdot(3.1416)=150.8 \\ V=150.8ft^3 \end{gathered}\)therefore, the volume of the cone is v=150.8ft³
10.1 is what percent of 8? Round to the nearest tenth.
Answers
Answer:
114.8
Step-by-step explanation:
I looked it up if you need an explanation