Solve the equation for solutions over the interval [0,2x) by first solving for the trigonometric function. 4 sinx+8 = 10 Select the correct choice below and, if necessary, fill in the answer box to co
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The trigonometric equation is 4sin x + 8 = 10. We will first solve for the trigonometric function and then find the solution over the interval [0, 2π)
We can solve the trigonometric equation 4sin x + 8 = 10 by first subtracting 8 from both sides of the equation, as shown below:4sin x + 8 - 8 = 10 - 8This simplifies to:4sin x = 2
Now, we will divide both sides by 4. This gives:sin x = 1/2We know that the sine of an angle is equal to the ratio of the length of the side opposite the angle to the length of the hypotenuse.
Hence, we can conclude that sin x = 1/2 if x is 30° or π/6 (in radians). Also, we know that sin x is positive in the first and second quadrants.
Therefore, we can conclude that the solutions to the equation 4sin x + 8 = 10 over the interval [0, 2π) are:x = π/6, 5π/6, 13π/6, 17π/6.
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Related Questions
HELP PLEASE
in order!!!
Answers
Answer:
m<6=54 m<4=126
Step-by-step explanation:
The Perimeter of a Pentagon is 20.5 centimeters. Four sides of this pentagon have the same length, in centimeters, x, and the other side has a length of 2.1 centimeters, as shown below. What is the value of x?
Answers
Answer:
\(4.6\ \text{cm}\)
Step-by-step explanation:
Perimeter of the pentagon = 20.5 cm
Length of 4 sides = \(x\)
Length of the other side = 2.1 cm
Perimeter of the pentagon will be
\(x+x+x+x+2.1=20.5\\\Rightarrow 4x+2.1=20.5\\\Rightarrow 4x=20.5-2.1\\\Rightarrow 4x=18.4\\\Rightarrow x=\dfrac{18.4}{4}\\\Rightarrow x=4.6\ \text{cm}\)
The value of \(x\) is \(4.6\ \text{cm}\).
Solve the quadratic equation using the quadratic formula. Simplify your answer.x² + 4x = -5
Answers
Solution
- The solution steps are given below:
\(\begin{gathered} \text{ Given the quadratic equation:} \\ ax^2+bx+c=0 \\ \text{ The qudartic formula for finding the variable }x\text{ is:} \\ x=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \\ \\ \text{ Thus, we can solve the question given to us using the above formula} \\ x^2+4x=-5 \\ \text{ Rewrite the equation} \\ x^2+4x+5=0 \\ \therefore a=1,b=4,c=5 \\ \\ x=\frac{-4\pm\sqrt{4^2-4(1)(5)}}{2(1)} \\ \\ x=\frac{-4\pm\sqrt{16-20}}{2} \\ \\ x=\frac{-4\pm\sqrt{-4}}{2}=\frac{-4\pm\sqrt{4\times-1}}{2} \\ \\ \text{ By the law of surds we have that:} \\ \sqrt{4\times-1}=\sqrt{4}\times\sqrt{-1} \\ \\ x=\frac{-4\pm(\sqrt{4}\times\sqrt{-1})}{2} \\ \\ x=\frac{-4\pm(2\times\sqrt{-1})}{2} \\ \\ x=-\frac{4}{2}\pm\frac{2\sqrt{-1}}{2} \\ \\ x=-2\pm\sqrt{-1} \\ \\ \text{ But we know that }\sqrt{-1}=i \\ \\ \therefore x=-2\pm i \end{gathered}\)Final Answer
\(x=-2\pm i\)help plea i am beg screenshot in
Answers
Answer:
SA = 105 in^2
Step-by-step explanation:
To find surface area, find the area of all the shapes and add it all together. This shape has 4 triangle faces. They are all the same. So we can find one of them and times by 4.
Area of a triangle:
A = 1/2b•h
= 1/2• 5 • 8
= 1/2 • 40
= 20
One triangle has area 20, so times by 4 (bc four triangles)
4•20
= 80
Area of square 5•5
= 25
Add the areas:
80 + 25
= 105 sq in
PLZZZ HELP ME ASAP! TAKING A TEST
Which expressions are equivalent to x+4/3 / 6/x when x ≠ 0? Select three options.
Answers
Answer:
Thx for free points. remember me? actually answer questions.
What exponential function can be used to determine the number of transistors in a car that doubles every TWO years? The number starts at 4100. For this function to work, we should be able to find the amount of transistors in a car after 5 years (or any odd number of years)
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Answer:
\(f(t) = 4100( {2}^{ \frac{t}{2} }) \)
how to find the last term of an arithmetic sequence
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The formula to find the last term (\(T_n\)) of an arithmetic sequence is Tn = a + (n - 1) * d.
To find the last term (denoted as "\(T_n\)") of an arithmetic sequence, you need to know the first term (denoted as "a"), the common difference (denoted as "d"), and the total number of terms (denoted as "n").
The formula to find the last term of an arithmetic sequence is:
\(T_n\) = a + (n - 1) * d
Where:
\(T_n\) = Last term of the arithmetic sequence
a = First term of the arithmetic sequence
d = Common difference between consecutive terms
n = Total number of terms in the sequence
By plugging in the values of "a," "d," and "n" into the formula, you can calculate the last term of the arithmetic sequence.
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In a plot of probability of finding the electron in the hydrogen ground state versus the distance from the nucleus, the maximum occurs
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In a plot of the probability of finding the electron in the hydrogen ground state versus the distance from the nucleus, the maximum occurs (A) at a0. the first Bohr radius.
What is an electron?The electron is a subatomic particle with a negative one elementary charge electric charge. Electrons are the first generation of the lepton particle family and are widely regarded as elementary particles due to the lack of known components or substructure.Electron in the hydrogen:
Hydrogen has the simplest electron configuration to write because it just contains one electron. There is essentially only one electron surrounding the Hydrogen nucleus. Because hydrogen only has one electron, its configuration is 1s1.The maximum occurs at a0, the first Bohr radius, in a plot showing the chance of finding the electron in the hydrogen ground state vs the distance from the nucleus.Therefore, in a plot of the probability of finding the electron in the hydrogen ground state versus the distance from the nucleus, the maximum occurs (A) at a0. the first Bohr radius.
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The complete question is given below:
In a plot of the probability of finding the electron in the hydrogen ground state versus the distance from the nucleus, the maximum occurs:
A. at a0. the first Bohr radius
B. at slightly less than a0
C. at slightly more than a0
D. at 2 a0
E. at a0/2
SOMEONE PLEASE HELP ME ON THIS!!!,
Answers
Answer:
did u just forget to attach a pic
Step-by-step explanation:
Rowan opens a savings account with $25 and saves $75 per month. Reem opens a savings account with $225 and saves $25 per month.
a) Write an equation for Rowan’s savings account balance. $225 and saves $25 per month
b) Write an equation for Reem’s savings account balance?
c) When will their account balances be the same? How much will they have? Justify your answer either through graphs and/or solving the equations.
Answers
Answer:
a.) y= 75x+25
b.) y= 25x+225
c.) Their account balances will be the same in 4 months and they'll have $325.
Step-by-step explanation:
For A and B: The variable is x which is the amount of months then add the initial amounts without a variable and equal it to y which is the amount in all.
For Rowan, they are saving $75 per month. This is where our variable goes and then we add the intial $25 dollars. The equation is y= 75x+25.
For Reem, they are saving $25 per month. This is where our variable goes and then we add the intial $225 dollars. The equation is y= 25x+225
C. You have to set the equations equal to each other and then solve for x.
75x+25 = 25x+225
Subtract 25 from each side
75x=25x+200
Subtract 25x from each side
50x=200
Divide each side by 50
X=4
For the amount they'll have, just plug 4 into one of the equations.
Rowan : y=75(4)+25
y=325
Reem: y=25(4)+225
y=325
please help me find the solution of the system shown in the graph!!
Answers
Answer:
(2,1.5)
Step-by-step explanation:
I think, by looking at the information given on this question, your just looking to see where the lines intersect (which is at 2, 1.5)
when the length of a rectangle is increased by $20\%$ and the width increased by $10\%$, by what percent is the area increased?
Answers
Use formula to calculate area increase in rectangle when length and width increase by percentages, resulting in a 32% increase.
To find the percent by which the area of a rectangle increases when the length and width are increased by certain percentages, we can use the formula:
\(${Percent increase in area} = (\text{Percent increase in length} + \text{Percent increase in width}) + (\text{Percent increase in length} \times \text{Percent increase in width})$\)
In this case, the percent increase in length is 20% and the percent increase in width is 10\%. Plugging these values into the formula, we get:
\($\text{Percent increase in area} = (20\% + 10\%) + (20\% \times 10\%)$\)
\($\text{Percent increase in area} = 30\% + 2\%$\)
\($\text{Percent increase in area} = 32\%$\)
Therefore, the area of the rectangle increases by 32%.
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Neeeddd Helpppp Plzzzz
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Answer:
answer is c vertical answers
Step-by-step explanation:
i think
As monte carlo simulation is essentially statistical sampling, the larger the number of trials used, the more precise is the result.
a. True
b. False
Answers
True, Monte Carlo simulation is used for statistical sampling where larger number of trials are used for the precise result.
Step by Step Explanation:
Monte Carlo simulation is a mathematical technique or statistical sampling which is used to predict all possible outcomes of any uncertain event.The larger the number of trials more is the accuracy as it is based on the past data to predict the future outcomes.example : For the prediction of first month sale of any new launch product you can revise more number of old data.It help to calculate probability more accurately.Therefore, it is true to have more number of trials in Monte Carlo simulation statistical sampling for precise result.
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A publisher needs to send many books to a local book retailer and will send the books in a combination of small and large boxes. Each small box can hold 20 books and each large box can hold 35 books. There were twice as many small boxes sent as large boxes, which altogether can hold 225 books. Determine the number of small boxes sent and the number of large boxes sent.
Answers
A publisher needs to send many books to a local book retailer and will send the books in a combination of small and large boxes. Each small box can hold 20 books and each large box can hold 35 books.
The system of equation will be x+y = 7 and 20x+35y = 225.
Let x be the no of small boxes and y be the no. of large boxes.
Given here each small box can hold 20 books and each large box can hold 35 books.
A total of 7 boxes were sent.
So, x+y = 7.......equation 1
Also given that 7 boxes can hold 225 books altogether.
So, 20x+35y = 225.....equation 2
Hence the system of equation will be x+y = 7 and 20x+35y = 225.
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Fractional part of a Circle with 1/3 & 1/2.
How do you Solve that Problem?
Thank you!
Answers
The fractional part of a circle with 1/2 is 1.571 π/2
A circle is a two-dimensional geometric figure that has no corners and consists of points that are all equidistant from a central point.
The circumference of a circle is the distance around the circle's border or perimeter, while the diameter is the distance from one side of the circle to the other.
The radius is the distance from the center to the perimeter.
A fractional part is a portion of an integer or a decimal fraction.
It is a fraction whose numerator is less than its denominator, such as 1/3 or 1/2.
Let's compute the fractional part of a circle with 1/3 and 1/2.
We will utilize formulas to compute the fractional part of the circle.
Area of a Circle Formula:
A = πr²Where, A = Area, r = Radius, π = 3.1416 r = d/2 Where, r = Radius, d = Diameter Circumference of a Circle Formula: C = 2πr Where, C = Circumference, r = Radius, π = 3.1416 Fractional part of a Circle with 1/3 The fractional part of a circle with 1/3 can be computed using the formula below:
F = (1/3) * A Here, A is the area of the circle.
First, let's compute the area of the circle using the formula below:
A = πr²Let's put in the value for r = 1/3 (the radius of the circle).
A = 3.1416 * (1/3)²
A = 3.1416 * 1/9
A = 0.349 π
We can now substitute this value of A into the equation of F to find the fractional part of the circle with 1/3.
F = (1/3) * A
= (1/3) * 0.349 π
= 0.116 π
Final Answer: The fractional part of a circle with 1/3 is 0.116 π
Fractional part of a Circle with 1/2 The fractional part of a circle with 1/2 can be computed using the formula below:
F = (1/2) * C
Here, C is the circumference of the circle.
First, let's compute the circumference of the circle using the formula below:
C = 2πr Let's put in the value for r = 1/2 (the radius of the circle).
C = 2 * 3.1416 * 1/2
C = 3.1416 π
We can now substitute this value of C into the equation of F to find the fractional part of the circle with 1/2.
F = (1/2) * C
= (1/2) * 3.1416 π
= 1.571 π/2
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The fractional part of a circle with 1/2 is 1/2.
To find the fractional part of a circle with 1/3 and 1/2, you need to first understand what the fractional part of a circle is. The fractional part of a circle is simply the ratio of the arc length to the circumference of the circle.
To find the arc length of a circle, you can use the formula:
arc length = (angle/360) x (2πr)
where angle is the central angle of the arc,
r is the radius of the circle, and π is approximately 3.14.
To find the circumference of a circle, you can use the formula:
C = 2πr
where r is the radius of the circle and π is approximately 3.14.
So, let's find the fractional part of a circle with 1/3:
Fractional part of circle with 1/3 = arc length / circumference
We know that the central angle of 1/3 of a circle is 120 degrees (since 360/3 = 120),
so we can find the arc length using the formula:
arc length = (angle/360) x (2πr)
= (120/360) x (2πr)
= (1/3) x (2πr)
Next, we can find the circumference of the circle using the formula:
C = 2πr
Now we can substitute our values into the formula for the fractional part of a circle:
Fractional part of circle with 1/3 = arc length / circumference
= (1/3) x (2πr) / 2πr
= 1/3
So the fractional part of a circle with 1/3 is 1/3.
Now, let's find the fractional part of a circle with 1/2:
Fractional part of circle with 1/2 = arc length / circumference
We know that the central angle of 1/2 of a circle is 180 degrees (since 360/2 = 180),
so we can find the arc length using the formula:
arc length = (angle/360) x (2πr)
= (180/360) x (2πr)
= (1/2) x (2πr)
Next, we can find the circumference of the circle using the formula:
C = 2πrNow we can substitute our values into the formula for the fractional part of a circle:
Fractional part of circle with 1/2 = arc length / circumference
= (1/2) x (2πr) / 2πr
= 1/2
So the fractional part of a circle with 1/2 is 1/2.
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Write an equation of a vertical line that contains the point (-2,5)
Answers
Answer:
x=-2
Step-by-step explanation:
The line is vertical and/or undefined and it passes through the point (-2,5).
Is 12.7 a rational number?
Answers
Answer:
It could be written as a rational number but it is not one the rational number form would be 12.7:100 i think
Step-by-step explanation:
Two friends, Abigail and Nathan, took summer jobs. Abigail earned $203 in 7 hours. The graph below represents Nathan's earnings in dollars and cents, y, for working x hours.
Answers
Nathan worked less than Abigail per hour.
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
Abigail earned $203 in 7 hours.
So, Abigail earned in 1 hour
= 203/7
= $29
and, Nathan Earn $210 in 10 hour.
So, Nathan earned in 1 hour
= 210/10
= $21
Hence, Nathan worked less than Abigail per hour.
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17.9 + d = 35.8
what is d as a number?
Answers
Answer:
d = 17.9
Step-by-step explanation:
35.8-17.9=17.9
Answer:
D = 17.9
Step-by-step explanation:
will mark brainliest
The measure of angle P is ___ degrees, rounded to the nearest hundredth.
Answers
Answer:
53°
Step-by-step explanation:
Use sine cosine or tangent (SOHCAHTOA). For this example I'll use sine.
For sine you'd use the equation sin(x)=\(\frac{opp}{hyp}\) where x is the missing angle measure
the opposite side from x is 45 cm and the hypotenuse is 53 cm
sin(x)=\(\frac{45}{53}\)
then rearrange the equation like this x=\(sin^{-1}\)(\(\frac{45}{53}\))
most graphing calculators should solve it from there if you plug it in, hope this helps! :)
Solve the rational equation:
7/(s + 8) = −2/(9s + 1)
Answer: s=?
Answers
Answer:
s = (-23/65)
Step-by-step explanation:
7 -2
------ = -------
(s + 8) (9s + 1)
7 (9s + 1) -2 (s + 8)
------ = -------
(s + 8) (9s + 1) (9s + 1) (s + 8)
7 (9s + 1) -2 (s + 8)
(------------------ = ---------------------) ((9s + 1) (s + 8))
(s + 8) (9s + 1) (9s + 1) (s + 8)
7 (9s + 1) = -2 (s + 8)
63s + 7 = -2s - 16
+2s +2s
65s + 7 = -16
-7 -7
65s = -23
÷65s ÷65s
s = (-23/65)
Cristian,Iris,and Morgan each get an equal share of 1/2 of a pizza. Which model represents the fraction of the pizza each person gets?
Answers
Answer:
Step-by-step explanation:
1/6
1/2 ÷ 3
1/2 × 1/3
1/6
A simple random sample of 500 elements generates a sample proportion p= 0.81. Provide the 90% confidence interval for the population proportion (to 4 decimals). b.Provide 95% the confidence interval for the population proportion (to 4 decimals).
Answers
a) The 90% confidence interval for the population proportion is approximately (0.7777, 0.8423).
b) The 95% confidence interval for the population proportion is approximately (0.7737, 0.8463).
To calculate the confidence intervals for the population proportion, we can use the formula:
Confidence Interval = sample proportion ± margin of error
The margin of error can be calculated using the formula:
Margin of Error = critical value * standard error
where the critical value is determined based on the desired confidence level and the standard error is calculated as:
Standard Error = \(\sqrt{((p * (1 - p)) / n)}\)
Given that the sample proportion (p) is 0.81 and the sample size (n) is 500, we can calculate the confidence intervals.
a. 90% Confidence Interval:
To find the critical value for a 90% confidence interval, we need to determine the z-score associated with the desired confidence level. The z-score can be found using a standard normal distribution table or calculator. For a 90% confidence level, the critical value is approximately 1.645.
Margin of Error = \(1.645 * \sqrt{(0.81 * (1 - 0.81)) / 500)}\)
≈ 0.0323
Confidence Interval = 0.81 ± 0.0323
≈ (0.7777, 0.8423)
Therefore, the 90% confidence interval for the population proportion is approximately (0.7777, 0.8423).
b. 95% Confidence Interval:
For a 95% confidence level, the critical value is approximately 1.96.
Margin of Error = \(1.96 * \sqrt{(0.81 * (1 - 0.81)) / 500)}\)
≈ 0.0363
Confidence Interval = 0.81 ± 0.0363
≈ (0.7737, 0.8463)
Thus, the 95% confidence interval for the population proportion is approximately (0.7737, 0.8463).
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What is the answer to the problem below
Answers
\(90 \sqrt{72} \)
which is equal to 763.6753236815
The measure of an exterior angle of a regular polygon is 45 degrees name then shape of the polygon
Answers
Given
Exterior angle of a regular polygon = 45 degree.
Find
Name of the shape of polygon
Explanation
As we know that sum of exterior angle of exterior angle is 360 degree.
given each angle = 45 degree
so,
number of sides of regular polygon =
\(\begin{gathered} \frac{360\degree}{45\degree} \\ \\ 8 \end{gathered}\)number of sides = 8
Final Answer
The shape of the regular polygon = octagon
Carmen draws this area model to help her divide 1,800 by 9. She says the quotient is 20. Does Carmen's model make sense? Use the drop-down menus to explain.
Answers
Answer:
No shes wrong
Step-by-step explanation:
IF you divide 1800 divided by 9 you will get 200 not 20 so she is wrong.
Factor in this expression 6z ^ 4 - 4 + 9(y ^ 3 + 3)
Answers
Answer:
6z ^ 4-4 is a factor
Step-by-step explanation:
Given data
6z ^ 4 - 4 + 9(y ^ 3 + 3)
open bracket
6z ^ 4 - 4 + 9y ^ 3 + 27
collect like terms
6z ^ 4+9y^3 - 4 +27
6z ^ 4+9y^3 - 23
From the above expression 6z ^ 4-4
Answer:
its a.
(y^3+3)
Step-by-step explanation:
common sense
Danielle has her finals coming up and she's worried she'll fail her class. Her past 3 test grades were a 72. an 85, and a 68. She needs a 70 to pass the class. What grade does she need to make on the final to get a 70?
Answers
Answer:
55
Step-by-step explanation:
A meter is a unit of length approximately equal to 39.37 inches. If someone is 1.64 meters tall, what is his or her approximate height in inches?
Answers
Answer:
64.5668 inches tall
Step-by-step explanation:
If you set up a proportion, you would have to do 1.64 times 39.37, which would equal 64.5668 inches.