Solve the equation in the interval [0°,360°). Use an algebraic method. 13 sin 0-6 sin 0=5 .. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. Th
Answers
The correct choice is: OA. The equation has a solution in the interval [0°, 360°). the equation using an algebraic method.
To solve the equation 13sin(θ) - 6sin(θ) = 5 in the interval [0°, 360°), we can use algebraic methods.
First, combine like terms on the left side of the equation:
13sin(θ) - 6sin(θ) = 5
(13 - 6)sin(θ) = 5
7sin(θ) = 5
Next, isolate sin(θ) by dividing both sides of the equation by 7:
sin(θ) = 5/7
Now, we need to find the values of θ in the given interval [0°, 360°) that satisfy this equation. To do that, we can take the inverse sine (or arcsine) of both sides of the equation:
θ = arcsin(5/7)
Using a calculator or a table of trigonometric values, we can find the value of arcsin(5/7) to be approximately 48.59°.
So, the solution to the equation in the interval [0°, 360°) is:
θ ≈ 48.59°
Learn more about algebraic method here:
https://brainly.com/question/32641211
#SPJ11
Related Questions
Laurie Corporation uses the FIFO method in its process costing system. Department A is the first stage of Laurie Corporation's production process. The following information is available for conversion costs for the month of May for Department A:
Units Work in process, beginning (25% complete with respect to conversion costs) 8.000 Started in May 40,000 Completed in May and transferred to Department B 38,000 Work in process, ending (60% complete with respect to conversion costs) 10.000
How many are the equivalent units of production for conversion costs for the month? O
A. 42,000 units
B. 36,000 units
C. 44,000 units
D. 38,000 units
Answers
Answer:
A.
Step-by-step explanation:
42,000 units
if an indifference curve is straight (i.e., it doesn't "bow" inward), the marginal rate of substitution is always constant.
T/F
Answers
If an indifference curve is straight, the marginal rate of substitution (MRS) is indeed constant.
The MRS represents the rate at which a consumer is willing to exchange one good for another while maintaining the same level of satisfaction. A straight indifference curve means that the consumer is indifferent between two goods, regardless of the quantity of each good they have. Therefore, the MRS between these goods remains constant, regardless of the quantity of each good consumed. On the other hand, if an indifference curve is bowed inward, the MRS is not constant and changes as the consumer moves along the curve. Yes, if an indifference curve is straight and does not bow inward, it implies that the marginal rate of substitution (MRS) is constant. In this case, the consumer is willing to substitute one good for another at a fixed rate, regardless of the quantity of goods consumed. This constant MRS reflects the consumer's equal preference for both goods, and thus, the indifference curve remains linear.
To know more about MRS visit:
https://brainly.com/question/30763866
#S[PJ11
Two stores each have the same number of lawn mowers for sale. The lawn mowers at Store A have a median price of $150. The lawn mowers at Store B have a median price of $200.
What can best be inferred from this data?
A. Store A has more expensive lawn mowers.
B. Store B has more expensive lawn mowers.
C. The stores have the same amount of expensive lawn mowers.
D. It is impossible to say which store has more expensive lawn mowers.
Answers
Answer:
Store B has more expensive lawn mowers.
Step-by-step explanation:
The median price is the price in the middle of the possible prices which means that if you double the median price you will get about what the highest price can be.
What can be inferred from the data is store B has more expensive lawn mowers.
What does median mean?Median can be described as the number that occurs in the middle of a set of numbers that are arranged either in ascending or descending order. Median is a measure of central tendency. For example 3 is the median in this dataset: 1, 3, 6
To learn more about median, please check: https://brainly.com/question/14746682
Meg plotted the graph below to show the relationship between the temperature of her city and the number of people at a swimming pool:
Main title on the graph is Swimming Pool Population. Graph shows 0 to 30 on x axis at increments of 5 and 0 to 12 on y axis at increments of 1. The label on the x axis is Temperature in degree C, and the label on the y axis is Number of People at the Pool. Dots are made at the ordered pairs 2.5, 1 and 5, 2 and 7.5, 2 and 7.5, 3 and 7.5, 4 and 10, 5 and 10, 6 and 12.5, 6 and 15, 7 and 15, 8 and 17.5, 5 and 17.5, 7 and 20, 9 and 22.5, 7 and 22.5, 9 and 25, 11 and 27.5, 12.
Part A: In your own words, describe the relationship between the temperature of the city and the number of people at the swimming pool. (5 points)
Part B: Describe how you can make the line of best fit. Write the approximate slope and y-intercept of the line of best fit. Show your work, including the points that you use to calculate slope and y-intercept. (5 points)
Answers
Answer:
Step-by-step explanation:
Part A: Based on the given graph, we can observe that as the temperature of the city increases, the number of people at the swimming pool generally tends to increase as well. This suggests a positive correlation between temperature and the pool's population. In other words, when it gets hotter, more people are likely to visit the swimming pool. The relationship is not strictly linear, but it shows a general trend of increasing pool population with increasing temperature.
Part B: To determine the line of best fit, we can calculate the approximate slope and y-intercept using the given data points. Let's select two points from the data, such as (2.5, 1) and (12, 12):
Slope (m) = (change in y) / (change in x)
= (12 - 1) / (12 - 2.5)
= 11 / 9.5
≈ 1.16
To find the y-intercept (b), we can choose one of the points and substitute the values into the slope-intercept form (y = mx + b). Let's use the point (2.5, 1):
1 = 1.16 * 2.5 + b
1 = 2.9 + b
b ≈ -1.9
Therefore, the approximate slope of the line of best fit is 1.16, and the approximate y-intercept is -1.9.
for excersises 1 and 2 show the algebraic analysis that leads to the derivative of the unction. find the derivative by the specified method. F(x) =2x^3-3x^2+3/x^2. rewrite f(x) as a polynomial first. then apply the power rule to find f'(x)
Answers
For exercise 1, the derivative of F(x) = 2x^3 - 3x^2 + 3/x^2 is f'(x) = 6x^2 - 6x + 6/x^3, obtained by applying the power rule. For exercise 2, the derivative of F(x) = (x^2 + 2x)(3x^2 - 4) is f'(x) = 12x^3 - 8x + 18x^2 - 8, obtained by expanding and differentiating each term separately using the power rule.
Exercise 1:
Given: F(x) = 2x^3 - 3x^2 + 3/x^2
To find the derivative f'(x), we first rewrite F(x) as a polynomial:
F(x) = 2x^3 - 3x^2 + 3x^(-2)
Applying the power rule to find f'(x), we differentiate each term separately:
For the first term, 2x^3, we apply the power rule:
f'(x) = 3 * 2x^(3-1) = 6x^2
For the second term, -3x^2, the power rule gives:
f'(x) = -2 * 3x^(2-1) = -6x
For the third term, 3x^(-2), we use the power rule and the chain rule:
f'(x) = -2 * 3x^(-2-1) * (-1/x^2) = 6/x^3
Combining these derivatives, we get the overall derivative:
f'(x) = 6x^2 - 6x + 6/x^3
Exercise 2:
Given: F(x) = (x^2 + 2x)(3x^2 - 4)
To find the derivative f'(x), we expand the expression first:
F(x) = 3x^4 - 4x^2 + 6x^3 - 8x
Applying the power rule to find f'(x), we differentiate each term separately:
For the first term, 3x^4, we apply the power rule:
f'(x) = 4 * 3x^(4-1) = 12x^3
For the second term, -4x^2, the power rule gives:
f'(x) = -2 * 4x^(2-1) = -8x
For the third term, 6x^3, we apply the power rule:
f'(x) = 3 * 6x^(3-1) = 18x^2
For the fourth term, -8x, the power rule gives:
f'(x) = -1 * 8x^(1-1) = -8
Combining these derivatives, we get the overall derivative:
f'(x) = 12x^3 - 8x + 18x^2 - 8
To know more about derivative ,
https://brainly.com/question/19481279
#SPJ11
In a sample of 20 items, you found six defective. In constructing a confidence interval for the proportion of defectives, you should use: the plus four method. the large-sample interval. neither of these two methods.
Answers
To construct a confidence interval for the proportion of defectives, we should use the plus four method.
Since the sample size is 20, which is not very large, the large-sample interval is not appropriate. Instep, we ought to utilize a strategy that's suitable for little test sizes.
The plus four method is one such method that is commonly used when the sample size is small. Therefore, to construct a confidence interval for the proportion of defectives, we should use the plus four method.
The plus four strategies may be a strategy for building a certainty interim for an extent when the test estimate is little.
To utilize this strategy, we to begin with include four fanciful perceptions to our test, two of which are flawed and two of which are not imperfect.
This increments the test estimate to 24, which permits us to utilize the typical guess to the binomial dispersion to build the certainty interim.
The equation for the certainty interim utilizing the also four strategies is:
p ± zα/2 √((p + 2) (1 - p + 2) / n + 4)
where:
p is the test extent (number of defectives/test estimate)
zα/2 is the basic esteem from the standard typical dissemination at the level of importance α/2
n is the test estimate (counting the included four nonexistent perceptions)
Therefore, to construct a confidence interval for the proportion of defectives, we should use the plus four method.
learn more about the plus four method
brainly.com/question/31504643
#SPJ4
a salesperson has found that the probability of a sale on a single contact is approximately .03. if the salesperson contacts 100 prospects, what is the approximate probability of making at least one sale?
Answers
The probability of making no sales in 100 tries is 0.97^100. That's equal to about 0.0476, so the probability of getting at least one sale is 0.9524. About 95%.
If the probability of making a sale is 0.03 then the probability of not making a sale must be 1-0.03 which is 0.97.
So looking at contacting 100 prospects, you could say there are two general outcomes. Either the salesman makes no sales at all, or he makes at least one sale. There are no other possible outcomes, so the probability of those two outcomes must add up to 1.
So the probability of making of at least one sale is 1 minus the probability of making no sales.
The probability of making no sales in 100 tries is 0.97^100. That's equal to about 0.0476, so the probability of getting at least one sale is 0.9524. About 95%.
learn more about of probability here
https://brainly.com/question/16904657
#SPJ4
Gloria has $4500 saved to take a trip to Disney World Florida. The entire trip will cost her $6,375. She plans to go in 3 years. How much does she have to save each month to take the trip to Florida?
Answers
Answer:
$52.08
Step-by-step explanation:
There are 12 months in a year, so 3 years will have 36 months.
Find how much money she has to save in total:
6375 - 4500
= 1875
Divide this by 36 to find how much she has to save each month:
1875/36
= $52.08
So, she will have to save approximately $52.08 each month
what is the area of a circle when the circumference is 25 in
Answers
Answer:
49.735919716217
Step-by-step explanation:
Area =
C2 / 4π
Answer 49.735 diameter 202.126
show that if n ∣ m, where n and m are integers greater than 1, and if a ≡ b (mod m), where a and b are integers, then a ≡ b (mod n).
Answers
if n ∣ m and a ≡ b (mod m), then a ≡ b (mod n) is true.
The statement "n ∣ m" means that m is a multiple of n, or in other words, there exists an integer k such that m = nk. Similarly, the statement "a ≡ b (mod m)" means that a and b have the same remainder when divided by m, or in other words, there exists an integer j such that a - b = jm.
Now, let's use these facts to prove that "a ≡ b (mod n)" is true. We know that a - b = jm, and we know that m = nk, so we can substitute nk for m in the equation:
a - b = jnk
Now, let's rearrange the equation to get:
a - b = jn(k)
This shows that a - b is a multiple of n, or in other words, a and b have the same remainder when divided by n. Therefore, we can conclude that:
a ≡ b (mod n)
Learn more about integers
brainly.com/question/15276410
#SPJ11
Consider a 1-D harmonic oscillator and a trial wavefunction of the form ψ(x)=A/(x^2 + α^(2)), [20] where A is the normalization constant and α is an adjustable parameter. (a) Determine A. [3] (b) Estimate the ground-state energy of the harmonic oscillator. [12] (c) Check whether ⟨H⟩ overestimates or underestimates the solution you obtained in 3(b), and hence describe the validity of the variational principle in this case. [5]
Answers
a.we get, `A = √(2α³/π)`.
b.`⟨H⟩ = (3/4)hω - (h²/4ma²)` where `a = α/√(mω/h)`.
c.we can say that the variational principle is valid in this case.
(a) Let's find the normalization constant A.
We know that the integral over all space of the absolute square of the wave function is equal to 1, which is the requirement for normalization. `∫⟨ψ|ψ⟩dx= 1`
Hence, using the given trial wavefunction, we get, `∫⟨ψ|ψ⟩dx = ∫ |A/(x^2+α²)|²dx= A² ∫ dx / (x²+α²)²`
Using a substitution `x = α tan θ`, we get, `dx = α sec² θ dθ`
Substituting these in the above integral, we get, `A² ∫ dθ/α² sec^4 θ = A²/(α³) ∫ cos^4 θ dθ`
Using the identity, `cos² θ = (1 + cos2θ)/2`twice, we can write,
`A²/(α³) ∫ (1 + cos2θ)²/16 d(2θ) = A²/(α³) [θ/8 + sin 2θ/32 + (1/4)sin4θ/16]`
We need to evaluate this between `0` and `π/2`. Hence, `θ = 0` and `θ = π/2` limits.
Using these limits, we get,`⟨ψ|ψ⟩ = A²/(α³) [π/16 + (1/8)] = 1`
Therefore, we get, `A = √(2α³/π)`.
Hence, we can now write the wavefunction as `ψ(x) = √(2α³/π)/(x²+α²)`.
(b) Using the wave function found in part (a), we can now determine the expectation value of energy using the time-independent Schrödinger equation, `Hψ = Eψ`. We can write, `H = (p²/2m) + (1/2)mω²x²`.
The first term represents the kinetic energy of the particle and the second term represents the potential energy.
We can write the first term in terms of the momentum operator `p`.We know that `p = -ih(∂/∂x)`Hence, we get, `p² = -h²(∂²/∂x²)`Using this, we can now write, `H = -(h²/2m) (∂²/∂x²) + (1/2)mω²x²`
The expectation value of energy can be obtained by taking the integral, `⟨H⟩ = ⟨ψ|H|ψ⟩ = ∫ψ* H ψ dx`Plugging in the expressions for `H` and `ψ`, we get, `⟨H⟩ = - (h²/2m) ∫ψ*(∂²/∂x²)ψ dx + (1/2)mω² ∫ ψ* x² ψ dx`Evaluating these two integrals, we get, `⟨H⟩ = (3/4)hω - (h²/4ma²)` where `a = α/√(mω/h)`.
(c) Since we have an approximate ground state wavefunction, we can expect that the expectation value of energy ⟨H⟩ should be greater than the true ground state energy.
Hence, the value obtained in part (b) should be greater than the true ground state energy obtained by solving the Schrödinger equation exactly.
Therefore, we can say that the variational principle is valid in this case.
To know more about time-independent Schrödinger equation,visit:
https://brainly.com/question/31642338
#SPJ11
first person 2 answer will give u brainliest need to submit by 2 nite :)
Two angles are Complementary, if the measure of one of the angles is 66.7 degrees what is the measure of the other angle? Answer to the first decimal place, IE 79.5.
Answers
Answer:
probly 79.5
Step-by-step explanation:
i d k
The probability of an event is 0.28. Describe the likely hood of the event
Answers
Answer:
Step-by-step explanation
Remark
The likelihood of an event happening is 28 times out of a hundred.
The chances of it not happening is 72 chances out of a hundred.
Answer:
Unlikely!
Step-by-step explanation:
Calculate the area of this figure. Show all work and include proper units.
Check photo for units
Answers
Answer:
92 ft²Step-by-step explanation:
If you complete the square, you will add a right triangle with legs 10 - 6 = 4 ft.
The area of the figure is:
A = 10² - 1/2*4*4 = 100 - 8 = 92 ft²Write f(x)=|x-2| as a piecewise function.
Answers
Answer:
Hi! A piecewise function is a function defined by multiple sub-functions, or pieces of different functions over different intervals. Piecewise definition is a way of expressing the function and is not actually integral to the function itself.
f(x) = |x - 2| is an absolute value function. As a piecewise function, it's written like this:
f(x) = {x - 2, x ≥ 2
{-x + 2, x < 2
Hope this helps! Have a great day.
SIMPLE FRACTIONS BUT I FORGOT
Answers
4/3 im not sure though oof
Find the missing side length. Round to the nearest tenth if needed.
Answers
Answer:
b = 10.24 units.
Step-by-step explanation:
Pythagorean Theorem The Pythagorean Theorem explains the connection between a right triangle's three sides. The area of the square produced on the hypotenuse of any right triangle is equal to the sum of the areas of the squares formed on its legs: a2 + b2 = c2.a, is the shortest leg of the triangle or the opposite.b, is the adjacent leg of the triangle. This leg typically forms the right angle of the triangle.c, is the hypotenuse. This is the longest leg of the triangle. Applying the theorem\(a^{2} + b^{2} = c^{2}\)\(4^{2} + b^{2} = 11^{2}\)\(16 + b^{2} = 121\)\(b^{2} = 121-16\)\(b^{2} = 105\)\(\sqrt{b^{2}} = \sqrt{105}\)\(b = 10.24\)The adjacent is 10.24 units long.
Please let me know if this helped!!!
Find the largest area for a rectangle that is inscribed in a semicircle with radius 4 inches.
Answers
Answer:
16 square inches
Step-by-step explanation:
You want the largest rectangle that can be inscribed in a semicircle with radius 4 inches.
AreaThe equation of a circle centered at the origin with radius 4 is ...
x² +y² = 16
The height (y) of a rectangle whose corner is on the circle will be ...
y = √(16 -x²)
The width of such a rectangle is 2x, so the area of it is ...
A = WH = (2x)√(16 -x²)
MaximumThe maximum area will be had when the derivative of the area with respect to x is zero.
A' = 2√(16 -x²) - 2x²/√(16 -x²) = 0
Multiplying by √(16 -x²)/2 gives ...
16 -x² -x² = 0
16 = 2x²
x = √(16/2) = 2√2
The corresponding area of the rectangle is ...
A = 2(2√2)√(16 -(2√2)²) = 16
The largest rectangle has an area of 16 square inches.
__
Additional comment
As is often the case with rectangle optimization problems, the largest rectangle that can be inscribed in the quarter circle in each quadrant is a square. It has a diagonal of 4 inches, so an area of 4²/2 = 8 square inches.
The attachment shows the cubic curve representing the area of that square as a function of its width. As above, the rectangle area is double this value.
Find x.
I need help please
Answers
Answer:
\( x = 4 \sqrt{3} \)
Step-by-step explanation:
By geometric mean theorem and Pythagoras theorem:
\( {x}^{2} = { (\sqrt{8 \times 4} )}^{2} + {4}^{2} \\ \\ {x}^{2} = { (\sqrt{32} )}^{2} + {4}^{2} \\ \\ {x}^{2} = 32 + 16 \\ \\ {x}^{2} = 48 \\ \\ x = \sqrt{48} \\ \\ x = 4 \sqrt{3} \)
aldosterone stimulates the reabsorption of sodium while enhancing potassium secretion.
a. true b. false
Answers
I believe that may be false
Answer:
Step-by-step explanation:
True.
Aldosterone is a hormone produced by the adrenal gland that plays an important role in regulating electrolyte and water balance in the body. It acts on the cells of the distal tubules and collecting ducts of the kidneys to increase the reabsorption of sodium ions and the secretion of potassium ions.
This helps to increase blood volume and blood pressure by retaining more sodium and water in the body while getting rid of excess potassium. Aldosterone release is regulated by the renin-angiotensin-aldosterone system, which is activated in response to low blood pressure or low sodium levels in the blood.
know more about Aldosterone: brainly.com/question/31670445
#SPJ11
a line has a slope of 8 and a y intercept of 9 what is its equation in slope intercept form
Answers
Answer:
y= 8x +9
Step-by-step explanation:
Slope-intercept form:
y= mx +c, where m is the slope and c is the y-intercept.
Given that the slope is 8, m= 8.
Substitute m= 8 into the equation:
y= 8x +c
Given that the y-intercept is 9, c= 9.
Substitute c= 9 into the equation:
y= 8x +9
Thus, the equation of the line is y= 8x +9.
Help me please no one is helping me its due in 5 minutes
its a scientific notation not fraction.
Answers
Answer:
343
Step-by-step explanation:
Not sure how to explain it
scores on a college entrance exam are normally distributed with a mean of 500 and a standard deviation of 80. find the score at the 35th percentile.
Answers
The score at 35th percentile is 469.6 marks according to standard deviation and mean.
What is standard deviation?
Standard Deviation could be a measure that shows what quantity variation (such as unfold, dispersion, spread,) from the mean exis
Main body:
Given:
mean of μ = 500 and standard deviation of σ = 80
To answer this, we must find the z-score that is closest to the value 0.35 in the z table. This value turns out to be -0.38:
We can then plug this value into the percentile formula:
Percentile Value = μ + zσ
35th percentile = 500 + (-0.38)*80
35th percentile = 469.6
the score at the 15th percentile weighs about 469.6 marks.
Hence marks at 35th percentile is 469.6
To know more about standard deviation click on the link below
https://brainly.com/question/26941429
#SPJ1
I attached a photo please answer as quickly as possible.
Answers
The smallest integer value in the set is 7.
What is an integer?The grouping of positive and negative numbers is known as integers. Integers, like whole numbers, do not include the fractional portion. Integers can therefore be defined as numbers that can be positive, negative, or zero but not as fractions.
Since an integer is a whole number, it can reach both positive and negative infinity. 0 is the smallest non-negative number.
Consider the given term as -3(x-4) = 12
Then, -3x + 12 = 12
or, -3x = 0
or, x = 0
So, the value of x is either x > 0 or x < 0
Based on the given option, the smallest integer value is 7.
So, the required answer is 7.
To learn more about an integer
https://brainly.com/question/1768255
#SPJ1
#7:
Costco marks up the price of a $500.00 couch by 25%
and then has a 25% off sale. What is the selling price of
the couch?
Answers
Answer: 468.75
is ya answer
i think
sorry if im wrong
Answer:
468.75
Step-by-step explanation:
First we need to add 25% to 500.00 which is 625.
Next we need to subtract 25% from 625.
Now we have 468.75.
The selling price of the couch is $468.75.
If $500 is shared in the ratio 2:3:9 then the difference between the largest and the smallest shares is
Answers
Answer:
$250
Step-by-step explanation:
Total parts:
2+3+9 = 14
500/14 = 250/7
2×250/7 : 3×250/7 : 9×250/7
500/7 : 750/7 : 2250/7
The largest share is 2250/7, the smallest share is 500/7.
Find the difference.
2250/7 - 500/7 = 250
Answer:
$250
Step-by-step explanation:
2x+3x+9x= $500
9x-2x= 7x=?
14x= $500
7x= $500/2= $250
3 3/5 as decimal. Anyone help
Answers
Answer:
3.6
Step-by-step explanation:
You can make this fraction 60/100, which will tell you that is 3.6. You can also use your calculator to divide 3/5 and it will give you .6 :)
x 2 +2x−8=
The answer is (x-2) (x+4)
Answers
Answer:
x3 - 2x2 - 4x - 10
x
Step-by-step explanation:
i think
10 1/4 divided by 2 1/2
Answers
Answer: 4.1
Step-by-step explanation:
Answer:
4 1/10
hope this helps have a good day :)
Labour content in the production of an article is \( 16 \frac{2}{3} \% \) of total cost. How much is the labour cost if the total cost is \( \$ 456 ? \) The labour cost is \( \$ \) (Type an integer or
Answers
According to the statement the labour cost is $393 (Type an integer or a decimal rounded to two decimal places.) or simply $393.
Given information:Labour content in the production of an article is 16 2/3% of total cost.
Total cost is $456
To find:The labour costSolution:Labour content in the production of an article is 16 2/3% of total cost.
In other words, if the total cost is $100, then labour cost is $16 2/3.
Let the labour cost be x.
So, the total cost will be = x + 16 2/3% of x
According to the question, total cost is 456456 = x + 16 2/3% of xx + 16 2/3% of x = $456
Convert the percentage to fraction:16 \frac{2}{3} \% = \frac{50}{3} \% = \frac{50}{3 \times 100} = \frac{1}{6}
Therefore,x + \frac{1}{6}x = 456\Rightarrow \frac{7}{6}x = 456\Rightarrow x = \frac{456 \times 6}{7} = 393.14$
So, the labour cost is $393.14 (Type an integer or a decimal rounded to two decimal places.)
The labour cost is $393 (Type an integer or a decimal rounded to two decimal places.) or simply $393.
To know more about integer visit :
https://brainly.com/question/490943
#SPJ11