for acute angle x, sinx-cosx=0.2. Find sinx+cosx
Answers
sin(x) + cos(x) is approximately 1.355.
To solve the equation sin(x) - cos(x) = 0.2, we need to find the value of x that satisfies this equation. Once we find x, we can calculate sin(x) + cos(x).
Let's simplify the equation sin(x) - cos(x) = 0.2 by rearranging it:
sin(x) = cos(x) + 0.2
Now, let's square both sides of the equation to eliminate the square roots:
sin^2(x) = (cos(x) + 0.2)^2
Using the identity sin^2(x) + cos^2(x) = 1, we can substitute 1 - cos^2(x) for sin^2(x):
1 - cos^2(x) = (cos(x) + 0.2)^2
Expanding the right side of the equation:
1 - cos^2(x) = cos^2(x) + 0.4cos(x) + 0.04
Rearranging and simplifying:
2cos^2(x) + 0.4cos(x) - 0.96 = 0
Now, we have a quadratic equation in terms of cos(x). We can solve this quadratic equation to find the value(s) of cos(x). Once we have cos(x), we can calculate sin(x) using the identity sin^2(x) + cos^2(x) = 1.
Let's solve the quadratic equation:
2cos^2(x) + 0.4cos(x) - 0.96 = 0
We can factor this quadratic equation:
(2cos(x) + 2)(cos(x) - 0.48) = 0
From this equation, we have two possible solutions:
2cos(x) + 2 = 0 --> cos(x) = -1 (which implies x = π)
cos(x) - 0.48 = 0 --> cos(x) = 0.48
Since we are looking for an acute angle, the second solution cos(x) = 0.48 is the appropriate choice.
Now, we can calculate sin(x):
sin(x) = √(1 - cos^2(x))
sin(x) = √(1 - 0.48^2)
sin(x) ≈ 0.875
Finally, we can find sin(x) + cos(x):
sin(x) + cos(x) ≈ 0.875 + 0.48 ≈ 1.355
Therefore, sin(x) + cos(x) is approximately 1.355.
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Related Questions
Find cosif sin = is in the third quadrant.035OA. -OB.OC. 20OD.Reset Selection-
Answers
ANSWER
\(A.\text{ }-\frac{4}{5}\)EXPLANATION
We want to find the value of cosθ for:
\(\sin\theta=-\frac{3}{5}\)We are given that θ is in the third quadrant. This implies that it is between 180° and 270°.
First, we have to find the value of θ:
\(\begin{gathered} θ=\sin^{-1}(-\frac{3}{5}) \\ \\ θ=-36.87\degree\text{ or }216.87\degree \end{gathered}\)Since θ is in the third quadrant, it implies that:
\(θ=216.87\degree\)Now, find the value of cosθ:
\(\cos(216.87)=-0.8=-\frac{4}{5}\)The answer is option A.
why is the golden ratio positive?
(1±sqrt5)/2
why +
Answers
Answer:
A ratio must be positive.
Step-by-step explanation:
A ratio is comparing two things. For example, the number of sisters as a ratio to the number of brothers. If you have 2 sisters, and 1 brother, the ratio of sisters and brothers would be 2:1. this number does not make sense as -2:1.
The following statement tells one way to map preimage points to image points when performing a transformation in the coordinate plane. (x, y) → (x + 8, y − 3) This can be read, “The point with coordinates (x, y) is mapped to the point with coordinates (x, y) → (x + 8, y − 3).” With this transformaƟon, for example, (3, 5) is mapped to (3 + 8, 5 – 3) or (11, 2). The figure below shows how the triangle ABC is mapped to A′B′C′. Notice that the pre‐image and image appear to be congruent. Directions: Answer the following questions, showing all pertinent work. Paul has a 40 ft. by 30 ft. pole barn on his farm that he wants to move. The southeast corner of the pole barn is currently located 50 ft. west and 25 ft. north of the stock tank where the cows get their water. Paul wants to move the pole barn so the southeast corner of the barn is located 80 feet east and 80 feet south of the stock tank. 1. Complete the transformation statement for moving Paul’s pole barn. (x, y)→(x + _______ , y + _______ )
Answers
Answer: What are the answers to your question?
Step-by-step explanation:
X, and Y they are both axis's so most likely you might be using a grid but the arn't showing so make a grid and find the coordinats
For the function g(x) graphed here, find the following limits or explain why they do not exist. a. lim _x →-2 g(x) b. lim g(x) c. lim _x → 0 g(x) d. lim _x →-0.4 g(x)
Answers
We can write it as follows, lim_x→-0.4⁻g(x) = lim_x→-0.4⁺g(x) = 1
Given, the function g(x) is graphed as shown below: Function g(x) graph image
Therefore, the following are the limits of g(x) and the explanations for their existence:
Limit (a): lim_x→-2 g(x)
The value of lim_x→-2 g(x) is equal to
1. Since the limit from both sides is equal to 1, thus it exists.
We can write it as follows, lim_x→-2⁻g(x) = lim_x→-2⁺g(x) = 1
Limit (b): lim g(x)The value of lim g(x) is equal to
2: Since the left-hand limit and the right-hand limit are equal, the limit exists.
We can write it as follows, lim_x→-2⁻g(x) = lim_x→-2⁺g(x) = 2Limit (c): lim_x→0 g(x)The value of lim_x→0 g(x) does not exist.
Since the left-hand limit and the right-hand limit are not equal, thus the limit does not exist.
Limit (d): lim_x→-0.4 g(x)The value of lim_x→-0.4 g(x) is equal to 1.
Since the left-hand limit and the right-hand limit are equal, the limit exists.
We can write it as follows, lim_x→-0.4⁻g(x) = lim_x→-0.4⁺g(x) = 1
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Find the area of a circle with radius, R = 6.37m.
Give your answer rounded to 2 DP
Answers
Answer:
A = 127.48 rounded
Step-by-step explanation:
Area of a circle:
A = \(\pi r^{2}\)
A = \(\pi\)\((6.37)^{2}\)
A = 127.48 rounded
Answer:
It's 127.47
First we take the radius and square it
6.37^2
then we multiply it by pi
40.5769 x π = 127.47
select the square number
147, 41, 16, 103, 31
Answers
Answer:
16 is the square number
Step-by-step explanation:
16 is the square of 4 .If you want to get the square number then multiply any number two times then you will get your answer
Answer:
16
Step-by-step explanation:
4 is the square root of 16,please mark me brainliest.
given the four digits 2, 4, 6, and 7, how many different positive two-digit integers can be formed using these digits if a digit can be repeated in an integer?
Answers
There are 12 different positive two digit integers can be formed using these digits if a digit can be repeated in an integer.
Integer:
An integer is zero (0), a positive integer (1, 2, 3, etc.), or a negative integer with a minus sign (-1, -2, -3, etc.). A negative number is the additive reciprocal of the corresponding positive number. In mathematics languages, sets of integers are often denoted by a bold Z or a bold {Z}.
Given the question :
The number of different positive two integer number can be obtained by:
P(4, 2) = 4P2
We know that:
\(^nP_r\) = n! / (n - r)!
⁴P₂ = 4! / (4 - 2)!
⁴P₂ = 4! / 2!
⁴P₂ = (4 * 3 * 2 * 1) / ( 2 * 1)
⁴P₂ = 24 / 2
⁴P₂ = 12
Hence, 12 different positive two-digit integers can be formed using these digits if a digit may not be repeated in an integer.
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A project has five activities with the durations (days) listed
below:
Activity
Precedes
Expected
Duration
Variance
Start
A, B
-
-
A
C
40
0.31
B
E
32
0.25
C
D
21
0.35
Answers
The critical path is the path with the longest duration, which in this case is A -> B -> D -> E with a duration of 11 days.
To determine the critical path of the project, we need to find the longest path of activities that must be completed in order to finish the project on time. This is done by calculating the earliest start time (ES) and earliest finish time (EF) for each activity.
Starting with activity A, ES = 0 and EF = 4. Activity B can start immediately after A is complete, so ES = 4 and EF = 7. Activity C can start after A is complete, so ES = 4 and EF = 6. Activity D can start after B is complete, so ES = 7 and EF = 9. Finally, activity E can start after C and D are complete, so ES = 9 and EF = 11.
The variance for each activity is also given, which allows us to calculate the standard deviation and determine the probability of completing the project on time. The critical path is the path with the longest duration, which in this case is A -> B -> D -> E with a duration of 11 days.
Using the expected durations and variances, we can calculate the standard deviation of the critical path. This information can be used to determine the probability of completing the project on time.
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what substance do you drink to get strong bones
Answers
Answer:
milk
Step-by-step explanation:
journal articles and research reports are by far the most common secondary sources used in education.
Answers
Journal articles and research reports are widely recognized as the most common types of secondary sources used in education. In the field of education, secondary sources play a crucial role in providing researchers and educators with valuable information and scholarly insights.
Among the various types of secondary sources, journal articles and research reports hold a prominent position. These sources are often peer-reviewed and published in reputable academic journals or research institutions. They provide detailed accounts of research studies, experiments, analyses, and findings conducted by experts in the field. Journal articles and research reports serve as reliable references for educators and researchers, offering up-to-date information and contributing to the advancement of knowledge in the education domain. Their prevalence and credibility make them highly valued and frequently consulted secondary sources in educational settings.
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Please answer correctly !!!!!!!!!!!!!!!!! Will mark Brianliest !!!!!!!!!!!!!!!!!!
Answers
Answer:
106°
Step-by-step explanation:
they are parallel to each other
Answer: 106
Step-by-step explanation:
plz give correct answer (help) :(
Answers
Answer:
Answer:
(0,2) + (-6,6) =
Step-by-step explanation:
pls mark me as brainliest
Arthur has an april credit card balance of $325.24. his repayment date is the 25th of every month, with a grace period of 5 days. if his payment is late, the credit card company charges him a $25 late fee. arthur wants to repay the full amount to have a zero balance. how much should arthur pay if his online payment is processed on may 1?
a. $325.24, the april balance
b. $25, the april late fee
c. $350.24, the april balance plus the late fee
d. $300.24, the april balance minus the late fee
Answers
Answer:
c. $350.24, the april balance plus the late fee
Step-by-step explanation:
You want to know the required total payment when the balance being repaid is $325.24 and a late fee of $25 is charged.
Total owedArthur must pay both the balance due and the late fee. The total amount he must pay is ...
balance + late fee = $325.24 +25.00 = $350.24
what is the answer to 35 - 2a
Answers
Answer:
35 - 2a
Step-by-step explanation:
The answer would be 35 - 2a because thats the equation you have given us. If it were 35 - 2a = something then I would be able to answer it by a = something but for now based on the info its 35 - 2a
John sells frozen fruit bars at a stand in a park during the summer months. He records the average weekly temperature and number of frozen fruit bars sold for 6 weeks. A 2-column table with 6 rows. The first column is labeled temperature (degrees Fahrenheit) with entries 67, 71, 76, 76, 82, 87. The second column is labeled fruit bars sold with entries 50, 54, 63, 65, 65, 100. What type of correlation exists between the temperature and the number of fruit bars sold? What is the real-world meaning of the slope of the line of best fit for the given scenario? There are approximately more fruit bars sold for every degree(s) the temperature rises.
Answers
The correlation that exists between the temperature and the number of fruits sold is positive but is almost negligible.
What is the correlation coefficient?The correlation coefficient helps us to know how strong is the relation between two variables. Its value is always between +1 to -1, where, the numerical value shows how strong is the relation between them and, the '+' or '-' sign shows whether the relationship is positive or negative.
1 indicates a strong positive relationship.-1 indicates a strong negative relationship.A result of zero indicates no relationship at all, therefore, independent variable.
We know that the correlation coefficient is given by the formula,
\(r =\dfrac{\sum\left(x_{i}-\bar{x}\right)\left(y_{i}-\bar{y}\right)}{\sqrt{\sum\left(x_{i}-\bar{x}\right)^{2} \sum\left(y_{i}-\bar{y}\right)^{2}}}\)
r = correlation coefficient
\(x_{i}\) = values of the x-variable in a sample
\(\bar{x}\) = mean of the values of the x-variable
\(y_{i}\) = values of the y-variable in a sample
\(\bar{y}\) = mean of the values of the y-variable
Calculate the value of \((x_i-\bar{x})(y_i-\bar{y}),\ (x_i-\bar{x})^2,{ \rm and}\ (y_i-\bar{y})^2\) each separately, and then find the sum of them as shown below, therefore, the formula can be written as,
\(r =\dfrac{571.5}{261.5\times 1566.833333}= 0.0014\)
Hence, the correlation that exists between the temperature and the number of fruits sold is positive but is almost negligible.
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Answer:
1. positive
2. 2.2
3. 1
Step-by-step explanation:
Can you help me I need help
Answers
I disagree with Eva. The pool will be full at 11:45 pm thus option (D) will be correct.
What are work and time?Work is the completion of any task for example if you have done your homework in 5 hours then you have done 5 hours.
Another example of work is that if you have done your food by 1 hour it means your work duration is 1 hour so work is basically the time duration of any task which you have done.
As per the given table,
The pool filled out 1000 gallons every 15 minutes.
In 1 hour = 1000 x 4 = 4000 gallons,
To fill out a full pool of 15000 gallons,
15000/4 = 3 + 2000/3
3 hour + (15 + 15 + 15) minutes
⇒ 3 hours and 45 minutes
Since, it begins at 8:00 am thus 8 + 3 + 45 minutes = 11:45 am.
Hence "I don't concur with Eva. At 11:45 p.m., the pool will be filled".
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36 men can compete a piece of work in 18 days in how many days will 27 men compete the same work
Answers
Step-by-step explanation:
Explanation:
Less Men, means more Days {Indirect Proportion}
Let the number of days be x then,
27 : 36 :: 18 : x
[Please pay attention, we have written 27 : 36 rather than 36 : 27, in indirect proportion, if you get it then chain rule is clear to you :)]
=>27x = 36 * 18
=> x = 24
So 24 days will be required to get work done by 27 men..
Answer:
36 men can complete work in 18 days
so, one man can complete work in 18×36 days
Therefore, 27 can complete work in 18×36/27 = 24 days
Step-by-step explanation:
Erica has three times as many pieces of candy as Nellie. Together they have 248 pieces of candy. Write and solve and equation to find out howl much candy Nellie has.
Answers
Nellie has 62 pieces of candy,
62x3=186
186+62=248
when costprice and selling price is given how to calculate weather it is loss or profit?
Answers
Answer:
Selling price - cost price = profit, when Selling Price is more than Cost Price
Cost price - selling price = loss, when cost Price is more than sellIng Price
suppose that for some hypothesis test on the mean of a normally distributed population, standard deviation known, the p-value is computed as 0.11. if a level of significance of 0.05 is used, is rejecting the null hypothesis in favor of the alternative the correct decision?
Answers
If the p-value for a hypothesis test is greater than the chosen level of significance, then the null hypothesis cannot be rejected.
In this case, the p-value is 0.11 and the level of significance is 0.05. Since the p-value is greater than the level of significance, we cannot reject the null hypothesis.
Therefore, we do not have sufficient evidence to conclude that the population mean is different from the hypothesized value. In other words, we do not have enough evidence to support the alternative hypothesis.
Thus, rejecting the null hypothesis in favor of the alternative hypothesis is not the correct decision in this case.
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The following chips are placed in a bucket: 4 red, 1 yellow, 5 blue, and 5 green. One chip is randomly selected from the bucket.
What is the probability that the chip is blue?
Answers
Answer:Red
Step-by-step explanation:
Answer:
Step-by-step explanation:
5 blue out of 15 chips
for each increase of one unit on the x-axis (the horizontal axis), the amount on the y-axis (the vertical axis) increases by:
Answers
For each increase of one unit on the x-axis (the horizontal axis), the amount on the y-axis (the vertical axis) increases by the slope of the line.
Slope is the amount of change in the y-axis that occurs as a result of a one-unit change in the x-axis. It is also known as the rise over run.
A positive slope indicates that the line rises from left to right, while a negative slope indicates that the line falls from left to right. If the slope is zero, the line is horizontal.
If the line slopes up from left to right, it has a positive slope. As the value of x increases by one, the value of y also increases by the slope. If the line slopes downward from left to right, it has a negative slope. As the value of x increases by one, the value of y decreases by the slope.The slope of a horizontal line is zero, and the slope of a vertical line is undefined because the x or y coordinate does not change as the other changes.
Therefore, the slope of a line represents the amount by which the value on the y-axis increases for every increase of one unit on the x-axis
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What is h(p)=(p3+4p2-2) in distributive property
Answers
h
p
=
p
3
+
4
p
2
−
2
Step 1: Divide both sides by p.
h
p
p
=
p
3
+
4
p
2
−
2
p
h
=
p
3
+
4
p
2
−
2
p
Answer:
h
=
p
3
+
4
p
2
−
2
p
There are 50pupils in a class .Out of this number 1/10 speak French only and 4/5 of the reminder speak both French and English.lf the rest speak English only,find the number of student who speak
a.both French are English
b.only English
Answers
Answer:
40 pupils speak French and English
5 pupils speak only English
Step-by-step explanation:
**The grammar has some errors, but I hope I understood it correctly to answer your question correctly!**
Here's what we know about the question:
- 1/10 of the 50 pupils speak only FRENCH
- 4/5 of the 50 pupils speak FRENCH and ENGLISH
- rest of the pupils speak only ENGLISH
Here's what we're trying to find:
- # of pupils that speaks FRENCH and ENGLISH
- # of pupils that speak only ENGLISH
Let's start of with find how many pupils speak French:
1/10 of the 50 pupils speak French. To find the # of pupils, divide 50 by 10:
50/10 = 5
5 pupils speak only French
Now let's find out how many pupils speak French and English:
4/5 of the 50 pupils speak French and English. We are going to divide 50 by 5 and then multiply the result by 4:
50/5 = 10
10 * 4 = 40
40 pupils speak French and English
Finally, let's find the number of pupils that speak only English:
The question only says that the rest of the 50 pupils speak only English.
We are going to add the other pupils who don't speak only English, then subtract that value from 50:
40 + 5 = 45
50 - 45 = 5
5 pupils speak only English
Hope that helps (●'◡'●)
Una piscina tarda en llenarse 6 horas con un grifo y con otro grifo mayor tarda 4 horas.
¿Cuánto tiempo tardaría en llenarse la piscina con los dos grifos a la vez?
Answers
Usando la tasa conjunta, se encuentra que se tardaría 2.4 horas en llenarse la piscina con los dos grifos a la vez.
¿Cuál es la tasa conjunta?La tasa conjunta es la suma de cada tasa por separado.
En este problemas, las tasas por separadas són dadas por 1/6 y 1/4. Por eso, la tasa conjunta es dada por:
\(\frac{1}{x} = \frac{1}{6} + \frac{1}{4}\)
\(\frac{1}{x} = \frac{2 + 3}{12}\)
\(\frac{1}{x} = \frac{5}{12}\)
\(5x = 12\)
\(x = 2.4\)
Se tardaría 2.4 horas en llenarse la piscina con los dos grifos a la vez.
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find the radius of convergence and interval of convergence of the series x[infinity] n=1 2 · 4 · 6 · · · 2n 3 · 5 · 7 · · ·(2n 1) x 2n 1 .
Answers
The radius of convergence is 0, and the interval of convergence is the single point x = 0.
To obtain the radius of convergence and interval of convergence of the series we can use the ratio test.
\(\[ \sum_{n=1}^{\infty} \frac{2 \cdot 4 \cdot 6 \cdots (2n)}{3 \cdot 5 \cdot 7 \cdots (2n+1)}x^{2n+1} \]\)
The ratio test states that if \(\( L = \lim_{n \to \infty} \left| \frac{a_{n+1}}{a_n} \right| \)\), then the series converges if \(\( L < 1 \)\) and diverges if \(\( L > 1 \). If \( L = 1 \)\), the test is inconclusive.
Let's calculate the limit:
\(\[ L = \lim_{n \to \infty} \left| \frac{\frac{2 \cdot 4 \cdot 6 \cdots (2(n+1))}{3 \cdot 5 \cdot 7 \cdots (2(n+1)+1)}x^{2(n+1)+1}}{\frac{2 \cdot 4 \cdot 6 \cdots (2n)}{3 \cdot 5 \cdot 7 \cdots (2n+1)}x^{2n+1}} \right| \]\)
Simplifying the expression:
\(\[ L = \lim_{n \to \infty} \left| \frac{(2n+2)(2n+1)x^{2n+3}}{(2n+1)(2n)x^{2n+1}} \right| \]\)
\(\[ L = \lim_{n \to \infty} \left| \frac{(2n+2)x^2}{x^2} \right| \]\)
\(\[ L = \lim_{n \to \infty} 2(n+1) = \infty \]\\\)
Since the limit is infinity, the series diverges for all values of x , except when x = 0 and hence the radius of convergence is 0, and the interval of convergence is the single point x = 0.
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Avery leans a 24-foot ladder against a wall so that it forms an angle of 80
with the ground. How high up the wall does the ladder reach? Round your answer to the nearest tenth of a foot if necessary.
Answers
The height of the wall where the ladder reaches will be 23.6 feet.
What is a right-angle triangle?It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.
Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.
Avery leans a 24-foot ladder against a wall so that it forms an angle of 80° with the ground.
The height of the wall where the ladder reaches is given as,
\(\text{sin 80}^\circ \sf =\dfrac{h}{24}\)
\(\sf h = 24 \times \text{sin 80}^\circ\)
\(\sf = 24 \times \text{0.9848}\)
\(\sf h = 23.63\thickapprox\bold{23.6 \ feet}\)
The height of the wall where the ladder reaches will be 23.6 feet.
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is one over one-third a unit rate
Answers
Answer: NO it is not a unit rate
Step-by-step explanation:
No, a unit rate is the amount for 1 item or unit. and 1/ 1/3, 1/3 is on the bottom
1/3≠1 so no
In space, how many planes can be perpendicular to a given line at a given point on that line in space?
A. 1
B.0
C. 3
D. infinitely many
Answers
In space, there can be infinitely many planes that are perpendicular to a given line at a given point on that line.
The correct answer is Option D.
The key concept here is that a plane is defined by having at least three non-collinear points.
When a line is given, we can choose any two points on that line, and then construct a plane that contains both the line and those two points. By doing so, we ensure that the plane is perpendicular to the given line at the chosen point.
Since we can select an infinite number of points on the given line, we can construct an infinite number of planes that are perpendicular to the line at various points.
Thus, the correct answer is D. infinitely many planes can be perpendicular to a given line at a given point in space.
The correct answer is Option D.
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5+(-2)= ? Please help! I don’t know the answer
Answers
Answer:
It will be 3 because its take away hope this helped