Given cos theta= 2/3 and angle theta is in Quadrant I, what is the exact value of sin theta in simplest form? Simplify all radicals if needed.
Answers
Given cos theta= 2/3 and angle theta is in Quadrant I, what is the exact value of sin theta in simplest form√5/3.
Given that cos(theta) = 2/3 and theta is in Quadrant I, we can find the exact value of sin(theta) using the Pythagorean identity:
sin^2(theta) + cos^2(theta) = 1
Substitute the given value of cos(theta):
sin^2(theta) + (2/3)^2 = 1
sin^2(theta) + 4/9 = 1
To find sin^2(theta), subtract 4/9 from 1:
sin^2(theta) = 1 - 4/9 = 5/9
Now, take the square root of both sides to find sin(theta):
sin(theta) = √(5/9)
Since theta is in Quadrant I, sin(theta) is positive:
sin(theta) = √5/3
To know more about Quadrant, visit:
https://brainly.com/question/29296837
#SPJ11
The exact value of sin(theta) in simplest form is √5/3.
The first step is to use the Pythagorean identity: sin^2(theta) + cos^2(theta) = 1. Since we know cos(theta) = 2/3, we can solve for sin(theta):
sin^2(theta) + (2/3)^2 = 1
sin^2(theta) + 4/9 = 1
sin^2(theta) = 5/9
Taking the square root of both sides, we get:
sin(theta) = ±√(5/9)
Since the angle is in Quadrant I, sin(theta) must be positive. Therefore:
sin(theta) = √(5/9)
We can simplify this by factoring out a √5 from the numerator:
sin(theta) = √(5/9) = (√5/√9) * (√1/√5) = (√5/3) * (1/√5) = √5/3
So the exact value of sin(theta) in simplest form is √5/3.
Know more about Pythagorean identity here:
https://brainly.com/question/24287773
#SPJ11
Related Questions
Crystal earns $5.50 per hour mowing lawns.
• Write a rule to describe how the amount of money m earned is a function of the number of hours h spent mowing lawns.
• How much does Crystal earn if she works 3 hours and 45 minutes
Answers
2)Crystal earns $20.625 in 3 hours and 45 minutes.
Step-by-step explanation:
Given : Crystal earns $5.50 per hour mowing lawns.
To find :
1) Write a rule to describe how the amount of money m earned is a function of the number of hours h spent mowing lawns.
It is given that Crystal earns $5.50 per hour mowing lawns.
Let m is the amount of money earned
and h is the number of hours spent
So, The equation form by the statement is
2) How much does Crystal earn if she works 3 hours and 45 minutes
1 hour=60 minutes
So, for 3 hours and 45 minutes
In 1 hour she earn $5.50
In 3.75 hours she earn
Crystal earns $20.625 in 3 hours and 45 minutes.
what is the median of 99 88 107 97 100 109
Answers
The median of the set is 99.5
What is median?
The median is the value dividing a data sample, a population, or a probability distribution's upper and lower halves.
Arranging the given numbers in numerical order:
88, 97, 99, 100, 107, 109
The middle number(s) is/are the one(s) that divide(s) the set into two equal parts. Since there are 6 numbers in this set, there is no exact middle number. Instead, we find the average of the two middle numbers.
The two middle numbers are 99 and 100, so their average is:
(99 + 100) / 2 = 199 / 2 = 99.5
Therefore, the median of the set {99, 88, 107, 97, 100, 109} is 99.5.
To know more about median visit,
https://brainly.com/question/26151333
#SPJ1
Two linear functions are represented in different ways. One linear function is represented by the equation y =−3x.
Answers
Answer: Y = -3x
Step-by-step explanation:not needed
What is the line's slope?
Answers
Answer:
slope = -1/4
Step-by-step explanation:
(-2,5) to (-1,1)
repost of my question i need help quicklyy help plzz
Answers
Answer:
According to logarithmic properties.... The right hand side can be written as
log base 7 (180/3).....which is log base 7 60
So according to the question cancel out the log base 7 from both sides....
Then we get 8r + 20 = 60
That is 8r = 40..
That is r = 5......
Therefore the value of r is 5
find the missing side lengths. leave your answers as radicals in simplest form
Answers
Using trigonometric relations we can see that:
y = 20
x = 40
How to find the missing side lengths?Here we can see a right triangle and we want to find the missing side lengths, to do so we need to use trigonometric relations.
Remember that:
tan(a) = (opposite cathetus)/(adjacent cathetus)
Replacing what we know we will get:
tan(60°) = 20√3/y
Solving for x:
y = 20√3/(tan(60°)
y = 20
And for the hypotenuse we can use:
sin(a) = (opposite cathetus)/hypotenuse
sin(60°) = 20√3/x
Solving for y:
x = 20√3/sin(60°)
x = 2*20 = 40
Learn more about right triangles at:
https://brainly.com/question/2217700
#SPJ1
If you flip two coins, what is the probability that both will be heads?
Answers
Answer:
1/2 x 1/2 = 1/4
Step-by-step explanation:
P(H,H) = 1/2 x 1/2 = 1/4
P(T,T) = 1/2 x 1/2 = 1/4
P(H,T) = 1/2 x 1/2 = 1/4
P(T,H) = 1/2 x 1/2 = 1/4
What is the simplified expression for negative 2 a squared b a squared minus 5 a b 3 a b squared minus b squared 2 (a squared b 2 a b)? a squared minus 9 a b 3 a b squared a squared 9 a b minus b squared 3 a b squared 10 a b a squared minus b squared 3 a b squared a squared minus b squared minus a b
Answers
The simplified expression for the given expression is "a squared minus b squared minus a b."
To simplify the given expression, let's break it down step by step:
- Negative 2 a squared b a squared: This term remains the same in the simplified expression.
- Minus 5 a b: This term remains the same in the simplified expression.
- 3 a b squared minus b squared: This can be simplified as (3 a b squared) - (b squared) = 3 a b squared - b squared.
- 2 (a squared b 2 a b): This can be simplified as 2 (a squared b) - 2 (a b) = 2 a squared b - 2 a b.
Now, combining all the simplified terms, we have:
-2 a squared b a squared - 5 a b + 3 a b squared - b squared + 2 a squared b - 2 a b
Simplifying further, we can group like terms:
-2 a squared b + 2 a squared b - 5 a b - 2 a b + 3 a b squared - b squared
Combining like terms, we get:
0 - 7 a b + 3 a b squared - b squared
Finally, rearranging the terms in decreasing order of degree, we have:
- b squared + 3 a b squared - 7 a b
Learn more about squared here:
brainly.com/question/14198272
#SPJ11
if y varies inversely as x, and y=5 when x=15, find y when x=150
Answers
Answer:
Y=50
Step-by-step explanation:
5/15 = 50/150
these are some maths gcse questions pls answer
Answers
Answer:
The difference between 5 and a certain number is divided by 3. find the number if is equal to 7.
Pa help po thank you:))
Answers
Answer:
here are some examples of quadrilateral things( just pick 2), pinili ko sila dahil lahat sila ay rectangle( which i believe is one of the types of quadrilaterals):
- A (wooden) door
- A bill( 100 pesos or 1 dollar bill, whatever currency you use).
- A T.V.
- A Laptop
- A book
_______________________ follow the format:
" (choose 2 from above) A _______ and a _______ are examples of a two- dimensional shape or quadrilateral, which means they have 4 straight sides, 4 angles and 4 vertices. Both ______ and _______ are classified as rectangle because both opposite sides are equal."
there you go! i hope you pass and thank me later:)
What is the equation of the line?
Answers
Answer:
y=0
Step-by-step explanation:
One thing that many students think about when they register for classes at a university is how many textbooks they are going to have to buy for the class and how much the books are going to cost. To add to this, a lot of the students wonder if they are even going to use the books that they are required to buy. In fact, some students don’t buy books for their classes because they are convinced that they don’t really need them to achieve an acceptable grade.
This is exactly the line of thinking that textbook writers are afraid of—they want students to have to use their books to get good grades in their classes, and they want professors to think that students need their books so that they require them as part of their classes.
Even though textbooks have a definite value—they are available to students who use them when their professors are not—there is some debate on whether they are really needed as part of university classes.
Recently, a researcher conducted an experiment to address this question. In the experiment, the researcher compared two sections of his introductory statistics course, a course required for all liberal arts and sciences students. Students who were enrolled in the fall semester of the course were told that buying the textbook was optional, whereas students enrolled in the spring semester were told that buying the textbook was required. All 380 of the students (190 in the fall and 190 in the spring) completed the course, and they all took the final exam, which consisted of some calculations and several conceptual essay questions.
When the professor finished scoring the essays, he compared the final exam grades of both sections of the class. He found just what he thought he would—there were no differences in the scores on the exams between the section that thought the textbook was optional and the section that thought the textbook was required. The average grade for the fall semester was 84.3%, and for the spring semester it was 85.2%.
Based on this study, the researcher concluded that textbooks were not necessary or helpful for learning, since there were no differences in scores between the two sections.
No control or comparison group
No random assignment
Participant bias
Small sample size
Poor sample selection
Attrition or mortality
Experimenter bias
Confuse correlation with causality
DV is not reliable, precise or accurate
DV is not valid
DV is not objectively scored
Premature generalization of results
Answers
The study conducted by the researcher suffers from several limitations, including the absence of a control group, small sample size, participant bias, and experimenter bias. Furthermore, the sample selection is inadequate, as all the participants are students of one course in a single university.
Moreover, the study fails to account for extraneous variables that might affect the results. Therefore, that textbooks are not necessary or helpful for learning is premature and cannot be generalized to other courses or universities. T he study is flawed, and more research is needed to assess the effect of textbooks on learning.
The study conducted by the researcher suffers from several limitations. First, there is no control group, which makes it difficult to determine whether the results are due to the absence or presence of the textbook. Second, the sample size is small, which reduces the generalizability of the findings.
Third, there is participant bias, as some students might have bought the textbook even though it was optional, while others might not have bought it even though it was required. Fourth, there is experimenter bias, as the professor who scored the essays knew which section had the textbook and which did not.
Fifth, the sample selection is inadequate, as all the participants are students of one course in a single university. Moreover, the study fails to account for extraneous variables that might affect the results, such as the students' prior knowledge, motivation, and study habits.
Therefore, the textbooks are not necessary or helpful for learning is premature and cannot be generalized to other courses or universities. The study is flawed, and more research is needed to assess the effect of textbooks on learning.
To know more about extraneous variables :
brainly.com/question/31561984
#SPJ11
Find the surface area (the triangle are right triangles).
Answers
Answer:
67.5
Step-by-step explanation:
Well area of a triange is 1/2bh so we can find the side closest to us by doing
1/2(3x4) which is 12
the other side would be 1/2 (3x5) which is 7.5
the bottom side would be 1/2(8x4) so 16
and 1/2 (3x8) so 12
1/2 (8x5) so 20
add those together to get 67.5
Hope this helped ya!
80 divided by 192.0!!!!!!!!!!!!!!!
Answers
Answer: .416666667
Step-by-step explanation: Take 80 and divide it by 192.0= .416666667
Convert the equation into Slope-Intercept Form:
x - y = 11
Answers
Use the formula y=mx+b to help you convert problems like this into slope - intercept form.
Question 1
What is -13a + 5b + 4a - 10b ?
Answers
Answer:
-9a -5b
Step-by-step explanation:
Answer:
-9a - 5b
Step-by-step explanation:
Step 1. Collect like Terms
-13a + 5b + 4a - 10b (-13a + 4a = -9a)
-9a + 5b - 10b (5b - 10b = -5b)
Leaves you with -9a - 5b
to properly measure the volume of water in a calibrated glass device, such as a graduated cylinder, one should________
Answers
The lowest point should be used for measurement. To acquire a correct reading, students must read the meniscus at eye level. In order to read the meniscus at eye level, students need first set the graduated cylinder on the table and then stoop.
A measuring cylinder, often referred to as a graded cylinder, a cylinder measuring cylinder, or a mixing cylinder, is a piece of lab apparatus used to gauge the quantity of fluids, chemicals, or solutions used during a typical lab session. Compared to common laboratory flasks and beakers, graduated cylinders offer higher precision and accuracy. The graduated cylinder is a scientific tool that employs the metric system rather than the American standard system, so measurements are made in millilitres rather than ounces. The volume of an object or quantity of liquid is measured using a graduated cylinder, a common piece of laboratory glassware. It is a glass cylinder with side markings resembling those on a measuring cup, as its name suggests.
To know more about graduated cylinder here
https://brainly.com/question/24869562
#SPJ4
What is 1.405 as a fraction?
Answers
The area of a square is 108 ft^2, what is the length of one side?
Answers
Answer: 10.3923
Step-by-step explanation: yes
The water level (in feet) in Bostom Harbor during a certain 24-hour period is approximated by the formula H=4.8sin[?/6(t-10)]+7.6, 0 <= t <= 24 where t=0 corresponds to 12 A.M.
a. What is the average water level in Boston Harbor over the 24-hour period on that day?
b. At what times of the day did the water level in Boston Harbor equal the average water level? (Use Mean Value Theorem for Integrals)
Answers
a. To find the average water level in Boston Harbor over the 24-hour period,
we need to calculate the definite integral of the water level function H(t) over the interval [0, 24] and then divide it by the length of the interval.
The average value of a function f(x) over the interval [a, b] is given by the formula:
Average value = (1 / (b - a)) * ∫[a to b] f(x) dx.
In our case, the function H(t) = 4.8sin[(π/6)(t - 10)] + 7.6 represents the water level in Boston Harbor at time t, where t is measured in hours and ranges from 0 to 24.
The average water level can be calculated as:
Average water level = (1 / (24 - 0)) * ∫[0 to 24] (4.8sin[(π/6)(t - 10)] + 7.6) dt.
We can evaluate this integral to find the average water level:
Average water level = (1 / 24) * ∫[0 to 24] (4.8sin[(π/6)(t - 10)] + 7.6) dt.
The integral can be evaluated as follows:
Average water level = (1 / 24) * [- (48/π)cos[(π/6)(t - 10)] + 7.6t] from t = 0 to t = 24.
Plugging in the values, we get:
Average water level = (1 / 24) * [-(48/π)cos[(π/6)(24 - 10)] + 7.6(24) - (-(48/π)cos[(π/6)(0 - 10)] + 7.6(0)].
Simplifying the expression:
Average water level = (1 / 24) * [-(48/π)cos[(π/6)(14)] + 182.4].
Calculating the numerical value:
Average water level ≈ 7.198 feet.
Therefore, the average water level in Boston Harbor over the 24-hour period is approximately 7.198 feet.
b. To find the times of the day when the water level in Boston Harbor equals the average water level, we can use the Mean Value Theorem for Integrals. According to the theorem, if the average value of a function is equal to a constant, then there must exist at least one point in the interval where the function takes that value.
In our case, the average water level is approximately 7.198 feet. To find the times when the water level equals this value, we can set the water level function H(t) equal to 7.198 and solve for t:
4.8sin[(π/6)(t - 10)] + 7.6 = 7.198.
Simplifying the equation:
4.8sin[(π/6)(t - 10)] = 7.198 - 7.6,
4.8sin[(π/6)(t - 10)] = -0.402.
To find the values of t that satisfy this equation, we can use inverse trigonometric functions. Taking the arcsine of both sides:
[(π/6)(t - 10)] = arcsin(-0.402) + 2πn,
where n is an integer representing the number of complete cycles of the sine function.
Now, solve for t:
t - 10 = (6/π) * [arcsin(-0.402) + 2πn],
t = 10 +
(6/π) * [arcsin(-0.402) + 2πn].
These values of t represent the times of the day when the water level in Boston Harbor equals the average water level of 7.198 feet.
Learn more about integral here: brainly.com/question/31744185
#SPJ11
Given that TR(x)=20x and TC(x)=120+10x what is the break-even point?
Answers
The break-even point is the level of output at which total revenue (TR) equals total cost (TC). In this case, with TR(x) = 20x and TC(x) = 120 + 10x, we need to find the value of x where TR(x) = TC(x).
To find the break-even point, we set TR(x) equal to TC(x) and solve for x.
TR(x) = TC(x) can be expressed as:
20x = 120 + 10x
Simplifying the equation, we combine like terms:
20x - 10x = 120
10x = 120
To isolate x, we divide both sides of the equation by 10:
x = 12
Therefore, the break-even point occurs when x is equal to 12. At this level of output, the total revenue is equal to the total cost.
Learn more about break-even point here
https://brainly.com/question/32507413
#SPJ11
What is 4x/7 - 2/3
Fraction help
Answers
Answer:
2/21 * (6x-7)
Step-by-step explanation:
1/21 * (3*4x - 14)
1/21* (12x-14)
1/21* 2(6x-7)
2*1/21 * (6x-7)
2/21* (6x-7)
Ms. Maynard grates 23/30 of a block of cheese. Mr. Connor then eats another 3/30 of the cheese. What fraction of the cheese is left over?
Answers
Ms. Maynard grates 23/30 of a block of cheese, leaving the fraction of 7/30 of the cheese. Mr. Connor then eats 3/30 of the cheese, leaving the fraction of 4/30 of the cheese remaining.
Let us suppose the total block of cheese as 1.
If Ms. Maynard grates 23/30 of a block of cheese, then the fraction of cheese left is:
Remaining cheese = 1 - 23/30 = 7/30
After Mr. Connor eats 3/30 of the cheese, the fraction of cheese left is:
Remaining cheese = 7/30 - 3/30 = 4/30
Therefore, 4/30 of the cheese is left over after grating by Ms. Maynard and Mr. Connor respectively.
To know more about Fraction:
https://brainly.com/question/10354322
#SPJ4
Will mark as brainliest:A ball is thrown from an initial height of 3 meters with an initial upward velocity of 25 m/s. The ball's helght h (In meters) after t seconds is given by the following. h=3+25t-5t Find all values of t for which the ball's height is 13 meters, Round your answer(s) to the nearest hundredth. (If there is more than one answer, use the "or" button.)
Answers
t = 4.56 sec or 0.44 sec
Explanation:The equation:
h = 3 + 25t - 5t²
If height = 13 meters, we need to represent h with 13 to get time in seconds
13 = 3 + 25t - 5t²
13 -3 = 25t - 5t²
10 = 2t - 25t²
5t²- 25t + 10 = 0
using quadratic formula:
\(\begin{gathered} t\text{ = }\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ a\text{ = 5, b = -25, c = 10} \end{gathered}\)\(\begin{gathered} t\text{ = }\frac{-(-25)\pm\sqrt[]{(-25)^2-4(5)(10)}}{2(5)} \\ t\text{ = }\frac{25\pm\sqrt[]{625-200}}{10} \end{gathered}\)\(\begin{gathered} t\text{ = }\frac{25\pm\sqrt[]{425}}{10}\text{ =}\frac{25\pm\sqrt[]{25\times17}}{10} \\ t\text{ = }\frac{25\pm5\sqrt[]{17}}{10}=\frac{5\pm\sqrt[]{17}}{2} \end{gathered}\)In decimal:
\(\begin{gathered} t\text{ = }\frac{5+\sqrt[]{17}}{2}or\frac{5-\sqrt[]{17}}{2} \\ t\text{ = }\frac{9.12}{2}\text{ sec or }\frac{0.88}{2} \\ t\text{ = 4}.56sec\text{ or or 0.44sec} \end{gathered}\)
Given a conditional statement pq, which statement is logically equivalent?
Opa
Oq-p
O q P
Op-q
Answers
The conditional statement P→Q is logically equivalent to its contrapositive ¬Q→ ¬P .
A conditional statement is one that has the syntax "If P then Q," with P and Q denoting sentences.
A statement in mathematics is a declarative utterance that can only be either true or false. A proposal is another name for a statement. It's important that there be no ambiguity.
When we reverse the hypothesis and the conclusion in a statement and refute both of them, you have a contrapositive statement.
To put it another way, we must first determine the inverse of the conditional statement that is supplied before switching the positions of the hypothesis and conclusion to discover the contrapositive.
Given the statement p→q , therefore the inverse of both the statements is given by ¬p and ¬q .
So the contrapositive statement will be ¬p → ¬q
To learn more about conditional statements visit:
https://brainly.com/question/18152035
#SPJ1
Need help with a bunch of trig will give 15 pnts
Answers
The value of the trigonometric equation is (1/2, √3/2)
What is trigonometry?Recall that the Branch of mathematics that studies triangles and the relationships between their sides and the angles between these sides.
Trigonometry deals with the relationship between ratios of the sides of a right-angled triangle with its angles
The given equation reads that
CosX = 1/2
This implies that
CosX = 0.5
Taking the cosine inverse of 0.5 we have
X = Cos⁻¹0.5
X = 60⁰
The solution over (0, 2π) = (1/2, √3/2)
In conclusion the value of CosX = 1/2 is (1/2, √3/2)
Study more about trigonometric ratios on https://brainly.com/question/23130410
#SPJ1
The domain of y = x3 is
Answers
The domain of \(\sf y=x^3\) are all real numbers, or R due to the fact that \(\sf x^3\) is a polynomial, which means its domain is R too.
SolutionThe domain of a particular expression is all real numbers except in the place where expression is undefined. The domain of any graph includes all the x-values that are solutions.
Interval Notation:
\(\sf (-\)
Set-Builder Notation:
\(\{\text{x}|\text{x} \ \in \mathbb{R}\}\)
Determine the domain from the graph:
Thus, the domain of is:
\(\bold{(-\infty,\infty), \{x|x \ \in \mathbb{R}\}}}\)
Learn more about the domain of polynomial at:
https://brainly.com/question/31084975
#SPJ1
Find all solutions of the equation algebraically.
|x2 + 9x| = 6x + 54
Answers
The solutions to the equation are x= -9 and x = 6
How to determine the valueFrom the information given, we have that;
|x2 + 9x| = 6x + 54
To solve the quadratic equation, collect the like terms, we have;
x² + 9x - 6x = 54
subtract the terms
x² + 3x = 54
Put in standard form
x² + 3x - 54 = 0
Find the pair factors of -54 that add up to give 3 and substitute the values
x² + 9x - 6x - 54 = 0
group in pairs
(x² + 9x) - (6x - 54) = 0
factorize the expressions
x(x + 9) - 6(x + 9) = 0
Then, we have;
x- 6 = 0
x = 6
x + 9 = 0
x = -9
Learn about quadratic equations at: https://brainly.com/question/1214333
#SPJ1
Brad get an allowance of $16 each week, and his younger sister Samantha gets an allowance of $9 each week. Brad save one-half of his allowance and Samantha saves two-thirds oh her allowance. Suppose brad started with $0 savings and Samantha started with $40. How many weeks will it take until they have the same amount in savings?
Answers
Answer:
160
Step-by-step explanation: