Cos= 1/4, csc —>0 Find sin —/2
Please please help this is due by 11:59 and I’m struggling
Answers
The value of sin(θ/2) is √6/4.
What is the value of sin (θ/2)?
We can start by using the identity:
sin(θ/2) = ±√[(1 - cosθ)/2]
However, before we apply this identity, we need to determine the quadrant in which θ lies, so that we can determine the sign of sin(θ/2).
From the given information, we know that cos θ = 1/4. Using the unit circle or a trigonometric table, we find that θ is a first quadrant angle whose reference angle is arc cos(1/4) ≈ 75.52°.
Since csc > 0, we know that sinθ > 0, which means that θ is either in the first or second quadrant.
However, since cosθ is positive (i.e., in the first or fourth quadrant), we know that θ must be in the first quadrant, and so sinθ > 0.
Now we can use the half-angle identity:
sin(θ/2) = ±√[(1 - cosθ)/2]
Plugging in cosθ = 1/4, we get:
sin(θ/2) = ±√[(1 - 1/4)/2] = ±√(3/8) = ±(√3/2)(√2/2) = ±(√3/2)(1/√2)
Since θ is in the first quadrant, we know that sin(θ/2) > 0, so we take the positive root:
sin(θ/2) = (√3/2)(1/√2) = √3/2√2 = √6/4
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Related Questions
Estimate by rounding
$14.49 + $68.64 + $128.05
Answers
Answer:
$211 if rounding to nearest whole number (this may be what looking for)
$211.20 if rounding to nearest tenth
Step-by-step explanation:
The answer depends on what precision of rounding is done so i am providing 2 answers
Rounding to the nearest whole number:
14,49 rounded = 14
68.64 rounded = 69
128.05 rounded = 128
$14.49 + $68.64 + $128.05 = 14 + 69 + 128
= $211
Rounding to the tenths:
14,49 rounded = 14.5
68.64 rounded = 68.6
128.05 rounded = 128.1
$14.49 + $68.64 + $128.05= 14.5 + 68.6 + 128.1 = $211.20
A chart for beans and carrots are shown below. You can find the number of seeds per row by dividing the length of the garden by the distance between the seeds. Then you subtract 1 since the seeds cannot be planted at the edge of the garden.
Answers
Answer:
See the attached worksheet.
Step-by-step explanation:
This assumes that the second "Beans" entry was supposed to be "Carrots, instead.
Note how the equations match the describtion in the paragraph. The multiply the only portion of the equation not explained is the (3y+5) expression in both equations. By process of elimination (marked), this must be the area of the garden.
Since we are not given an actual numeric value for the area, the only thing we can write in Part B is to duplicate the simplified equations from Part A.
Please help meeeeeee
Answers
Answer:
She earns $2,560
Step-by-step explanation:
She earns 2,560 because this is 8% of 32000. How do we know?
Multiply 32000 by 0.088, which is 8% of 100.
The random variable X is distributed as Bernoulli(p). Given X = x the random variable Y ~ Poisson(12) for 1> 0. (a) Derive the distribution of Y (b) Evaluate E(Y)
Answers
(a) The distribution of Y is P(Y = y) = (12^y * e^-12)/y!
(b) E(Y) = 12.
The random variable X is distributed as Bernoulli(p). Given X = x the random variable Y ~ Poisson(12) for 1> 0.
(a) The distribution of Y ~ Poisson(12) is given by:
P(Y = y) = (12^y * e^-12)/y!
(b) The expected value of a Poisson distribution is simply the mean, which in this case is 12. Therefore, E(Y) = 12.
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Please help quickly! Both circles have the same center. The circumference of the inner circle is 125.6 inches. What is the area of the shaded region?
Use 3.14 for pi. Write your answer as a whole number or decimal rounded to the nearest hundredth.
Answers
Answer:
The area of the shaded region can be calculated by subtracting the area of the inner circle from the area of the outer circle. The area of the inner circle is pi multiplied by the square of the radius, or 3.14 * (125.6/2)^2, which equals 19644.8. The area of the outer circle is pi multiplied by the square of the radius, or 3.14 * (125.6)^2, which equals 49766.56. Subtracting the inner circle’s area from the outer circle's area, the area of the shaded region is 30121.76, rounded to the nearest hundredth
Step-by-step explanation:
Find the Value of "h" h² +4h+111=0
Answers
Answer: h=−2+i√107,−2−i√107
Symbolize as a system in x and y but do not solve it: The sum of
one number and half another is
negative five. Twelve less than twice the second number yields the
first number.
Answers
The system of equations according to the given instructions are x + (1/2)y = -5; 2y - 12 = x
The sum of one number and half another is negative five. Twelve less than twice the second number yields the first number.
Let x represent the first number and y represent the second number.
System:
x + (1/2)y = -5
2y - 12 = x
The system of equations that represents this situation is:
x + (1/2)y = -5
2y - 12 = x
Where x represents the first number and y represents the second number.
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For the directed line segment whose endpoints are A(-5,-2) and B(5,3), find the coordinates of the point that partitions the segment BA into a ratio of 3 to 2.
Answers
The coordinates of the point that partitions the segment BA into a ratio of 3 to 2 is (-1, 0).
What is meant by Directed Line Segment?Directed line segments are line segments which has an initial point and the terminal point along with the direction.
Given a directed line segment BA.
The coordinates of A are (-5, -2) and the coordinates of B are (5, 3).
Let P be the required point which partitions the segment BA in to 3 : 2.
P would be at a 3/5 along the line from B to A.
Write the components of the segment using the end points.
Components = < (x₂ − x₁),(y₂ − y₁) >
= < (-5 - 5) , (-2 - 3) >
= < -10, -5 >
Components of BP = < 3/5 (-10, -5) >
= < -6, -3 >
Coordinates of P = Coordinates of initial point + component of BP.
= (5 + -6, 3 + -3)
= (-1, 0)
Hence the required coordinates is (-1, 0).
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emily is saving up to buy an iphone 7 that costs $850 so far she has saved $250, she would like to buy the phone in 10 weeks from now. how much must she save every week to have enough money to purchase the phone in 10 weeks
HELPPP
Answers
Answer:
60
Step-by-step explanation:
850-250=600
600/10=60
60
Answer:
she must save $60 each week to have enought money to purchase the iPhone 10
Step-by-step explanation:
Because 850-250=600
600/10=60
jane has a kitten named Fluff-ball. Fluff-ball usually sleeps in a cat bed 20 meters from the kitchen and hardly ever moves. But whenever Jane opens a can of cat food, the kitten comes running into the kitchen as fast as he can. If Fluff-ball takes 5 seconds to reach the kitchen, how fast can he run? Please answer in meters per second.
Answers
Fluff-ball can run at a speed of 4 meters per second.
What is speed ?Speed is a measure of how fast an object is moving. It is typically measured in units of distance per unit time, such as meters per second (m/s) or miles per hour (mph). Speed is a scalar quantity, meaning it has magnitude but no direction.
According to given information :Fluff-ball can run at a speed of 4 meters per second.
This is because speed is equal to distance divided by time, and in this case the distance is 20 meters and the time is 5 seconds:
Speed = distance/time = 20 meters/5 seconds = 4 meters per second.
Therefore, Fluff-ball can run at a speed of 4 meters per second.
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DBA QUESTION #4
How would you identify a perfect square trinomial?
Give an example by identifying a perfect square trinomial and then simplifying it.
Answers
Answer:
A perfect square trinomial is a trinomial expression of the form:
a^2 + 2ab + b^2
Where a and b are constants, it can also be written as (a + b)^2.
To identify a perfect square trinomial, we can check if the first and last terms are perfect squares and if the middle term is twice the product of the square roots of the first and last terms.
For example, let's consider the expression:
x^2 + 4x + 4
The first term is x^2, which is a perfect square. The last term is 4, which is also a perfect square. The middle term is 4x, twice the product of the square roots of x^2 and 4 (i.e., 2x). Therefore, this expression is a perfect square trinomial:
x^2 + 4x + 4 = (x + 2)^2
To simplify this expression, we can use the fact that (a + b)^2 = a^2 + 2ab + b^2:
(x + 2)^2 = x^2 + 2(x)(2) + 2^2 = x^2 + 4x + 4
Therefore, the perfect square trinomial x^2 + 4x + 4 is equivalent to (x + 2)^2.
Step-by-step explanation:
Q1 A line passes through the point(5,10)and(−3,12)find. a. A point-alop equation of this line b. a slop-intercept equatice of this line. Q2 Find the equation of the liae which: 4. puses throogh(68)and purilled io the lise with equationy=2x−6b. pases throogh (12,3) and perpendicular to the line with equationy=c. pasies through the point(1,2)and (5,6) Q3 Letf(x)=3x+5andg(x)=1/(vx−3). Find a.(f+g)(x)b.(f⋅g)(x)c.(2f+3g)(x)d.(3g−4)(x)Q4 Letf(x)=x2andg(x)=vx+1. Find a.(f2g)mb.(∘f min Q5 Deternine tle domsh and the range of the foctowing functens:
Answers
f(x)=3x+5
g(x)=1/(x-3)
Q1 The point-slope equation of the line passing through the points (5,10) and (-3,12) is y-10=2(x-5) and the slope-intercept equation of the same line is y=2x-9.
Q2 a) The equation of the line which passes through (8,0) and is parallel to the line with equation y=2x-6 is y=2x.
b) The equation of the line which passes through (12,3) and is perpendicular to the line with equation y=2x-6 is y=-1/2x+9.
c) The equation of the line which passes through the points (1,2) and (5,6) is y=2x-1.
Q3 a) (f+g)(x) = 3x+5 + 1/(x-3)
b) (f⋅g)(x) = 3x+5 * 1/(x-3)
c) (2f+3g)(x) = 6x+10 + 3/(x-3)
d) (3g-4)(x) = 3/(x-3) - 4
Q4 a) (f2g)(x) = (x2)2/(x+1)
b) (∘f min g)(x) = x/(x+1)
Q5 The domain of the function f(x)=3x+5 and g(x)=1/(x-3) is all real numbers except 3 and the range of both the functions is all real numbers.
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If possible, simplify the following expression. Otherwise, use the "Simplified" button. (15x^(2)+13x+2)/(3x-2) where x!=(2)/(3)
Answers
The final simplified expression is (3x+1)(5x+2)/(3x-2).
The given expression is (15x^(2)+13x+2)/(3x-2). We can try to simplify this expression by factoring the numerator and denominator, and then canceling out any common factors.
First, let's factor the numerator:
15x^(2)+13x+2 = (3x+1)(5x+2)
Now, let's factor the denominator:
3x-2 = (3x-2)
There are no common factors between the numerator and denominator, so we cannot simplify the expression any further.
Therefore, the simplified expression is:
(15x^(2)+13x+2)/(3x-2) = (3x+1)(5x+2)/(3x-2)
Since x!=(2)/(3), we do not need to worry about any undefined values.
So, the final simplified expression is:
(3x+1)(5x+2)/(3x-2)
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The legs of an isosceles trapezoid are 10. The bases are 9 and 21. Find the area of the trapezoid and the lengths of the diagonals
Answers
The area of the given isosceles trapezoid is 120 square units.
An isosceles trapezoid is a quadrilateral formed by a trapezium whose base angles are equal due to which the left and right sides are also equal in length.
In the given question,
Length of left/right side = 10
Length of bigger base = 21
Length of smaller base = 9
If we join the edges of the smaller base to the bigger base in such a way that we get 2 right-angled triangles formed by the legs of the trapezoid and the base,
we can say that the length of the base would be
=(bigger base-smaller base)/2
=(21-9)/2
=6
and we know that the length of the legs is 10
So to the Pythagorean theorem,
the height of the trapezoid would be
h=√(10² - 6²) = √64 = 8
Now that we know all the variables, we can easily calculate the area of the trapezoid by the formula
= height × (bigger base+smaller base)/2
= 8 ×(21+9)/2
= 4 × (30)
= 120 square units
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Restict the domain of the function f so that the
function is one-to-one and has an inverse function.
Then find the inverse function f-1 state the domain and range of f
and f-1.
Answers
To restrict the domain of the function f so that it is one-to-one and has an inverse function, we need to find a subset of the domain in which the function is one-to-one. This means that for every value of x in the restricted domain, there is exactly one value of f(x).
Once we have restricted the domain, we can find the inverse function f-1 by switching the x and y values in the original function and solving for y. The domain of the inverse function will be the range of the original function, and the range of the inverse function will be the domain of the original function.
For example, consider the function f(x) = x^2. This function is not one-to-one because for every value of x, there are two values of f(x) (one positive and one negative). However, if we restrict the domain to x ≥ 0, the function becomes one-to-one and we can find the inverse function.
The restricted function is f(x) = x^2 for x ≥ 0. The inverse function is f-1(x) = √x for x ≥ 0. The domain of f is x ≥ 0 and the range is f(x) ≥ 0. The domain of f-1 is x ≥ 0 and the range is f-1(x) ≥ 0.
In general, to restrict the domain of a function so that it is one-to-one and has an inverse function, we need to find a subset of the domain in which the function is one-to-one. Once we have restricted the domain, we can find the inverse function by switching the x and y values and solving for y. The domain of the inverse function will be the range of the original function, and the range of the inverse function will be the domain of the original function.
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An inequality is shown. -1/3x + 1/2 < 3.5 what is the solution to the inequality?
A. x > -12
B. x < -12
C. x > -9
D. x < -9
Answers
The solution to the inequality is option C. x > -9.
What is Linear Inequalities?Linear inequalities are defined as those expressions which are connected by inequality signs like >, <, ≤, ≥ and ≠ and the value of the exponent of the variable is 1.
The given inequality is,
-1/3x + 1/2 < 3.5
We have to find the solution of the inequality.
-1/3 x + 0.5 < 3.5
Subtracting both sides by 0.5, we get,
-1/3 x < 3.5 - 0.5
-1/3 x < 3
Multiplying both sides by -3,
x > -9
Hence the solution is x > -9.
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One auto repair shop chargers $30 for a dignosis and $25 per hour for labor. Another auto repair shop charges $35 per hour for labor. For how many hours are the total charges for both of the shops the same?
Answers
The total charges for both auto repair shops will be the same when 3 hours of labor have been performed.
Let's call the number of hours worked "h". The total charges for the first auto repair shop will be $30 (for the diagnosis) plus $25 per hour, or $30 + $25h. The total charges for the second auto repair shop will be $35 per hour, or $35h. We want to know when the total charges for both shops will be the same, so we can set the two equations equal to each other and solve for h:
$30 + $25h = $35h
$10h = $30
h = 3
So the total charges for both auto repair shops will be the same when 3 hours of labor have been performed.
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how many pennies would you receive if you cashed in 135 dimes
?
1 dime = 0.1 dollar
Answers
You would receive $13.50 if you cashed in 135 dimes. That's the equivalent of 1,350 pennies.
If you cashed in 135 dimes, you would receive 1,350 pennies.
This is because each dime is worth 0.1 dollars, or 10 pennies. So, to find the total number of pennies you would receive, you can simply multiply the number of dimes by the number of pennies in each dime:
135 dimes * 10 pennies/dime = 1,350 pennies
So, you would receive 1,350 pennies if you cashed in 135 dimes.
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Given the set of linear inequalities, determine if (1,4) is a solution of the set: y>5x+1 AND y>=(1)/(2)x-1.
Answers
No, the point (1,4) is not a solution of the set of linear inequalities y > 5x + 1 and y ≥ (1/2)x - 1 since the point does not satisfy both inequalities.
To determine if a point is a solution, we can substitute the x and y values of the point into the inequalities and see if they are true.
For the first inequality, y > 5x + 1:
4 > 5(1) + 1
4 > 6
This is not true, since 4 is not greater than 6. So the point (1,4) is not a solution for the first inequality.
For the second inequality, y ≥ (1/2)x - 1:
4 ≥ (1/2)(1) - 1
4 ≥ 0.5 - 1
4 ≥ -0.5
This is true, since 4 is greater than -0.5.
But since the point does not satisfy both inequalities, it is not a solution for the set of linear inequalities.
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HELP ME PLS ANYBODY
ITS DUE TODAY AND I NEED HELP ASAP
Answers
Answer:
1. around 4.86 or 4.9 for the nearest tenth
2. 17 months
Step-by-step explanation:
1. (1.7×10^6)/(3.5×10^5) = (1.7/3.5)×(10^6/10^5) = 0.4857×10 = 4.857
Therefore, 1.7×10^6 is about 4.857 times as great as 3.5×10^5.
2. start by finding out how much Erica still owes after the down payment:
Total cost - Down payment = $1,867 - $320 = $1,547
divide the amount still owed by the monthly payment to find out how many months Erica will be paying:
$1,547 ÷ $91 per month = 17 months (rounded up)
Therefore, Erica will be paying for the bike for 17 months
Plugging Into Exponential Formulas
A person places $8290 in an investment account earning an annual rate of 6%, compounded continuously. Using the formula V=Pe rt , where V is the value of the account in t years, P is the principal initially invested, e is the base of a natural logarithm, and r is the rate of interest, determine the amount of money, to the nearest cent, in the account after 12 years.
Answers
We have the following response after answering the given question: To interest the nearest penny, the balance in the account after 12 years is thus $17,821.76.
what is interest ?To calculate simple interest, divide the principal by the interest rate, the duration, and other variables. The marketing formula is simple return = capital + interest + hours. The easiest way to calculate interest is with this approach. The most popular method for calculating interest is as a percentage of the principal amount. For instance, if he borrows $100 from a friend and agrees to pay it back at 5% interest, he will only pay his portion of the 100% interest. $100 (0.05) = $5. Interest must be paid when you borrow money and must be added to any loans you make. The yearly percentage of the loan amount is frequently used to calculate interest. This percentage represents the loan's interest rate.
Continuously compounded interest is calculated as follows:
[tex]V = Pe^(rt) (rt)[/tex]
where: V = the investment's final value
P is the original investment's principle.
r equals the yearly interest rate (as a decimal)
t is the duration of the investment, in years.
P = $8290, r = 0.06 (6% as a decimal), and t = 12 years in this example.
So, [tex]V = 8290e^(0.06*12) = $17,821.76[/tex]
To the nearest penny, the balance in the account after 12 years is thus $17,821.76.
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Please help me did my homework for math
Answers
Answer:
1 = 128
2 = 52
3 = 52
4 = 128
5 = 128
6 = 52
7 = 52
8 = 128
(Please help me do my homework in mathematics) the “did” is past tenses
(Finance ) A total of k^(10),000 is to be invested. some in bonds and some in certificates of deposit (CDs ). If the amount invested in bonds is to exceed that in certificates of deposits by k^(3),000, how much will be invested in each type of investrient.
Answers
By applying Two-Variable Linear Equation it can be concluded that the amount invested in bonds is $6,500 and the amount invested in CDs is $3,500.
Two-Variable Linear Equation is a form of relation equal to the algebraic form which has two variables and both are raised to the power of one.
We will use this concept to calculate the amount of each type of investment.
The total amount invested is $10,000, with some going to bonds and some going to certificates of deposit (CDs). According to the question, the amount invested in bonds is to exceed that in CDs by $3,000. We can write this as an equation:
$10,000 = x + y , where:
x = the amount invested in bonds
y = the amount invested in CDs
We are also told that x = y + $3,000. We can substitute this into the first equation:
$10,000 = x + y
= y + $3,000 + y
= 2y + $3,000
2y = $7,000
y = $3,500
Now we can substitute this back into the equation for x:
x = y + $3,000
= $3,500 + $3,000
= $6,500
So the amount invested in bonds is $6,500 and the amount invested in CDs is $3,500.
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Math part 4 question 7
Answers
For the given function f(x) = (x - 4)² - 3, the following statements are correct -
B: relative minimum at (4,-3).
C: decreasing interval from (-∞, 4).
E: increasing interval is (4, ∞).
What is a function?
In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.
To find the relative maximum and minimum of the function, we need to find its critical points by setting the derivative of the function equal to zero -
f(x) = (x - 4)² - 3
f'(x) = 2(x - 4)
2(x - 4) = 0
x = 4
So, the only critical point of the function is x = 4.
Plug in the value of x = 4 in the equation -
(4 - 4)² - 3
0 - 3
-3
Since f''(4) is positive, the critical point at x = 4 is a relative minimum.
Therefore, the function has a relative minimum at (4, -3).
To find the increasing and decreasing intervals, we can look at the sign of the first derivative -
f'(x) = 2(x - 4)
For x < 4, f'(x) is negative, meaning that f(x) is decreasing on the interval (-∞, 4).
For x > 4, f'(x) is positive, meaning that f(x) is increasing on the interval (4, ∞).
Therefore, the decreasing interval is (-∞, 4), and the increasing interval is (4, ∞).
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what is 7.5cm = to in mm?
Answers
Answer:
75mm
Step-by-step explanation:
1cm = 10mm
u multiply 7.5 by 10
Answer:75
Step-by-step explanation:
What is the expression written using each base only once? 48 x 43 O A 411 O B. 1211 O C. 424 O D. 6411
Answers
The expression written using each base only once is 4¹¹ , the correct option is (a).
The expression 4⁸×4³ can be simplified using the rule of exponents,
The rule of exponents states that when we multiplying two exponential expressions with the same base, the exponents gets added.
which means that, nᵃ×nᵇ = nᵃ⁺ᵇ;
In this case the expression is: 4⁸×4³ , it has common base as "4",
So, by the rule of exponents, the power(exponents) gets added up ;
The expression "4⁸×4³" can be rewritten as 4⁸⁺³, which is equal to 4¹¹,
Therefore, Option(a)4¹¹, is the expression written using each base only once.
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The given question is incomplete, the complete question is
What is the expression written using each base only once? 4⁸×4³
(a) 4¹¹
(b) 12¹¹
(c) 4²⁴
(d) 64¹¹.
What is the y-intercept?
Answers
Answer:
The y-intercept is 1
at the point (0,1)
Step-by-step explanation:
The y-intercept is the point at which a graph crosses the y-axis.
\( \tan x \cdot \sin x+\cos x=? \) a) \( \sec x \) b) \( \csc x \) c) \( \cot x \) d) \( 1+\tan x \)
Answers
The correct answer is option d) \( 1+\tan x \), since \( \sec x=1+\tan x \).
The correct answer for the given expression \( \tan x \cdot \sin x+\cos x=? \) is option d) \( 1+\tan x \).
Step-by-step explanation:
We can start by using the identity \( \tan x = \frac{\sin x}{\cos x} \) to rewrite the expression:
\( \frac{\sin x}{\cos x} \cdot \sin x+\cos x=? \)
Next, we can simplify the expression by multiplying the numerator and denominator by \( \cos x \):
\( \frac{\sin^2 x+\cos^2 x}{\cos x}=? \)
Now, we can use the identity \( \sin^2 x+\cos^2 x=1 \) to further simplify the expression:
\( \frac{1}{\cos x}=? \)
Finally, we can use the identity \( \frac{1}{\cos x}=\sec x \) to rewrite the expression in terms of \( \sec x \):
\( \sec x=? \)
Therefore, the correct answer is option d) \( 1+\tan x \), since \( \sec x=1+\tan x \).
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I need help with this question
Answers
you multiply x by y and then multiply 5 to the power of 67 to then come to an answer of 500000000000x
23% of the people surveyed prefer country music. 2653 people said that they did not like country music. How many people said that they like country music?
Answers
793 people in the country said that they like country music if 23% of the people surveyed prefer country music.
The given data is as follows:
percentage of people prefer music = 23%
People did not like country music = 2653
Let us assume make this equation has equal properties,
0.23x = people who like country music
We know that 2,653 people did not like music. We can write this equation as:
x - 0.23x = 2653
0.77x = 2653
x = 2565 / 0.77
x = 3446.75
Taking the x value approximately, we get the x value as,
x = 3447
Now we can substitute the x value in the above equation, we get,
0.23x = 0.23(3447)
= 792.81
Therefore we can conclude that 793 people in the country said that they like country music.
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