The exact value of the trigonometric relation sin(θ/2) is √[(1 + √(17)/5)) / 2]
Given data:
The trigonometric relation is :
sin(θ) = (2√2) / 5 and π/2 < θ< π
Using the half-angle identity for sine:
sin(θ/2) = ± √[(1 - cos(θ)) / 2]
To determine the sign, look at the quadrant in which theta lies. Since π/2 < θ< π, θis in the second quadrant, where the sine function is positive. Therefore, we take the positive sign.
Now, let's calculate the cosine of θ. Using the Pythagorean identity for sine and cosine, we have:
sin²(θ) + cos²(θ) = 1
(2√2/5)² + cos²(θ) = 1
8/25 + cos²(θ) = 1
cos²(θ) = 1 - 8/25
cos²(θ) = 17/25
Taking the square root:
cos(θ) = ± √(17)/5
Since theta is in the second quadrant, take the negative sign:
cos(θ) = -√(17)/5
Now, substituting the values into the half-angle identity, we get:
sin(θ/2) = ± √[(1 - cos(θ)) / 2]
sin(θ/2) = ± √[(1 - (-√(17)/5))) / 2]
sin(θ/2) = ± √[(1 + √(17)/5)) / 2]
Since θ is in the second quadrant, where the sine function is positive, take the positive sign:
sin(θ/2) = √[(1 + √(17)/5)) / 2]
Therefore, the exact value of sin(θ/2) is √[(1 + √(17)/5)) / 2].
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How do you find the roots of a polynomial equation of degree 3?
We must factorize the provided polynomial equation in order to obtain a linear and quadratic equation before we can discover the roots of the three-degree polynomial.
what are polynomials?A mathematical expression made up of coefficients and uncertainty that only makes use of additions, subtractions, multiplications, and positive integer powers of variables is known as a polynomial. The formula x2 4x + 7 denotes a single indeterminate x polynomial. An expression in mathematics known as a polynomial is made up of variables (also known as indeterminates) and coefficients that may be added, subtracted, multiplied, and raised to negative integer powers of non-variables. An algebraic statement with variables and coefficients is called a polynomial. An expression can only contain the operations addition, subtraction, multiplication, and non-negative integer exponents. Polynomials are the name for these expressions.
We must factorize the provided polynomial equation in order to obtain a linear and quadratic equation before we can discover the roots of the three-degree polynomial. The zeros of the three-degree polynomial are then easily ascertainable.
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Is 25 a prime number?
No, 25 is not a prime number. It can be divided by 5 without a remainder, so it has factors other than 1 and itself.
A prime number is a positive integer greater than 1 that has no positive integer divisors other than 1 and itself. In other words, a prime number can only be divided evenly by 1 and by itself. They are considered to be the "building blocks" of the natural numbers, and are important in number theory and other branches of mathematics.
The factors of 25 are 1, 5 and 25. Prime numbers are numbers that are divisible by only 1 and themselves. So 25 is not a prime number.
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The ratio of the measures of the three angles in a triangle is 14:5:11. Find the measures of the angles.
The smallest angle =
The medium angle =
The largest angle =
Answer:
See below
Step-by-step explanation:
All of the interior angles of a triangle sum to 180 °
Smallest is 5 out of (14 + 5 + 11) = 5/30 ths of 180° = 30°
Middle is 11/30 ths = 66°
Largest is 14/30 ths = 84°
Answer:
30° , 66° , 84°
Step-by-step explanation:
sum the parts of the ratio, 14 + 5 + 11 = 30 parts
divide the sum of the angles in a triangle 180° by 30 to find the value of one part of the ratio.
180° ÷ 30 = 6° ← value of 1 part of the ratio , then
smallest angle = 5 × 6° = 30°
medium angle = 11 × 6° = 66°
largest angle = 14 × 6° = 84°
cos 2x + 3 = 4 can some one help me with finding all solutions
Answer:
x=0 or x=pi / x=πn
Step-by-step explanation:
cos2x + 3 = 4
subtract 3 from both sides
cos2x = 1
take the inverse cos/arccos of both sides
arccos(cos2x) = arccos(1)
2x=0 or 2x=2pi
divide both sides by 2
x=0 or x=pi
beyond (0,2pi) for every possible answer you should do x=(pi)n since any multiple of pi gives you the same answer
find ALL the missing side lengths and angle measurements.
Therefore ,the solution to the given problem of angles comes out to be
∠K= 66 degree,LK length = 2√2 unit LK length = 2√2 unit.
What are angles?In Geometrical, an angled is a structure made up of two rays, known as the angle's face, that converging at the vertex, or center, of the angle. It is feasible for two beams to form an angle within a plane depending on where they are placed. An angle is also created when two planes intersect. The nomenclature to them is diahedral angles. In plane geometry, light rays or lines with the same ending can have many different forms, or angles. The Latin word "angulus," which means "horn," is where the word "angle" in English comes from. The vertex, also known as the vertex of the angle, is the point at where the two rays meet.
Here,
Given: A right angle triangle MKL
∠M = 24 degree
and ∠K =90 degree
Thus,
=> ∠L + ∠M +∠K =180
=> 90 + 24 + ∠K = 180
=>∠K =180-114
=> ∠K= 66 degree
and
LK length = 2√2 unit
LK length = 2√2 unit
Therefore ,the solution to the given problem of angle comes out to be
∠K= 66 degree,LK length = 2√2 unit LK length = 2√2 unit.
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Chloe is trying to pick out outfit for the first day of school. she can choose from 4 pairs pair of pants 4 t-shirts, 2 pair of shoes. how many different outfits does chloe have choose from
Answer: 32
Since you have 4 choices of shirts, then 4 choices of shorts, and then 2 choices of shoes, the formula should be set up as 4 x 4 x 2. This gives you 32 outfit options.
The pentagonal prism below has a base area of 34 units² and a volume of 180.2 units³
. Find its height.
height of pentagonal prism is h unit.
What is pentagonal prism?
The prism is one that has two pentagonal bases from which one acts as bottom and the other acts as top. The pentagonal prism has five rectangular sides. This prism has 10 vertices and 15 edges. It is also said five-sided polygon prism.
What is the height of prism as stated above?given, area of pentagonal prism = 34 square unit
volume of pentagonal prism = 180.2 cubic unit
we know the formula for the area of the pentagonal prism.
Total surface area = 5ab + 5hb
Volume of pentagonal prism = 5/2 a b h
where, a =apothem length
b = base length
h = height of the prism
according to the given statement, 34 = 5 a b + 5 h b
180.2 = 5/2 a b h
from the above two equation, we get, the height of prism = h unit.
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Given JKL ~ NPM find jk
no just no because I'm too busy for this stupodnesss and ur in the matrix
What is the quotient of 2 3 and 2 9?
The formula to calculate the quotient of 2 3 and 2 9 is written as 2 3 divided by 2 9, or 2 3 / 2 9.
To calculate the answer, first divide 2 by 9, which is equal to 0.22. Then multiply 0.22 by 3, which is equal to 0.66. The final answer is 0.66.
In order to solve this problem, the division operation was used. The first number, 2 3, was divided by the second number, 2 9. The division operation was used to determine how many times the second number could fit into the first number. The answer of 0.66 means that 2 9 can fit into 2 3 0.66 times. This answer can be written as 0.66, or as a fraction, 2/3.
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A pediatric dentist office has a toy chest with 7 puzzles, 4 squishy balls, 5 pairs of play sunglasses, and 9 fidget spinners. If a child is allowed to pick two prizes, without looking and without replacement, then what is the probability that the child will select a pair of sunglasses both times?
The probability that the child will select a pair of sunglasses both times is; 1/25
What is the probability of selection?We are given the contents of the toy chest as;
7 puzzles
4 squishy balls
5 pairs of play sunglasses
9 fidget spinners
Total toy chest = 7 + 4 + 5 + 9
= 25
Probability of first choice being sunglasses = 5/25 = 1/5
Probability of second choice being sunglasses = 5/25 = 1/5
P(two choices being sunglasses) = 1/5 * 1/5 = 1/25
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we have 5^x/(1+5^x)=2/5 find A=125^x/(1+125^x)
By solving the algebraic expression A=125^x/(1+125^x) the answer is 8/35.
What is algebraic expression?When addition, subtraction, multiplication, division, and other mathematical operations are performed on variables and constants, the result is a mathematical statement known as an algebraic expression. Any combination of terms that have undergone operations like addition, subtraction, multiplication, division, etc. is known as an algebraic expression (or variable expression).
given that 5^x/(1+5^x)=2/5
or (1+5^x)/5^x = 5/2
⇒ 1/5^x + 1 = 5/2
⇒ 1/5^x = 5/2 - 1
⇒ 1/5^x = (5-2)/2
⇒ 1/5^x = 3/2
or 5^x = 2/3
now,
A = 125^x/(1+125^x)
⇒ A = (5^3)^x/{1+(5^3)^x}
⇒ A = 5^3x/(1+5^3x)
⇒ A = (5^x)^3/{1+(5^x)^3}
⇒ A = (2/3)^3/{1+(2/3)^3}
⇒ A = (8/27)/(1+8/27)
⇒ A = (8/27)/{(27+8)/27}
⇒ A = (8/27)/(35/27)
⇒ A = 8/35
So that A=125^x/(1+125^x) = 8/35
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A florit want to put a rope around hi rectangular garden with ide 7. 8m by 4. 7m. What length of rope mut he have
As per the area of rectangle, the required length of rope is 36.66 square meter.
The formula to calculate the area of rectangle is written as,
=> A = l x b
Where l refers the length and b refers the breadth.
Here we have given that a florist want to put a rope around his rectangular garden with the dimensions 7. 8m by 4. 7m.
In order to put the rope we have to find the area of the garden,
The area of the garden is calculated by using the area of rectangle formula, as 7.8 as length and 4.7 as breadth
=> A = 7.8 x 4.7
=> A = 36.66
Therefore, 36.66 square meter is required.
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Find the measure of angle TSB.
The measure of angle TSB is m ∠TSB = 40°.
What is inscribed angle?
In terms of geometry, an inscribed angle is the angle created when two chords intersect within a circle. It can also be described as the angle formed by two specified points on a circle at a given point on the circle. Two chords of the circle sharing an endpoint are equivalently used to define an inscribed angle.
Given:
The measure of arc BR = 100°.
We have to find the measure of angle TSB.
Since the measure of half of the arc is 180°.
⇒ TR = 180°
TS + BR = 180°
TS + 100° = 180°
TS = 180° - 100°
TS = 80°
The measure of arc TS is 80°.
Since,
TS = 2 m ∠TSB
⇒ m ∠TSB = 1/2TS
m ∠TSB = 1/2(80°)
m ∠TSB = 40°.
Hence, the measure of angle TSB is m ∠TSB = 40°.
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How do you check if a value is present in a table?
Use the exists condition to determine whether a record in a MySQL table exists or not. Subquery and the exists condition are both compatible.
what is sequence ?Informally, a sequence in mathematics is a list of items that are in some order (or events). It possesses members, much like a set (also called elements, or terms). The length of the sequence is the quantity of ordered elements (which may be infinite). You should be familiar with the following four main categories of sequences: arithmetic, geometric, quadratic, and special. Lists of numbers connected by a rule are known as number sequences. The subsequent numbers in the series can be calculated if the rule is understood. Each of the numbers in this example differ by 6, thus that is the case. It follows that adding 6 each time is the rule for this sequence.
given
Use the exists condition to determine whether a record in a MySQL table exists or not. Subquery and the exists condition are both compatible. When a row is present in the table, it returns true; otherwise, false is returned. False is represented as 0, whereas true is represented as 1.
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Copy and complete this sentence to describe the shaded region: The locus of points inside triangle ABC that are closer to AB / BC / AC than to AB / BC / AC A B 40° 40° C
The locus of points inside triangle [tex]ABC[/tex] that are closer to [tex]AB[/tex] than [tex]BC[/tex].
Subtract (6.25x + 12) - (4.25x "-7)"
Answer: 2x+19
Step-by-step explanation:
Simplify the expression by combining the like terms
How do you find the area of a triangle rectangle?
The area of a triangle rectangle can be calculated using the formula A = 1/2 * b * h, where b is the base of the triangle and h is the height.
To calculate the area of a triangle rectangle, first measure the length of the base and the height of the triangle. To calculate the area, first we need to measure the base and the height of the triangle rectangle.Then, multiply the two values together and divide the result by two. For example, if the base of the triangle measures 10 cm and the height measures 8 cm, then the area of the triangle rectangle is 10 cm x 8 cm = 80 cm2, and the area of the triangle rectangle is 80 cm2/2 = 40 cm2.
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What is the quotient of the following division problem? x + 2 x + 1 x2 + 3x + 2 0.
The quotient of the division problem is (x + 1)/(x +2). The result is obtained by determining the factors of the two quadratic equations.
How to find the factors of a quadratic equation?The quadratic equation can be expressed as
ax² + bx + c = 0
Where c is a constant.
To find the factors of a quadratic equation, follow these steps!
Find the two numbers that the product is equal to ac and the sum is equal to b.Use them as the common factors and simplify.Find the quotient of (x² + 2x + 1)/(x² + 3x + 2) = 0!
For quadratic equation x² + 2x + 1:
a = 1, b = 2, c = 1.ac = 1The two numbers are 1 and 1 → 1+1 = 2 and 1×1 = 1.The common factors: (x + 1)(x + 1)
For quadratic equation x² + 3x + 2:
a = 1, b = 3, c = 2.ac = 2The two numbers are 2 and 1 → 2+1 = 3 and 2×1 = 2.The common factors: (x + 2)(x + 1)
The quotient of the quadratic equations is
(x² + 2x + 1)/(x² + 3x + 2) = 0
(x + 1)(x + 1)/(x + 2)(x + 1) = 0
(x + 1)/(x + 2) = 0
Hence, the quotient of the quadratic equations is (x + 1)/(x + 2) = 0.
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I can't find #13 please help
What are the 6 types of triangle explain with example?
Answer:
There are six types of triangles based on their side lengths:
Equilateral Triangle: A triangle with all sides of equal length. For example, a triangle with sides of 3cm each is an equilateral triangle.
Isosceles Triangle: A triangle with two sides of equal length. For example, a triangle with sides of 2cm, 2cm, and 3cm is an isosceles triangle.
Scalene Triangle: A triangle with no sides of equal length. For example, a triangle with sides of 2cm, 3cm, and 4cm is a scalene triangle.
Acute Triangle: A triangle with all angles measuring less than 90 degrees. For example, a triangle with angles measuring 60, 75, and 45 degrees is an acute triangle.
Right Triangle: A triangle with one angle measuring exactly 90 degrees. For example, a triangle with angles measuring 45, 45, and 90 degrees is a right triangle.
Obtuse Triangle: A triangle with one angle measuring more than 90 degrees. For example, a triangle with angles measuring 90, 45, and 45 degrees is an obtuse triangle.
Step-by-step explanation:
In this triangle below, what is the side adjacent?
By analyzing the question, The side adjacent to angle L is D)JR.
What is adjacent side of triangle?In a triangle, adjacent sides are sides that share a common vertex (or corner) and are next to each other.
What is angle?An angle is the amount of rotation between two lines or planes that share a common point. It is typically measured in degrees or radians.
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Pleeeassee heeeelp! This is due tomorrow
The amount of money Mina will receive in dollars is $13.33 USD.
How to find the amount received in dollars?Mina returned from a trip and needs to exchange 18 pounds GBP back to USD. She finds that the current exchange rate is 1.35 pounds GBP to $1.00 USD.
Therefore, the amount of money Mina will receive in dollars can be calculated as follows:
Therefore,
1.35 pounds = 1.00 dollars
18 pounds = ?
cross multiply
Therefore,
amount of money in dollars she will receive = 18 × 1.00 / 1.35
amount of money in dollars she will receive = 18 / 1.35
Therefore,
amount of money in dollars she will receive = 13.33 dollars
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Do the lengths 5 12 and 13 form a right triangle?
Answer:no
Step-by-step explanation:
1. [Maximum mark: 6]
Solve n!-(n-1)!=16(n-2)!
n!-(n-1)!=16(n-2)! by factorizing it by n! and dividing it by n! we get n is equal to 2 .
what is polynomial ?The intersection point in mathematics is the location on the y-axis where the slope of the line passes. a point where a line or curve's y-axis crosses it. This is demonstrated using the equation for the straight line, Y = mx+c, where m denotes the slope and c the y-intercept. The equation's intercept form highlights the line's slope (m) and y-intercept (b). The slope is m and the y-intercept is b when an equation has the intercept form (y=mx+b). It is also possible to rewrite some equations so that they resemble slope intercepts. For example, the slope and y-intercept are both modified to 1 if y=x is rewritten as y=1x+0.
given
n! + (n+1)! = (n+2)!
Let us rewrite:
n!+ (n+1)n! = (n+2)(n+1)n!
Factorize n!
n!(1+n+1) = (n+2)(n+1)n!
Divide by n!
==> n+2 = (n+2)(n+1)
No divide by (n+2)
==> 1= n+1
==> n = 0
to verify substitute with n=0
==> 0! + 1! = 2!
==> 1+1 = 2
==> 2=2
n!-(n-1)!=16(n-2)! by factorizing it by n! and dividing it by n! we get n is equal to 2 .
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1. Which polygon or polygons are regular? (2 points)
Answer: 1st, 2nd, and 3rd
Step-by-step explanation: the last one isn't because not all of the sides are the same length
A magician asks a volunteer to think of two different positive integers without telling her what they are. She then asks him to calculate x, the sum of the larger number with the square of the smaller, and y, the difference between the numbers. The volunteer tells her that x = 9 and y = 3. Find the original numbers.
Answer:
the original numbers are 5 and 2
Step-by-step explanation:
fistly it says inorder to find x one has to add the larger number to the square of the smaller number. So in this case start off with smaller guesses of positive integers as it is simpler that way.
the first guesses that would end up giving you 9 as an answer is 5 and 2
5+(2×2)=9So now that the integers chosen fit in when calculating x we have to check if it also checks out in calculating y.
For y the difference between the 2 integers have to give an answer of 3. after calculations it the numbers comply to the statement for y;
5-2=3hence the answers are 5 and 2
a businessman bought x bags of maize at a cost of shs.960 per bag. he spend she 15 per bag on transport. he later sold the maize39 per tine making a profit of shs.515 per bag. (a) calculate the number of tins in one bag. (b) if the business man made total of sha 29,640. how many bags had he sol? (c) the businessman later used the total sales to buy more maize at shs.926.25 per bag he sold half of the bags to the maize millers the rate of shs.1,390 per bag and retailed the remaining at his stall to consumers at shs.39 per tin. which option would earn more profit and by how much? (2mk) (d) express the difference as a percentage of the sales to the consumers.
a) To calculate the number of tins in one bag, we can use the information given in the problem: "he later sold the maize39 per tine"
So we can assume that one bag of maize is divided into tins and the price per tin is 39 shs.
b) To find out how many bags the businessman sold, we can use the information that he made a total of 29,640 shs in profit.
We know from the problem that the profit per bag is 515 shs, so to find out how many bags he sold we can divide the total profit by the profit per bag: 29,640 shs / 515 shs/bag = 57.5 bags
c) To find out how much profit the businessman made by selling half of the bags to the maize millers, we can use the information that he bought the bags at 926.25 shs and sold them at 1,390 shs.
We know that he sold half of the total number of bags, so we can divide the total number of bags by 2: 57.5 bags / 2 = 28.75 bags
To find out the total profit he made, we can multiply the number of bags sold by the profit per bag: 28.75 bags * (1,390 shs - 926.25 shs) = 22,447.5 shs
d) To express the difference as a percentage of the sales to the consumers, we can use the information that the businessman sold the bags to the maize millers at 1,390 shs and to the consumers at 39 shs.
To find the difference, we can subtract the price he sold the bags to the consumers from the price he sold the bags to the maize millers: 1,390 shs - 39 shs = 1351 shs
To find the percentage of the difference, we can divide the difference by the price he sold the bags to the consumers and multiply by 100: (1351 shs / 39 shs) * 100 = 34,641.03%
How can you convert 5 gallons to quarts?
Answer: There are 4 quarts in a gallon so to convert 5 gallons to quarts you would multiply 5 x 4 = 20 quarts.
6.
In George's classroom, there are 6 girls for every 2 boys. What is the ratio of boys to the total number of students
A. 1:3
B. 3:1
C. 1:4
D. 4:1
On solving the provided question, we can say that there are 6 girls for every 2 boys, ratio = 3:1
what is ratio?Ratios show how often one number is contained in another in mathematics. For instance, the ratio of oranges to lemons in a fruit dish is 8 to 6 if there are 8 oranges and 6 lemons present. In a similar vein, the proportion of oranges to whole fruit is 8, while that of lemons to oranges is 6:8. A ratio is an ordered pair of numbers a and b that is expressed as a / b, with b not equal to zero. An equation equating two ratios is known as a ratio. The ratio can be expressed as 1:3, for instance, if there is 1 boy and 3 girls (for every boy she has 3 girls) 3/4 are girls, while 1/4 are boys.
there are 6 girls for every 2 boys.
ratio will be
6/2 = 3/1
ratio = 3:1
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What are the steps in substitution method?
The substitution method is a process used to solve a system of equations. It involves replacing one variable with the expression of the other variable in one equation, and then solving for the remaining variable.
The steps in substitution methodWrite the system of equations in the form Ax + By = C.Choose one of the equations and solve for one of the variables.Substitute the solved variable into the other equation.Solve the new equation.Substitute the solved variable into either equation and solve for the other variable.Check your answer by substituting both values into the original equations.Learn more about Substitution: https://brainly.com/question/22340165
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